/usr/include/deal.II/lac/constraint_matrix.h is in libdeal.ii-dev 6.3.1-1.1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 | //---------------------------------------------------------------------------
// $Id: constraint_matrix.h 21358 2010-06-24 23:38:14Z bangerth $
// Version: $Name$
//
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__constraint_matrix_h
#define __deal2__constraint_matrix_h
#include <base/config.h>
#include <base/exceptions.h>
#include <base/index_set.h>
#include <base/subscriptor.h>
#include <base/template_constraints.h>
#include <lac/vector.h>
#include <lac/trilinos_vector.h>
#include <vector>
#include <map>
#include <set>
#include <utility>
#include <complex>
#include <boost/scoped_ptr.hpp>
DEAL_II_NAMESPACE_OPEN
template<int dim, class T> class Table;
template <typename> class FullMatrix;
class SparsityPattern;
class CompressedSparsityPattern;
class CompressedSetSparsityPattern;
class CompressedSimpleSparsityPattern;
class BlockSparsityPattern;
class BlockCompressedSparsityPattern;
class BlockCompressedSetSparsityPattern;
class BlockCompressedSimpleSparsityPattern;
template <typename number> class SparseMatrix;
template <typename number> class BlockSparseMatrix;
class BlockIndices;
namespace internals
{
struct GlobalRowsFromLocal;
}
/**
* This class implements dealing with linear (possibly inhomogeneous)
* constraints on degrees of freedom. In particular, it handles constraints of
* the form $x_{i_1} = \sum_{j=2}^M a_{i_j} x_{i_j} + b_i$. In the context of
* adaptive finite elements, such constraints appear most frequently as
* "hanging nodes" and for implementing Dirichlet boundary conditions in
* strong form. The class is meant to deal with a limited number of
* constraints relative to the total number of degrees of freedom, for example
* a few per cent up to maybe 30 per cent; and with a linear combination of
* $M$ other degrees of freedom where $M$ is also relatively small (no larger
* than at most around the average number of entries per row of a linear
* system). It is <em>not</em> meant to describe full rank linear systems.
*
* The algorithms used in the implementation of this class are described in
* some detail in the @ref hp_paper "hp paper".
*
*
* <h3>Using the %ConstraintMatrix for hanging nodes</h3>
*
* For example, when using Q1 and Q2 elements (i.e. using
* FE_Q<dim,spacedim>(1) and FE_Q<dim,spacedim>(2)) on the two
* marked cells of the mesh
*
* @image html hp-refinement-simple.png
*
* there are three constraints: first $x_2=\frac 12 x_0 + \frac 12 x_1$,
* then $x_4=\frac 14 x_0 + \frac 34 x_1$, and finally the identity
* $x_3=x_1$. All three constraints fit the form given above. Similar
* constraints occur as hanging nodes even if all used finite elements are
* identical. While they are most frequent for hanging nodes, constraints of
* the given form appear also in other contexts, see for example the
* application the step-11 tutorial program.
*
* Homogenous constraints of this form also arise in the context of vector-valued
* fields, for example if one wants to enforce boundary conditions of the form
* $\vec{v}\cdot\vec{n}=0$. For example, the
* VectorTools::compute_no_normal_flux_constraints function computes
* such constraints.
*
*
* <h3>Using the %ConstraintMatrix for Dirichlet boundary conditions</h3>
*
* The ConstraintMatrix provides an alternative for implementinging
* Dirichlet boundary conditions (the standard way that is extensively
* discussed in the tutorial programs is to use
* MatrixTools::apply_boundary_values). The general principle of Dirichlet
* conditions are algebraic constraints of the form $x_{i} = b_i$, which
* fits into the form described above.
*
*
* <h3>Description of constraints</h3>
*
* Each "line" in objects of this class corresponds to one constrained degree
* of freedom, with the number of the line being $i_1$, and the entries in
* this line being pairs $(i_j,a_{i_j})$. Note that the constraints are linear
* in the $x_i$, and that there might be a constant (non-homogeneous) term in
* the constraint. This is exactly the form we need for hanging node
* constraints, where we need to constrain one degree of freedom in terms of
* others. There are other conditions of this form possible, for example for
* implementing mean value conditions as is done in the step-11
* tutorial program. The name of the class stems from the fact that these
* constraints can be represented in matrix form as $X x = b$, and this object
* then describes the matrix $X$ (as well as, incidentally, the vector $b$ --
* originally, the ConstraintMatrix class was only meant to handle homogenous
* constraints where $b=0$, thus the name). The most frequent way to
* create/fill objects of this type is using the
* DoFTools::make_hanging_node_constraints() function. The use of these
* objects is first explained in step-6.
*
* Matrices of the present type are organized in lines (rows), but only those
* lines are stored where constraints are present. New constraints are added
* by adding new lines using the add_line() function, and then populating it
* using the add_entry() function to a given line, or add_entries() to add
* more than one entry at a time. The right hand side element, if nonzero, can
* be set using the set_inhomogeneity() function. After all constraints have
* been added, you need to call close(), which compresses the storage format
* and sorts the entries.
*
* <h3>Eliminating constraints</h3>
*
* Constraint matrices are used to handle hanging nodes and other constrained
* degrees of freedom. When building the global system matrix and the right
* hand sides, one can build them without taking care of the constraints,
* purely on a topological base, i.e. by a loop over cells. In order to do
* actual calculations, you have to 'condense' the linear system: eliminate
* constrained degrees of freedom and distribute the appropriate values to the
* unconstrained dofs. This changes the sparsity pattern of the sparse
* matrices used in finite element calculations and is thus a quite expensive
* operation. The general scheme of things is then that you build your system,
* you eliminate (condense) away constrained nodes using the condense()
* functions of this class, then you solve the remaining system, and finally
* you compute the values of constrained nodes from the values of the
* unconstrained ones using the distribute() function. Note that the
* condense() function is applied to matrix and right hand side of the linear
* system, while the distribute() function is applied to the solution
* vector.
*
* This scheme of first building a linear system and then eliminating
* constrained degrees of freedom is inefficient, and a bottleneck if there
* are many constraints and matrices are full, i.e. especially for 3d and/or
* higher order or hp finite elements. We therefore offer a second way of
* building linear systems, using the add_entries_local_to_global() and
* distribute_local_to_global() functions discussed below. The resulting
* linear systems are equivalent to what one gets after calling the condense()
* functions.
*
*
* <h4>Condensing matrices and sparsity patterns</h4>
*
* As mentioned above, the first way of using constraints is to build linear
* systems without regards to constraints and then "condensing" them away.
* Condensation of a matrix is done in four steps: first one builds the
* sparsity pattern (e.g. using DoFTools::create_sparsity_pattern()); then the
* sparsity pattern of the condensed matrix is made out of the original
* sparsity pattern and the constraints; third, the global matrix is
* assembled; and fourth, the matrix is finally condensed. To do these steps,
* you have (at least) two possibilities:
*
* <ul>
* <li> Use two different sparsity patterns and two different matrices: you
* may eliminate the lines and rows connected with a constraint and create a
* totally new sparsity pattern and a new system matrix. This has the
* advantage that the resulting system of equations is smaller and free from
* artifacts of the condensation process and is therefore faster in the
* solution process since no unnecessary multiplications occur (see
* below). However, there are two major drawbacks: keeping two matrices at the
* same time can be quite unacceptable if you're short of memory. Secondly,
* the condensation process is expensive, since <em>all</em> entries of the
* matrix have to be copied, not only those which are subject to constraints.
