/usr/include/deal.II/lac/solver_bicgstab.h is in libdeal.ii-dev 8.1.0-4.
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 | // ---------------------------------------------------------------------
// $Id: solver_bicgstab.h 31349 2013-10-20 19:07:06Z maier $
//
// Copyright (C) 1998 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__solver_bicgstab_h
#define __deal2__solver_bicgstab_h
#include <deal.II/base/config.h>
#include <deal.II/base/logstream.h>
#include <deal.II/lac/solver.h>
#include <deal.II/lac/solver_control.h>
#include <cmath>
#include <deal.II/base/subscriptor.h>
DEAL_II_NAMESPACE_OPEN
/*!@addtogroup Solvers */
/*@{*/
/**
* Bicgstab algorithm by van der Vorst.
*
* For the requirements on matrices and vectors in order to work with
* this class, see the documentation of the Solver base class.
*
* Like all other solver classes, this class has a local structure called
* @p AdditionalData which is used to pass additional parameters to the
* solver, like damping parameters or the number of temporary vectors. We
* use this additional structure instead of passing these values directly
* to the constructor because this makes the use of the @p SolverSelector and
* other classes much easier and guarantees that these will continue to
* work even if number or type of the additional parameters for a certain
* solver changes.
*
* The Bicgstab-method has two additional parameters: the first is a
* boolean, deciding whether to compute the actual residual in each step (@p
* true) or to use the length of the computed orthogonal residual (@p
* false). Note that computing the residual causes a third
* matrix-vector-multiplication, though no additional preconditioning, in
* each step. The reason for doing this is, that the size of the
* orthogonalized residual computed during the iteration may be larger by
* orders of magnitude than the true residual. This is due to numerical
* instabilities related to badly conditioned matrices. Since this
* instability results in a bad stopping criterion, the default for this
* parameter is @p true. Whenever the user knows that the estimated residual
* works reasonably as well, the flag should be set to @p false in order
* to increase the performance of the solver.
*
* The second parameter is the size of a breakdown criterion. It is
* difficult to find a general good criterion, so if things do not
* work for you, try to change this value.
*/
template <class VECTOR = Vector<double> >
class SolverBicgstab : public Solver<VECTOR>
{
public:
/**
* There are two possibilities to compute the residual: one is an estimate
* using the computed value @p tau. The other is exact computation using
* another matrix vector multiplication. This increases the costs of the
* algorithm, so it is should be set to false whenever the problem allows
* it.
*
* Bicgstab is susceptible to breakdowns, so we need a parameter telling us,
* which numbers are considered zero.
*/
struct AdditionalData
{
/**
* Constructor.
*
* The default is to perform an exact residual computation and breakdown
* parameter 1e-10.
*/
AdditionalData(const bool exact_residual = true,
const double breakdown = 1.e-10) :
exact_residual(exact_residual),
breakdown(breakdown)
{}
/**
* Flag for exact computation of residual.
*/
bool exact_residual;
/**
* Breakdown threshold.
*/
double breakdown;
};
/**
* Constructor.
*/
SolverBicgstab (SolverControl &cn,
VectorMemory<VECTOR> &mem,
const AdditionalData &data=AdditionalData());
/**
* Constructor. Use an object of type GrowingVectorMemory as a default to
* allocate memory.
*/
SolverBicgstab (SolverControl &cn,
const AdditionalData &data=AdditionalData());
/**
* Virtual destructor.
*/
virtual ~SolverBicgstab ();
/**
* Solve primal problem only.
*/
template<class MATRIX, class PRECONDITIONER>
void
solve (const MATRIX &A,
VECTOR &x,
const VECTOR &b,
const PRECONDITIONER &precondition);
protected:
/**
* Computation of the stopping criterion.
*/
template <class MATRIX>
double criterion (const MATRIX &A, const VECTOR &x, const VECTOR &b);
/**
* Interface for derived class. This function gets the current iteration
* vector, the residual and the update vector in each step. It can be used
* for a graphical output of the convergence history.
*/
virtual void print_vectors(const unsigned int step,
const VECTOR &x,
const VECTOR &r,
const VECTOR &d) const;
/**
* Auxiliary vector.
*/
VECTOR *Vx;
/**
* Auxiliary vector.
*/
VECTOR *Vr;
/**
* Auxiliary vector.
*/
VECTOR *Vrbar;
/**
* Auxiliary vector.
*/
VECTOR *Vp;
/**
* Auxiliary vector.
*/
VECTOR *Vy;
/**
* Auxiliary vector.
*/
VECTOR *Vz;
/**
* Auxiliary vector.
*/
VECTOR *Vt;
/**
* Auxiliary vector.
*/
VECTOR *Vv;
/**
* Right hand side vector.
*/
const VECTOR *Vb;
/**
* Auxiliary value.
*/
double alpha;
/**
* Auxiliary value.
*/
double beta;
/**
* Auxiliary value.
*/
double omega;
/**
* Auxiliary value.
*/
double rho;
/**
* Auxiliary value.
*/
double rhobar;
/**
* Current iteration step.
*/
unsigned int step;
/**
* Residual.
*/
double res;
/**
* Additional parameters.