*
* This procedure is therefore not advocated and not discussed in the @ref
* Tutorial.
*
* <li> Use only one sparsity pattern and one matrix: doing it this way, the
* condense functions add nonzero entries to the sparsity pattern of the large
* matrix (with constrained nodes in it) where the condensation process of the
* matrix will create additional nonzero elements. In the condensation process
* itself, lines and rows subject to constraints are distributed to the lines
* and rows of unconstrained nodes. The constrained lines remain in place,
* however, unlike in the first possibility described above. In order not to
* disturb the solution process, these lines and rows are filled with zeros
* and an appropriate positive value on the main diagonal (we choose an
* average of the magnitudes of the other diagonal elements, so as to make
* sure that the new diagonal entry has the same order of magnitude as the
* other entries; this preserves the scaling properties of the matrix). The
* corresponding value in the right hand sides is set to zero. This way, the
* constrained node will always get the value zero upon solution of the
* equation system and will not couple to other nodes any more.
*
* This method has the advantage that only one matrix and sparsity pattern is
* needed thus using less memory. Additionally, the condensation process is
* less expensive, since not all but only constrained values in the matrix
* have to be copied. On the other hand, the solution process will take a bit
* longer, since matrix vector multiplications will incur multiplications with
* zeroes in the lines subject to constraints. Additionally, the vector size
* is larger than in the first possibility, resulting in more memory
* consumption for those iterative solution methods using a larger number of
* auxiliary vectors (e.g. methods using explicit orthogonalization
* procedures).
*
* Nevertheless, this process is overall more efficient due to its lower
* memory consumption and the one among the two discussed here that is
* exclusively discussed in the @ref Tutorial.
* </ul>
*
* This class provides two sets of @p condense functions: those taking two
* arguments refer to the first possibility above, those taking only one do
* their job in-place and refer to the second possibility.
*
* The condensation functions exist for different argument types. The
* in-place functions (i.e. those following the second way) exist for
* arguments of type SparsityPattern, SparseMatrix and
* BlockSparseMatrix. Note that there are no versions for arguments of type
* PETScWrappers::SparseMatrix() or any of the other PETSc or Trilinos
* matrix wrapper classes. This is due to the fact that it is relatively
* hard to get a representation of the sparsity structure of PETSc matrices,
* and to modify them; this holds in particular, if the matrix is actually
* distributed across a cluster of computers. If you want to use
* PETSc/Trilinos matrices, you can either copy an already condensed deal.II
* matrix, or build the PETSc/Trilinos matrix in the already condensed form,
* see the discussion below.
*
*
* <h5>Condensing vectors</h5>
*
* Condensing vectors works exactly as described above for matrices. Note that
* condensation is an idempotent operation, i.e. doing it more than once on a
* vector or matrix yields the same result as doing it only once: once an
* object has been condensed, further condensation operations don't change it
* any more.
*
* In contrast to the matrix condensation functions, the vector condensation
* functions exist in variants for PETSc and Trilinos vectors. However,
* using them is typically expensive, and should be avoided. You should use
* the same techniques as mentioned above to avoid their use.
*
*
* <h5>Treatment of inhomogeneous constraints</h5>
*
* In case some constraint lines have inhomogeneities (which is typically
* the case if the constraint comes from implementation of inhomogeneous
* boundary conditions), the situation is a bit more complicated. This is
* because the elimination of the non-diagonal values in the matrix generate
* contributions in the eliminated rows in the vector. This means that
* inhomogeneities can only be handled with functions that act
* simultaneously on a matrix and a vector. This means that all
* inhomogeneities are ignored in case the respective condense function is
* called without any matrix (or if the matrix has already been condensed
* before).
*
* The use of ConstraintMatrix for implementing Dirichlet boundary conditions
* is discussed in the step-22 tutorial program.
*
*
* <h3>Avoiding explicit condensation</h3>
*
* Sometimes, one wants to avoid explicit condensation of a linear system
* after it has been built at all. There are two main reasons for wanting to
* do so:
*
* <ul>
* <li>
* Condensation is an expensive operation, in particular if there
* are many constraints and/or if the matrix has many nonzero entries. Both
* is typically the case for 3d, or high polynomial degree computations, as
* well as for hp finite element methods, see for example the @ref hp_paper
* "hp paper". This is the case discussed in the hp tutorial program, @ref
* step_27 "step-27", as well as in step-22 and @ref step_31
* "step-31".
*
* <li>
* There may not be a condense() function for the matrix you use (this
* is, for example, the case for the PETSc and Trilinos wrapper classes,
* where we have no access to the underlying representation of the matrix,
* and therefore cannot efficiently implement the condense()
* operation). This is the case discussed in step-17, @ref
* step_18 "step-18", and step-31.
* </ul>
*
* In this case, one possibility is to distribute local entries to the final
* destinations right at the moment of transferring them into the global
* matrices and vectors, and similarly build a sparsity pattern in the
* condensed form at the time it is set up originally.
*
* This class offers support for these operations as well. For example, the
* add_entries_local_to_global() function adds nonzero entries to a sparsity
* pattern object. It not only adds a given entry, but also all entries that
* we will have to write to if the current entry corresponds to a constrained
* degree of freedom that will later be eliminated. Similarly, one can use the
* distribute_local_to_global() functions to directly distribute entries in
* vectors and matrices when copying local contributions into a global matrix
* or vector. These calls make a subsequent call to condense() unnecessary.
*
* Note that, despite their name which describes what the function really
* does, the distribute_local_to_global() functions has to be applied to
* matrices and right hand side vectors, whereas the distribute() function
* discussed below is applied to the solution vector after solving the linear
* system.
*
*
* <h3>Distributing constraints</h3>
*
* After solving the condensed system of equations, the solution vector has
* to be redistributed. This is done by the two distribute() functions, one
* working with two vectors, one working in-place. The operation of
* distribution undoes the condensation process in some sense, but it should
* be noted that it is not the inverse operation. Basically, distribution
* sets the values of the constrained nodes to the value that is computed
* from the constraint given the values of the unconstrained nodes plus
* possible inhomogeneities. This is usually necessary since the condensed
* linear systems only describe the equations for unconstrained nodes, and
* constrained nodes need to get their values in a second step.
*
* @ingroup dofs
* @author Wolfgang Bangerth, Martin Kronbichler, 1998, 2004, 2008, 2009
*/
class ConstraintMatrix : public Subscriptor
{
public:
/**
* Constructor
*/
ConstraintMatrix (const IndexSet & local_constraints = IndexSet());
/**
* Copy constructor
*/
ConstraintMatrix (const ConstraintMatrix &constraint_matrix);
/**
* Reinit the ConstraintMatrix object and
* supply an IndexSet with lines that may
* be constrained. This function is only
* relevant in the distributed case, to
* supply a different IndexSet. Otherwise
* this routine is equivalent to calling
* clear(). Normally an IndexSet with all
* locally_active_dofs should be supplied
* here.
*/
void reinit (const IndexSet & local_constraints = IndexSet());
/**
* Determines if we can store a
* constraint for the given @p
* line_index. This routine only matters
* in the distributed case and checks if
* the IndexSet allows storage of this
* line. Always returns true if not in
* the distributed case.
*/
bool can_store_line(unsigned int line_index) const;
/**
* This function copies the content of @p
* constraints_in with DoFs that are
* element of the IndexSet @p
* filter. Constrained dofs are
* transformed to local index space of
* the filter, and elements not present
* in the IndexSet are ignored.
*
* This function provides an easy way to
* create a ConstraintMatrix for certain
* vector components in a vector-valued
* problem from a full ConstraintMatrix,
* i.e. extracting a diagonal subblock
* from a larger ConstraintMatrix. The
* block is specified by the IndexSet
* argument.
*/
void add_selected_constraints (const ConstraintMatrix &constraints_in,
const IndexSet &filter);
/**
* @name Adding constraints
* @{
*/
/**
* Add a new line to the
* matrix. If the line already
* exists, then the function
* simply returns without doing
* anything.
*/
void add_line (const unsigned int line);
/**
* Call the first add_line() function for
* every index <code>i</code> for which
* <code>lines[i]</code> is true.
*
* This function essentially exists to
* allow adding several constraints of
* the form $x_i=0$ all at once, where
* the set of indices $i$ for which these
* constraints should be added are given
* by the argument of this function. On
* the other hand, just as if the
* single-argument add_line() function
* were called repeatedly, the
* constraints can later be modified to
* include linear dependencies using the
* add_entry() function as well as
* inhomogeneities using
* set_inhomogeneity().
*/
void add_lines (const std::vector<bool> &lines);
/**
* Call the first add_line() function for
* every index <code>i</code> that
* appears in the argument.
*
* This function essentially exists to
* allow adding several constraints of
* the form $x_i=0$ all at once, where
* the set of indices $i$ for which these
* constraints should be added are given
* by the argument of this function. On
* the other hand, just as if the
* single-argument add_line() function
* were called repeatedly, the
* constraints can later be modified to
* include linear dependencies using the
* add_entry() function as well as
* inhomogeneities using
* set_inhomogeneity().
*/
void add_lines (const std::set<unsigned int> &lines);
/**
* Call the first add_line() function for
* every index <code>i</code> that
* appears in the argument.
*
* This function essentially exists to
* allow adding several constraints of
* the form $x_i=0$ all at once, where
* the set of indices $i$ for which these
* constraints should be added are given
* by the argument of this function. On
* the other hand, just as if the
* single-argument add_line() function
* were called repeatedly, the
* constraints can later be modified to
* include linear dependencies using the
* add_entry() function as well as
* inhomogeneities using
* set_inhomogeneity().
*/
void add_lines (const IndexSet &lines);
/**
* Add an entry to a given
* line. The list of lines is
* searched from the back to the
* front, so clever programming
* would add a new line (which is
* pushed to the back) and
* immediately afterwards fill
* the entries of that line. This
* way, no expensive searching is
* needed.
*
* If an entry with the same
* indices as the one this
* function call denotes already
* exists, then this function
* simply returns provided that
* the value of the entry is the
* same. Thus, it does no harm to
* enter a constraint twice.
*/
void add_entry (const unsigned int line,
const unsigned int column,
const double value);
/**
* Add a whole series of entries,
* denoted by pairs of column indices
* and values, to a line of
* constraints. This function is
* equivalent to calling the preceeding
* function several times, but is
* faster.
*/
void add_entries (const unsigned int line,
const std::vector<std::pair<unsigned int,double> > &col_val_pairs);
/**
* Set an imhomogeneity to the
* constraint line <i>i</i>, according
* to the discussion in the general
* class description.
*/
void set_inhomogeneity (const unsigned int line,
const double value);
/**
* Close the filling of entries. Since
* the lines of a matrix of this type
* are usually filled in an arbitrary
* order and since we do not want to
* use associative constainers to store
* the lines, we need to sort the lines
* and within the lines the columns
* before usage of the matrix. This is
* done through this function.
*
* Also, zero entries are discarded,
* since they are not needed.
*
* After closing, no more entries are
* accepted. If the object was already
* closed, then this function returns
* immediately.
*
* This function also resolves chains
* of constraints. For example, degree
* of freedom 13 may be constrained to
* $u_{13}=u_3/2+u_7/2$ while degree of
* freedom 7 is itself constrained as
* $u_7=u_2/2+u_4/2$. Then, the
* resolution will be that
* $u_{13}=u_3/2+u_2/4+u_4/4$. Note,
* however, that cycles in this graph
* of constraints are not allowed,
* i.e. for example $u_4$ may not be
* constrained, directly or indirectly,
* to $u_{13}$ again.
*/
void close ();
/**
* Merge the constraints represented by
* the object given as argument into
* the constraints represented by this
* object. Both objects may or may not
* be closed (by having their function
* @p close called before). If this
* object was closed before, then it
* will be closed afterwards as
* well. Note, however, that if the
* other argument is closed, then
* merging may be significantly faster.
*
* Note that the constraints in each of
* the two objects (the old one
* represented by this object and the
* argument) may not refer to the same
* degree of freedom, i.e. a degree of
* freedom that is constrained in one
* object may not be constrained in the
* second. If this is nevertheless the
* case, an exception is thrown.
*
* However, the following is possible:
* if DoF @p x is constrained to dofs
* @p x_i for some set of indices @p i,
* then the DoFs @p x_i may be further
* constrained by the constraints
* object given as argument, although
* not to other DoFs that are
* constrained in either of the two
* objects. Note that it is not
* possible that the DoFs @p x_i are
* constrained within the present
* object.
*
* Because of simplicity of
* implementation, and also to avoid
* cycles, this operation is not
* symmetric: degrees of freedom that
* are constrained in the given
* argument object may not be
* constrained to DoFs that are
* themselves constrained within the
* present object.
*
* The aim of these merging operations
* is that if, for example, you have
* hanging nodes that are constrained
* to the degrees of freedom adjacent
* to them, you cannot originally,
* i.e. within one object, constrain
* these adjacent nodes
* further. However, that may be
* desirable in some cases, for example
* if they belong to a symmetry
* boundary for which the nodes on one
* side of the domain should have the
* same values as those on the other
* side. In that case, you would first
* construct a costraints object
* holding the hanging nodes
* constraints, and a second one that
* contains the constraints due to the
* symmetry boundary. You would then
* finally merge this second one into
* the first, possibly eliminating
* constraints of hanging nodes to
* adjacent boundary nodes by
* constraints to nodes at the opposite
* boundary.
*/
void merge (const ConstraintMatrix &other_constraints);
/**
* Shift all entries of this matrix
* down @p offset rows and over @p
* offset columns.
*
* This function is useful if you are
* building block matrices, where all
* blocks are built by the same @p
* DoFHandler object, i.e. the matrix
* size is larger than the number of
* degrees of freedom. Since several
* matrix rows and columns correspond
* to the same degrees of freedom,
* you'd generate several constraint
* objects, then shift them, and
* finally @p merge them together
* again.
*/
void shift (const unsigned int offset);
/**
* Clear all entries of this
* matrix. Reset the flag determining
* whether new entries are accepted or
* not.
*
* This function may be called also on
* objects which are empty or already
* cleared.
*/
void clear ();
/**
* @}
*/
/**
* @name Querying constraints
* @{
*/
/**
* Return number of constraints stored in
* this matrix.
*/
unsigned int n_constraints () const;
/**
* Return whether the degree of freedom
* with number @p index is a
* constrained one.