*/
AdditionalData additional_data;
private:
/**
* Everything before the iteration loop.
*/
template <class MATRIX>
SolverControl::State start(const MATRIX &A);
/**
* The iteration loop itself.
*/
template<class MATRIX, class PRECONDITIONER>
bool
iterate(const MATRIX &A, const PRECONDITIONER &precondition);
};
/*@}*/
/*-------------------------Inline functions -------------------------------*/
#ifndef DOXYGEN
template<class VECTOR>
SolverBicgstab<VECTOR>::SolverBicgstab (SolverControl &cn,
VectorMemory<VECTOR> &mem,
const AdditionalData &data)
:
Solver<VECTOR>(cn,mem),
additional_data(data)
{}
template<class VECTOR>
SolverBicgstab<VECTOR>::SolverBicgstab (SolverControl &cn,
const AdditionalData &data)
:
Solver<VECTOR>(cn),
additional_data(data)
{}
template<class VECTOR>
SolverBicgstab<VECTOR>::~SolverBicgstab ()
{}
template <class VECTOR>
template <class MATRIX>
double
SolverBicgstab<VECTOR>::criterion (const MATRIX &A, const VECTOR &x, const VECTOR &b)
{
A.vmult(*Vt, x);
Vt->add(-1.,b);
res = Vt->l2_norm();
return res;
}
template <class VECTOR >
template <class MATRIX>
SolverControl::State
SolverBicgstab<VECTOR>::start(const MATRIX &A)
{
A.vmult(*Vr, *Vx);
Vr->sadd(-1.,1.,*Vb);
res = Vr->l2_norm();
return this->control().check(step, res);
}
template<class VECTOR>
void
SolverBicgstab<VECTOR>::print_vectors(const unsigned int,
const VECTOR &,
const VECTOR &,
const VECTOR &) const
{}
template<class VECTOR>
template<class MATRIX, class PRECONDITIONER>
bool
SolverBicgstab<VECTOR>::iterate(const MATRIX &A,
const PRECONDITIONER &precondition)
{
//TODO:[GK] Implement "use the length of the computed orthogonal residual" in the BiCGStab method.
SolverControl::State state = SolverControl::iterate;
alpha = omega = rho = 1.;
VECTOR &r = *Vr;
VECTOR &rbar = *Vrbar;
VECTOR &p = *Vp;
VECTOR &y = *Vy;
VECTOR &z = *Vz;
VECTOR &t = *Vt;
VECTOR &v = *Vv;
rbar = r;
bool startup = true;
do
{
++step;
rhobar = r*rbar;
beta = rhobar * alpha / (rho * omega);
rho = rhobar;
if (startup == true)
{
p = r;
startup = false;
}
else
p.sadd(beta, 1., r, -beta*omega, v);
precondition.vmult(y,p);
A.vmult(v,y);
rhobar = rbar * v;
alpha = rho/rhobar;
//TODO:[?] Find better breakdown criterion
if (std::fabs(alpha) > 1.e10)
return true;
r.add(-alpha, v);
// check for early success, see the lac/bicgstab_early testcase as to
// why this is necessary
if (this->control().check(step, r.l2_norm()) == SolverControl::success)
{
Vx->add(alpha, y);
print_vectors(step, *Vx, r, y);
return false;
}
precondition.vmult(z,r);
A.vmult(t,z);
rhobar = t*r;
omega = rhobar/(t*t);
Vx->add(alpha, y, omega, z);
r.add(-omega, t);
if (additional_data.exact_residual)
res = criterion(A, *Vx, *Vb);
else
res = r.l2_norm();
state = this->control().check(step, res);
print_vectors(step, *Vx, r, y);
}
while (state == SolverControl::iterate);
return false;
}
template<class VECTOR>
template<class MATRIX, class PRECONDITIONER>
void
SolverBicgstab<VECTOR>::solve(const MATRIX &A,
VECTOR &x,
const VECTOR &b,
const PRECONDITIONER &precondition)
{
deallog.push("Bicgstab");
Vr = this->memory.alloc();
Vr->reinit(x, true);
Vrbar = this->memory.alloc();
Vrbar->reinit(x, true);
Vp = this->memory.alloc();
Vp->reinit(x, true);
Vy = this->memory.alloc();
Vy->reinit(x, true);
Vz = this->memory.alloc();
Vz->reinit(x, true);
Vt = this->memory.alloc();
Vt->reinit(x, true);
Vv = this->memory.alloc();
Vv->reinit(x, true);
Vx = &x;
Vb = &b;
step = 0;
bool state;
do
{
if (step != 0)
deallog << "Restart step " << step << std::endl;
if (start(A) == SolverControl::success)
break;
state = iterate(A, precondition);
}
while (state);
this->memory.free(Vr);
this->memory.free(Vrbar);
this->memory.free(Vp);
this->memory.free(Vy);
this->memory.free(Vz);
this->memory.free(Vt);
this->memory.free(Vv);
deallog.pop();
// in case of failure: throw exception
if (this->control().last_check() != SolverControl::success)
AssertThrow(false, SolverControl::NoConvergence (this->control().last_step(),
this->control().last_value()));
// otherwise exit as normal
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
|