*
* Note that if @p close was called
* before, then this function is
* significantly faster, since then the
* constrained degrees of freedom are
* sorted and we can do a binary
* search, while before @p close was
* called, we have to perform a linear
* search through all entries.
*/
bool is_constrained (const unsigned int index) const;
/**
* Return whether the dof is
* constrained, and whether it is
* constrained to only one other degree
* of freedom with weight one. The
* function therefore returns whether
* the degree of freedom would simply
* be eliminated in favor of exactly
* one other degree of freedom.
*
* The function returns @p false if
* either the degree of freedom is not
* constrained at all, or if it is
* constrained to more than one other
* degree of freedom, or if it is
* constrained to only one degree of
* freedom but with a weight different
* from one.
*/
bool is_identity_constrained (const unsigned int index) const;
/**
* Return the maximum number of other
* dofs that one dof is constrained
* to. For example, in 2d a hanging
* node is constrained only to its two
* neighbors, so the returned value
* would be @p 2. However, for higher
* order elements and/or higher
* dimensions, or other types of
* constraints, this number is no more
* obvious.
*
* The name indicates that within the
* system matrix, references to a
* constrained node are indirected to
* the nodes it is constrained to.
*/
unsigned int max_constraint_indirections () const;
/**
* Returns <tt>true</tt> in case the
* dof is constrained and there is a
* non-trivial inhomogeneous valeus set
* to the dof.
*/
bool is_inhomogeneously_constrained (const unsigned int index) const;
/**
* Returns <tt>false</tt> if all
* constraints in the ConstraintMatrix
* are homogeneous ones, and
* <tt>true</tt> if there is at least
* one inhomogeneity.
*/
bool has_inhomogeneities () const;
/**
* Print the constraint lines. Mainly
* for debugging purposes.
*
* This function writes out all entries
* in the constraint matrix lines with
* their value in the form <tt>row col
* : value</tt>. Unconstrained lines
* containing only one identity entry
* are not stored in this object and
* are not printed.
*/
void print (std::ostream &) const;
/**
* Write the graph of constraints in
* 'dot' format. 'dot' is a program
* that can take a list of nodes and
* produce a graphical representation
* of the graph of constrained degrees
* of freedom and the degrees of
* freedom they are constrained to.
*
* The output of this function can be
* used as input to the 'dot' program
* that can convert the graph into a
* graphical representation in
* postscript, png, xfig, and a number
* of other formats.
*
* This function exists mostly for
* debugging purposes.
*/
void write_dot (std::ostream &) const;
/**
* Determine an estimate for the memory
* consumption (in bytes) of this
* object.
*/
unsigned int memory_consumption () const;
/**
* @}
*/
/**
* @name Eliminating constraints from linear systems after their creation
* @{
*/
/**
* Condense a given sparsity
* pattern. This function assumes the
* uncondensed matrix struct to be
* compressed and the one to be filled
* to be empty. The condensed structure
* is compressed afterwards.
*
* The constraint matrix object must be
* closed to call this function.
*
* @note The hanging nodes are
* completely eliminated from the
* linear system refering to
* <tt>condensed</tt>. Therefore, the
* dimension of <tt>condensed</tt> is
* the dimension of
* <tt>uncondensed</tt> minus the
* number of constrained degrees of
* freedom.
*/
void condense (const SparsityPattern &uncondensed,
SparsityPattern &condensed) const;
/**
* This function does much the same as
* the above one, except that it
* condenses the matrix struct
* 'in-place'. It does not remove
* nonzero entries from the matrix but
* adds those needed for the process of
* distribution of the constrained
* degrees of freedom.
*
* Since this function adds new nonzero
* entries to the sparsity pattern, the
* argument must not be
* compressed. However the constraint
* matrix must be closed. The matrix
* struct is compressed at the end of
* the function.
*/
void condense (SparsityPattern &sparsity) const;
/**
* Same function as above, but
* condenses square block sparsity
* patterns.
*/
void condense (BlockSparsityPattern &sparsity) const;
/**
* Same function as above, but
* condenses square compressed sparsity
* patterns.
*
* Given the data structure used by
* CompressedSparsityPattern, this
* function becomes quadratic in the
* number of degrees of freedom for
* large problems and can dominate
* setting up linear systems when
* several hundred thousand or millions
* of unknowns are involved and for
* problems with many nonzero elements
* per row (for example for
* vector-valued problems or hp finite
* elements). In this case, it is
* advisable to use the
* CompressedSetSparsityPattern class
* instead, see for example @ref
* step_27 "step-27", or to use the
* CompressedSimpleSparsityPattern
* class, see for example @ref step_31
* "step-31".
*/
void condense (CompressedSparsityPattern &sparsity) const;
/**
* Same function as above, but
* condenses compressed sparsity
* patterns, which are based on the
* std::set container.
*/
void condense (CompressedSetSparsityPattern &sparsity) const;
/**
* Same function as above, but
* condenses compressed sparsity
* patterns, which are based on the
* ''simple'' aproach.
*/
void condense (CompressedSimpleSparsityPattern &sparsity) const;
/**
* Same function as above, but
* condenses square compressed sparsity
* patterns.
*
* Given the data structure used by
* BlockCompressedSparsityPattern, this
* function becomes quadratic in the
* number of degrees of freedom for
* large problems and can dominate
* setting up linear systems when
* several hundred thousand or millions
* of unknowns are involved and for
* problems with many nonzero elements
* per row (for example for
* vector-valued problems or hp finite
* elements). In this case, it is
* advisable to use the
* BlockCompressedSetSparsityPattern
* class instead, see for example @ref
* step_27 "step-27" and @ref step_31
* "step-31".
*/
void condense (BlockCompressedSparsityPattern &sparsity) const;
/**
* Same function as above, but
* condenses square compressed sparsity
* patterns.
*/
void condense (BlockCompressedSetSparsityPattern &sparsity) const;
/**
* Same function as above, but
* condenses square compressed sparsity
* patterns.
*/
void condense (BlockCompressedSimpleSparsityPattern &sparsity) const;
/**
* Condense a given matrix. The
* associated matrix struct should be
* condensed and compressed. It is the
* user's responsibility to guarantee
* that all entries in the @p condensed
* matrix be zero!
*
* The constraint matrix object must be
* closed to call this function.
*/
template<typename number>
void condense (const SparseMatrix<number> &uncondensed,
SparseMatrix<number> &condensed) const;
/**
* This function does much the same as
* the above one, except that it
* condenses the matrix 'in-place'. See
* the general documentation of this
* class for more detailed information.
*/
template<typename number>
void condense (SparseMatrix<number> &matrix) const;
/**
* Same function as above, but
* condenses square block sparse
* matrices.
*/
template <typename number>
void condense (BlockSparseMatrix<number> &matrix) const;
/**
* Condense the given vector @p
* uncondensed into @p condensed. It is
* the user's responsibility to
* guarantee that all entries of @p
* condensed be zero. Note that this
* function does not take any
* inhomogeneity into account and
* throws an exception in case there
* are any inhomogeneities. Use
* the function using both a matrix and
* vector for that case.
*
* The @p VectorType may be a
* Vector<float>, Vector<double>,
* BlockVector<tt><...></tt>, a PETSc
* or Trilinos vector wrapper class, or
* any other type having the same
* interface.
*/
template <class VectorType>
void condense (const VectorType &uncondensed,
VectorType &condensed) const;
/**
* Condense the given vector
* in-place. The @p VectorType may be a
* Vector<float>, Vector<double>,
* BlockVector<tt><...></tt>, a PETSc
* or Trilinos vector wrapper class, or
* any other type having the same
* interface. Note that this function
* does not take any inhomogeneity into
* account and throws an exception in
* case there are any
* inhomogeneities. Use the function
* using both a matrix and vector for
* that case.
*/
template <class VectorType>
void condense (VectorType &vec) const;
/**
* Condense a given matrix and a given
* vector. The associated matrix struct
* should be condensed and
* compressed. It is the user's
* responsibility to guarantee that all
* entries in the @p condensed matrix
* and vector be zero! This function is
* the appropriate choice for applying
* inhomogeneous constraints.
*
* The constraint matrix object must be
* closed to call this function.
*/
template<typename number, class VectorType>
void condense (const SparseMatrix<number> &uncondensed_matrix,
const VectorType &uncondensed_vector,
SparseMatrix<number> &condensed_matrix,
VectorType &condensed_vector) const;
/**
* This function does much the same as
* the above one, except that it
* condenses matrix and vector
* 'in-place'. See the general
* documentation of this class for more
* detailed information.
*/
template<typename number, class VectorType>
void condense (SparseMatrix<number> &matrix,
VectorType &vector) const;
/**
* Same function as above, but
* condenses square block sparse
* matrices and vectors.
*/
template <typename number, class BlockVectorType>
void condense (BlockSparseMatrix<number> &matrix,
BlockVectorType &vector) const;
/**
* Delete hanging nodes in a
* vector. Sets all hanging node
* values to zero. The @p
* VectorType may be a
* Vector<float>, Vector<double>,
* BlockVector<tt><...></tt>, a
* PETSc or Trilinos vector
* wrapper class, or any other
* type having the same
* interface.
*/
template <class VectorType>
void set_zero (VectorType &vec) const;
/**
* @}
*/
/**
* @name Eliminating constraints from linear systems during their creation
* @{
*/
/**
* This function takes a vector of
* local contributions (@p
* local_vector) corresponding to the
* degrees of freedom indices given in
* @p local_dof_indices and distributes
* them to the global vector. In most
* cases, these local contributions
* will be the result of an integration
* over a cell or face of a
* cell. However, as long as @p
* local_vector and @p
* local_dof_indices have the same
* number of elements, this function is
* happy with whatever it is
* given.
*
* In contrast to the similar function
* in the DoFAccessor class, this
* function also takes care of
* constraints, i.e. if one of the
* elements of @p local_dof_indices
* belongs to a constrained node, then
* rather than writing the
* corresponding element of @p
* local_vector into @p global_vector,
* the element is distributed to the
* entries in the global vector to
* which this particular degree of
* freedom is constrained.
*
* Thus, by using this function to
* distribute local contributions to the
* global object, one saves the call to
* the condense function after the
* vectors and matrices are fully
* assembled. On the other hand, by
* consequence, the function does not
* only write into the entries enumerated
* by the @p local_dof_indices array, but
* also (possibly) others as necessary.
*
* Note that this function will apply all
* constraints as if they were
* homogeneous. For correctly setting
* inhomogeneous constraints, use the
* similar function with a matrix
* argument or the function with both
* matrix and vector arguments.
*
* Note: This function is not
* thread-safe, so you will need to make
* sure that only on process at a time
* calls this function.
*/
template <class InVector, class OutVector>
void
distribute_local_to_global (const InVector &local_vector,
const std::vector<unsigned int> &local_dof_indices,
OutVector &global_vector) const;
/**
* This function takes a vector of
* local contributions (@p
* local_vector) corresponding to the
* degrees of freedom indices given in
* @p local_dof_indices and distributes
* them to the global vector. In most
* cases, these local contributions
* will be the result of an integration
* over a cell or face of a
* cell. However, as long as @p
* local_vector and @p
* local_dof_indices have the same
* number of elements, this function is
* happy with whatever it is
* given.
*
* In contrast to the similar function in
* the DoFAccessor class, this function
* also takes care of constraints,
* i.e. if one of the elements of @p
* local_dof_indices belongs to a
* constrained node, then rather than
* writing the corresponding element of
* @p local_vector into @p global_vector,
* the element is distributed to the
* entries in the global vector to which
* this particular degree of freedom is
* constrained.
*
* Thus, by using this function to
* distribute local contributions to the
* global object, one saves the call to
* the condense function after the
* vectors and matrices are fully
* assembled. On the other hand, by
* consequence, the function does not
* only write into the entries enumerated
* by the @p local_dof_indices array, but
* also (possibly) others as
* necessary. This includes writing into
* diagonal elements of the matrix if the
* corresponding degree of freedom is
* constrained.
*
* The fourth argument
* <tt>local_matrix</tt> is intended to
* be used in case one wants to apply
* inhomogeneous constraints on the
* vector only. Such a situation could be
* where one wants to assemble of a right
* hand side vector on a problem with
* inhomogeneous constraints, but the
* global matrix has been assembled
* previously. A typical example of this
* is a time stepping algorithm where the
* stiffness matrix is assembled once,
* and the right hand side updated every
* time step. Note that, however, the
* entries in the columns of the local
* matrix have to be exactly the same as
* those that have been written into the
* global matrix. Otherwise, this
* function will not be able to correctly
* handle inhomogeneities.
*
* Note: This function is not
* thread-safe, so you will need to make
* sure that only on process at a time
* calls this function.
*/
template <typename VectorType>
void
distribute_local_to_global (const Vector<double> &local_vector,
const std::vector<unsigned int> &local_dof_indices,
VectorType &global_vector,
const FullMatrix<double> &local_matrix) const;
/**
* This function takes a pointer to a
* vector of local contributions (@p
* local_vector) corresponding to the
* degrees of freedom indices given in
* @p local_dof_indices and distributes
* them to the global vector. In most
* cases, these local contributions
* will be the result of an integration
* over a cell or face of a
* cell. However, as long as the
* entries in @p local_dof_indices
* indicate reasonable global vector
* entries, this function is happy with
* whatever it is given.
*
* If one of the elements of @p
* local_dof_indices belongs to a
* constrained node, then rather than
* writing the corresponding element of
* @p local_vector into @p
* global_vector, the element is
* distributed to the entries in the
* global vector to which this
* particular degree of freedom is
* constrained.
*
* Thus, by using this function to
* distribute local contributions to
* the global object, one saves the
* call to the condense function after
* the vectors and matrices are fully
* assembled. Note that this function
* completely ignores inhomogeneous
* constraints.
*
* Note: This function is not
* thread-safe, so you will need to
* make sure that only on process at a
* time calls this function.
*/
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
void
distribute_local_to_global (ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end,
ForwardIteratorInd local_indices_begin,
VectorType &global_vector) const;
/**
* This function takes a matrix of
* local contributions (@p
* local_matrix) corresponding to the
* degrees of freedom indices given in
* @p local_dof_indices and distributes
* them to the global matrix. In most
* cases, these local contributions
* will be the result of an integration
* over a cell or face of a
* cell. However, as long as @p
* local_matrix and @p
* local_dof_indices have the same
* number of elements, this function is
* happy with whatever it is given.
*
* In contrast to the similar function
* in the DoFAccessor class, this
* function also takes care of
* constraints, i.e. if one of the
* elements of @p local_dof_indices
* belongs to a constrained node, then
* rather than writing the
* corresponding element of @p
* local_matrix into @p global_matrix,
* the element is distributed to the
* entries in the global matrix to
* which this particular degree of
* freedom is constrained.
*
* With this scheme, we never write
* into rows or columns of constrained
* degrees of freedom. In order to make
* sure that the resulting matrix can
* still be inverted, we need to do
* something with the diagonal elements
* corresponding to constrained
* nodes. Thus, if a degree of freedom
* in @p local_dof_indices is
* constrained, we distribute the
* corresponding entries in the matrix,
* but also add the absolute value of
* the diagonal entry of the local
* matrix to the corresponding entry in
* the global matrix. Since the exact
* value of the diagonal element is not
* important (the value of the
* respective degree of freedom will be
* overwritten by the distribute() call
* later on anyway), this guarantees
* that the diagonal entry is always
* non-zero, positive, and of the same
* order of magnitude as the other
* entries of the matrix.
*
* Thus, by using this function to
* distribute local contributions to
* the global object, one saves the
* call to the condense function after
* the vectors and matrices are fully
* assembled.
*
* Note: This function is not
* thread-safe, so you will need to
* make sure that only on process at a
* time calls this function.
*/
template <typename MatrixType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const std::vector<unsigned int> &local_dof_indices,
MatrixType &global_matrix) const;
/**
* Does the same as the function above
* but can treat
* non quadratic matrices.
*/
template <typename MatrixType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const std::vector<unsigned int> &row_indices,
const std::vector<unsigned int> &col_indices,
MatrixType &global_matrix) const;
/**
* This function simultaneously writes
* elements into matrix and vector,
* according to the constraints
* specified by the calling
* ConstraintMatrix. This function can
* correctly handle inhomogeneous
* constraints as well.
*
* Note: This function is not
* thread-safe, so you will need to
* make sure that only on process at a
* time calls this function.
*/
template <typename MatrixType, typename VectorType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const Vector<double> &local_vector,
const std::vector<unsigned int> &local_dof_indices,
MatrixType &global_matrix,
VectorType &global_vector) const;
/**
* Do a similar operation as the
* distribute_local_to_global() function
* that distributed writing entries into
* a matrix for constrained degrees of
* freedom, except that here we don't
* write into a matrix but only allocate
* sparsity pattern entries.
*
* As explained in the
* @ref hp_paper "hp paper"
* and in step-27,
* first allocating a sparsity pattern
* and later coming back and allocating
* additional entries for those matrix
* entries that will be written to due to
* the elimination of constrained degrees
* of freedom (using
* ConstraintMatrix::condense() ), can be
* a very expensive procedure. It is
* cheaper to allocate these entries
* right away without having to do a
* second pass over the sparsity pattern
* object. This function does exactly
* that.
*
* Because the function only allocates
* entries in a sparsity pattern, all it
* needs to know are the degrees of
* freedom that couple to each
* other. Unlike the previous function,
* no actual values are written, so the
* second input argument is not necessary
* here.
*
* The third argument to this function,
* keep_constrained_entries determines
* whether the function shall allocate
* entries in the sparsity pattern at
* all for entries that will later be
* set to zero upon condensation of the
* matrix. These entries are necessary
* if the matrix is built
* unconstrained, and only later
* condensed. They are not necessary if
* the matrix is built using the
* distribute_local_to_global()
* function of this class which
* distributes entries right away when
* copying a local matrix into a global
* object. The default of this argument
* is true, meaning to allocate the few
* entries that may later be set to
* zero.
*
* By default, the function adds
* entries for all pairs of indices
* given in the first argument to the
* sparsity pattern (unless
* keep_constrained_entries is
* false). However, sometimes one would
* like to only add a subset of all of
* these pairs. In that case, the last
* argument can be used which specifies
* a boolean mask which of the pairs of
* indices should be considered. If the
* mask is false for a pair of indices,
* then no entry will be added to the
* sparsity pattern for this pair,
* irrespective of whether one or both
* of the indices correspond to
* constrained degrees of freedom.
*
* This function is not typically called
* from user code, but is used in the
* DoFTools::make_sparsity_pattern()
* function when passed a constraint
* matrix object.
*/
template <typename SparsityType>
void
add_entries_local_to_global (const std::vector<unsigned int> &local_dof_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries = true,
const Table<2,bool> &dof_mask = default_empty_table) const;
/**
* This function imports values from a
* global vector (@p global_vector) by
* applying the constraints to a vector
* of local values, expressed in
* iterator format. In most cases, the
* local values will be identified by
* the local dof values on a
* cell. However, as long as the
* entries in @p local_dof_indices
* indicate reasonable global vector
* entries, this function is happy with
* whatever it is given.
*
* If one of the elements of @p
* local_dof_indices belongs to a
* constrained node, then rather than
* writing the corresponding element of
* @p global_vector into @p
* local_vector, the constraints are
* resolved as the respective
* distribute function does, i.e., the
* local entry is constructed from the
* global entries to which this
* particular degree of freedom is
* constrained.
*
* In contrast to the similar function
* get_dof_values in the DoFAccessor
* class, this function does not need
* the constrained values to be
* correctly set (i.e., distribute to
* be called).
*/
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
void
get_dof_values (const VectorType &global_vector,
ForwardIteratorInd local_indices_begin,
ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end) const;
/**
* @}
*/
/**
* @name Dealing with constraints after solving a linear system
* @{
*/
/**
* Re-distribute the elements of the
* vector @p condensed to @p
* uncondensed. It is the user's
* responsibility to guarantee that all
* entries of @p uncondensed be zero!
*
* This function undoes the action of
* @p condense somehow, but it should
* be noted that it is not the inverse
* of @p condense.
*
* The @p VectorType may be a
* Vector<float>, Vector<double>,
* BlockVector<tt><...></tt>, a PETSc
* or Trilinos vector wrapper class, or
* any other type having the same
* interface.
*/
template <class VectorType>
void distribute (const VectorType &condensed,
VectorType &uncondensed) const;
/**
* Re-distribute the elements of the
* vector in-place. The @p VectorType
* may be a Vector<float>,
* Vector<double>,
* BlockVector<tt><...></tt>, a PETSc
* or Trilinos vector wrapper class, or
* any other type having the same
* interface.
*/
template <class VectorType>
void distribute (VectorType &vec) const;
/**
* @}
*/
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException0 (ExcMatrixIsClosed);
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException0 (ExcMatrixNotClosed);
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException1 (ExcLineInexistant,
unsigned int,
<< "The specified line " << arg1
<< " does not exist.");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException4 (ExcEntryAlreadyExists,
int, int, double, double,
<< "The entry for the indices " << arg1 << " and "
<< arg2 << " already exists, but the values "
<< arg3 << " (old) and " << arg4 << " (new) differ "
<< "by " << (arg4-arg3) << ".");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException2 (ExcDoFConstrainedToConstrainedDoF,
int, int,
<< "You tried to constrain DoF " << arg1
<< " to DoF " << arg2
<< ", but that one is also constrained. This is not allowed!");
/**
* Exception.
*
* @ingroup Exceptions
*/
DeclException1 (ExcDoFIsConstrainedFromBothObjects,
int,
<< "Degree of freedom " << arg1
<< " is constrained from both object in a merge operation.");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException1 (ExcDoFIsConstrainedToConstrainedDoF,
int,
<< "In the given argument a degree of freedom is constrained "
<< "to another DoF with number " << arg1
<< ", which however is constrained by this object. This is not"
<< " allowed.");
/**
* Exception
*
* @ingroup Exceptions
*/
DeclException1 (ExcRowNotStoredHere,
int,
<< "The index set given to this constraint matrix indicates "
<< "constraints for degree of freedom " << arg1
<< " should not be stored by this object, but a constraint "
<< "is being added.");
private:
/**
* This class represents one line of a
* constraint matrix.
*/
struct ConstraintLine
{
/**
* A data type in which we store the list
* of entries that make up the homogenous
* part of a constraint.
*/
typedef std::vector<std::pair<unsigned int,double> > Entries;
/**
* Number of this line. Since only
* very few lines are stored, we
* can not assume a specific order
* and have to store the line
* number explicitly.
*/
unsigned int line;
/**
* Row numbers and values of the
* entries in this line.
*
* For the reason why we use a
* vector instead of a map and the
* consequences thereof, the same
* applies as what is said for
* ConstraintMatrix@p ::lines.
*/
Entries entries;
/**
* Value of the inhomogeneity.
*/
double inhomogeneity;
/**
* This operator is a bit weird and
* unintuitive: it compares the
* line numbers of two lines. We
* need this to sort the lines; in
* fact we could do this using a
* comparison predicate. However,
* this way, it is easier, albeit
* unintuitive since two lines
* really have no god-given order
* relation.
*/
bool operator < (const ConstraintLine &) const;
/**
* This operator is likewise weird:
* it checks whether the line
* indices of the two operands are
* equal, irrespective of the fact
* that the contents of the line
* may be different.
*/
bool operator == (const ConstraintLine &) const;
/**
* Determine an estimate for the
* memory consumption (in bytes) of
* this object.
*/
unsigned int memory_consumption () const;
};
/**
* Store the lines of the matrix.
* Entries are usually appended in an
* arbitrary order and insertion into a
* vector is done best at the end, so
* the order is unspecified after all
* entries are inserted. Sorting of the
* entries takes place when calling the
* <tt>close()</tt> function.
*
* We could, instead of using a vector,
* use an associative array, like a map
* to store the lines. This, however,
* would mean a much more fractioned
* heap since it allocates many small
* objects, and would additionally make
* usage of this matrix much slower.
*/
std::vector<ConstraintLine> lines;
/**
* A list of unsigned integers that
* contains the position of the
* ConstraintLine of a constrained degree
* of freedom, or @p
* numbers::invalid_unsigned_int if the
* degree of freedom is not
* constrained. The @p invalid_unsigned
* int return value returns thus whether
* there is a constraint line for a given
* degree of freedom index. Note that
* this class has no notion of how many
* degrees of freedom there really are,
* so if we check whether there is a
* constraint line for a given degree of
* freedom, then this vector may actually
* be shorter than the index of the DoF
* we check for.
*
* This field exists since when adding a
* new constraint line we have to figure
* out whether it already
* exists. Previously, we would simply
* walk the unsorted list of constraint
* lines until we either hit the end or
* found it. This algorithm is O(N) if N
* is the number of constraints, which
* makes it O(N^2) when inserting all
* constraints. For large problems with
* many constraints, this could easily
* take 5-10 per cent of the total run
* time. With this field, we can save
* this time since we find any constraint
* in O(1) time or get to know that it a
* certain degree of freedom is not
* constrained.
*
* To make things worse, traversing the
* list of existing constraints requires
* reads from many different places in
* memory. Thus, in large 3d
* applications, the add_line() function
* showed up very prominently in the
* overall compute time, mainly because
* it generated a lot of cache
* misses. This should also be fixed by
* using the O(1) algorithm to access the
* fields of this array.
*
* The field is useful in a number of
* other contexts as well, e.g. when one
* needs random access to the constraints
* as in all the functions that apply
* constraints on the fly while add cell
* contributions into vectors and
* matrices.
*/
std::vector<unsigned int> lines_cache;
/**
* This IndexSet is used to limit the
* lines to save in the ContraintMatrix
* to a subset. This is necessary,
* because the lines_cache vector would
* become too big in a distributed
* calculation.
*/
IndexSet local_lines;
/**
* Store whether the arrays are sorted.
* If so, no new entries can be added.
*/
bool sorted;
/**
* Internal function to calculate the
* index of line @p line in the vector
* lines_cache using local_lines.
*/
unsigned int calculate_line_index (const unsigned int line) const;
/**
* Return @p true if the weight of an
* entry (the second element of the
* pair) equals zero. This function is
* used to delete entries with zero
* weight.
*/
static bool check_zero_weight (const std::pair<unsigned int, double> &p);
/**
* Dummy table that serves as default
* argument for function
* <tt>add_entries_local_to_global()</tt>.
*/
static const Table<2,bool> default_empty_table;
/**
* This function actually implements
* the local_to_global function for
* standard (non-block) matrices.
*/
template <typename MatrixType, typename VectorType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const Vector<double> &local_vector,
const std::vector<unsigned int> &local_dof_indices,
MatrixType &global_matrix,
VectorType &global_vector,
internal::bool2type<false>) const;
/**
* This function actually implements
* the local_to_global function for
* block matrices.
*/
template <typename MatrixType, typename VectorType>
void
distribute_local_to_global (const FullMatrix<double> &local_matrix,
const Vector<double> &local_vector,
const std::vector<unsigned int> &local_dof_indices,
MatrixType &global_matrix,
VectorType &global_vector,
internal::bool2type<true>) const;
/**
* This function actually implements
* the local_to_global function for
* standard (non-block) sparsity types.
*/
template <typename SparsityType>
void
add_entries_local_to_global (const std::vector<unsigned int> &local_dof_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries,
const Table<2,bool> &dof_mask,
internal::bool2type<false>) const;
/**
* This function actually implements
* the local_to_global function for
* block sparsity types.
*/
template <typename SparsityType>
void
add_entries_local_to_global (const std::vector<unsigned int> &local_dof_indices,
SparsityType &sparsity_pattern,
const bool keep_constrained_entries,
const Table<2,bool> &dof_mask,
internal::bool2type<true>) const;
/**
* Internal helper function for
* distribute_local_to_global
* function.
*
* Creates a list of affected
* rows for distribution.
*/
void
make_sorted_row_list (const std::vector<unsigned int> &local_dof_indices,
internals::GlobalRowsFromLocal &global_rows) const;
/**
* Internal helper function for
* distribute_local_to_global function.
*/
template <typename MatrixType>
void
make_sorted_row_list (const FullMatrix<double> &local_matrix,
const std::vector<unsigned int> &local_dof_indices,
MatrixType &global_matrix,
internals::GlobalRowsFromLocal &global_rows) const;
/**
* Internal helper function for
* add_entries_local_to_global function.
*/
template <typename SparsityType>
void
make_sorted_row_list (const std::vector<unsigned int> &local_dof_indices,
const bool keep_constrained_entries,
SparsityType &sparsity_pattern,
std::vector<unsigned int> &active_dofs) const;
/**
* Internal helper function for
* add_entries_local_to_global function.
*/
template <typename SparsityType>
void
make_sorted_row_list (const Table<2,bool> &dof_mask,
const std::vector<unsigned int> &local_dof_indices,
const bool keep_constrained_entries,
SparsityType &sparsity_pattern,
internals::GlobalRowsFromLocal &global_rows) const;
/**
* Internal helper function for
* distribute_local_to_global function.
*/
double
resolve_vector_entry (const unsigned int i,
const internals::GlobalRowsFromLocal &global_rows,
const Vector<double> &local_vector,
const std::vector<unsigned int> &local_dof_indices,
const FullMatrix<double> &local_matrix) const;
#ifdef DEAL_II_USE_TRILINOS
//TODO: Make use of the following member thread safe
/**
* This vector is used to import data
* within the distribute function.
*/
mutable boost::scoped_ptr<TrilinosWrappers::MPI::Vector> vec_distribute;
#endif
};
/* ---------------- template and inline functions ----------------- */
inline
ConstraintMatrix::ConstraintMatrix (const IndexSet &local_constraints)
:
lines (),
local_lines (local_constraints),
sorted (false)
{}
inline
ConstraintMatrix::ConstraintMatrix (const ConstraintMatrix &constraint_matrix)
:
Subscriptor (),
lines (constraint_matrix.lines),
lines_cache (constraint_matrix.lines_cache),
local_lines (constraint_matrix.local_lines),
sorted (constraint_matrix.sorted)
#ifdef DEAL_II_USE_TRILINOS
,vec_distribute ()
#endif
{}
inline
void
ConstraintMatrix::add_line (const unsigned int line)
{
Assert (sorted==false, ExcMatrixIsClosed());
// the following can happen when we
// compute with distributed meshes
// and dof handlers and we
// constrain a degree of freedom
// whose number we don't have
// locally. if we don't abort here
// the program will try to allocate
// several terabytes of memory to
// resize the various arrays below
// :-)
Assert (line != numbers::invalid_unsigned_int,
ExcInternalError());
const unsigned int line_index = calculate_line_index (line);
// check whether line already exists; it
// may, in which case we can just quit
if (is_constrained(line))
return;
// if necessary enlarge vector of
// existing entries for cache
if (line_index >= lines_cache.size())
lines_cache.resize (std::max(2*static_cast<unsigned int>(lines_cache.size()),
line_index+1),
numbers::invalid_unsigned_int);
// push a new line to the end of the
// list
lines.push_back (ConstraintLine());
lines.back().line = line;
lines.back().inhomogeneity = 0.;
lines_cache[line_index] = lines.size()-1;
}
inline
void
ConstraintMatrix::add_entry (const unsigned int line,
const unsigned int column,
const double value)
{
Assert (sorted==false, ExcMatrixIsClosed());
Assert (line != column,
ExcMessage ("Can't constrain a degree of freedom to itself"));
// if in debug mode, check whether an
// entry for this column already
// exists and if its the same as
// the one entered at present
//
// in any case: exit the function if an
// entry for this column already exists,
// since we don't want to enter it twice
Assert (lines_cache[calculate_line_index(line)] != numbers::invalid_unsigned_int,
ExcInternalError());
ConstraintLine* line_ptr = &lines[lines_cache[calculate_line_index(line)]];
Assert (line_ptr->line == line, ExcInternalError());
for (ConstraintLine::Entries::const_iterator
p=line_ptr->entries.begin();
p != line_ptr->entries.end(); ++p)
if (p->first == column)
{
Assert (p->second == value,
ExcEntryAlreadyExists(line, column, p->second, value));
return;
}
line_ptr->entries.push_back (std::make_pair(column,value));
}
inline
void
ConstraintMatrix::set_inhomogeneity (const unsigned int line,
const double value)
{
ConstraintLine* line_ptr = &lines[lines_cache[calculate_line_index(line)]];
line_ptr->inhomogeneity = value;
}
inline
bool
ConstraintMatrix::is_constrained (const unsigned int index) const
{
const unsigned int line_index = calculate_line_index(index);
return ((line_index < lines_cache.size())
&&
(lines_cache[line_index] != numbers::invalid_unsigned_int));
}
inline
bool
ConstraintMatrix::is_inhomogeneously_constrained (const unsigned int index) const
{
return (is_constrained(index) &&
lines[lines_cache[calculate_line_index(index)]].inhomogeneity != 0);
}
template <class InVector, class OutVector>
inline
void
ConstraintMatrix::
distribute_local_to_global (const InVector &local_vector,
const std::vector<unsigned int> &local_dof_indices,
OutVector &global_vector) const
{
Assert (local_vector.size() == local_dof_indices.size(),
ExcDimensionMismatch(local_vector.size(), local_dof_indices.size()));
distribute_local_to_global (local_vector.begin(), local_vector.end(),
local_dof_indices.begin(), global_vector);
}
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
inline
void ConstraintMatrix::
distribute_local_to_global (ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end,
ForwardIteratorInd local_indices_begin,
VectorType &global_vector) const
{
Assert (sorted == true, ExcMatrixNotClosed());
for ( ; local_vector_begin != local_vector_end;
++local_vector_begin, ++local_indices_begin)
{
if (is_constrained(*local_indices_begin) == false)
global_vector(*local_indices_begin) += *local_vector_begin;
else
{
const ConstraintLine& position =
lines[lines_cache[calculate_line_index(*local_indices_begin)]];
for (unsigned int j=0; j<position.entries.size(); ++j)
{
Assert (!(!local_lines.size()
|| local_lines.is_element(position.entries[j].first))
|| is_constrained(position.entries[j].first) == false,
ExcMessage ("Tried to distribute to a fixed dof."));
global_vector(position.entries[j].first)
+= *local_vector_begin * position.entries[j].second;
}
}
}
}
template <typename ForwardIteratorVec, typename ForwardIteratorInd,
class VectorType>
inline
void ConstraintMatrix::get_dof_values (const VectorType &global_vector,
ForwardIteratorInd local_indices_begin,
ForwardIteratorVec local_vector_begin,
ForwardIteratorVec local_vector_end) const
{
Assert (sorted == true, ExcMatrixNotClosed());
for ( ; local_vector_begin != local_vector_end;
++local_vector_begin, ++local_indices_begin)
{
if (is_constrained(*local_indices_begin) == false)
*local_vector_begin = global_vector(*local_indices_begin);
else
{
const ConstraintLine & position =
lines[lines_cache[calculate_line_index(*local_indices_begin)]];
typename VectorType::value_type value = position.inhomogeneity;
for (unsigned int j=0; j<position.entries.size(); ++j)
{
Assert (is_constrained(position.entries[j].first) == false,
ExcMessage ("Tried to distribute to a fixed dof."));
value += (global_vector(position.entries[j].first) *
position.entries[j].second);
}
*local_vector_begin = value;
}
}
}
inline unsigned int
ConstraintMatrix::calculate_line_index (const unsigned int line) const
{
//IndexSet is unused (serial case)
if (!local_lines.size())
return line;
Assert(local_lines.is_element(line),
ExcRowNotStoredHere(line));
return local_lines.index_within_set(line);
}
inline bool
ConstraintMatrix::can_store_line(unsigned int line_index) const
{
return !local_lines.size() || local_lines.is_element(line_index);
}
DEAL_II_NAMESPACE_CLOSE
#endif
|