/[escript]/trunk/paso/src/NewtonGMRES.c
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Contents of /trunk/paso/src/NewtonGMRES.c

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Revision 1639 - (show annotations)
Mon Jul 14 08:55:25 2008 UTC (10 years, 11 months ago) by gross
File MIME type: text/plain
File size: 4815 byte(s)


1 /* $Id:$ */
2
3 /*******************************************************
4 *
5 * Copyright 2008 by University of Queensland
6 *
7 * http://esscc.uq.edu.au
8 * Primary Business: Queensland, Australia
9 * Licensed under the Open Software License version 3.0
10 * http://www.opensource.org/licenses/osl-3.0.php
11 *
12 *******************************************************/
13
14 /*
15 * Purpose
16 * =======
17 *
18 * NewtonGMRES solves the non-linear system F(x)=0 using the
19 * restarted GMRES method.
20 *
21 * Convergence test: norm(F(x))< rtol*norm(F(x0))+atol
22 *
23 * x input initial guess
24 * output solution approximation
25 *
26 * based on code by C. T. Kelley, July 1, 1994.
27 *
28 */
29
30 #include "Common.h"
31 #include "Solver.h"
32 #include "PasoUtil.h"
33 #ifdef _OPENMP
34 #include <omp.h>
35 #endif
36 err_t Paso_Solver_NewtonGMRES(
37 Paso_Function *F, /* function evaluation */
38 double *x, /* in: initial guess, out: new approximation */
39 Paso_Options* options,
40 Paso_Performance* pp)
41
42 {
43 const double inner_tolerance_safety=.9;
44 dim_t gmres_iter;
45 double stop_tol, norm_f,norm_fo, reduction_f,old_inner_tolerance, gmres_tol, rtmp;
46 bool_t convergeFlag=FALSE, maxIterFlag=FALSE, breakFlag=FALSE;
47 double *f=NULL, *step=NULL;
48 err_t Status=SOLVER_NO_ERROR;
49 const bool_t debug=options->verbose;
50 const dim_t n = F->n;
51 dim_t iteration_count=0;
52 const double atol=options->absolute_tolerance; /* absolute tolerance */
53 const double rtol=options->tolerance; /* relative tolerance */
54 const dim_t maxit=options->iter_max; /* max iteration counter */
55 const dim_t lmaxit=options->inner_iter_max; /* max inner iteration counter */
56 const bool_t adapt_inner_tolerance=options->adapt_inner_tolerance;
57 const double max_inner_tolerance=options->inner_tolerance; /*inner tolerance counter */
58 double inner_tolerance=max_inner_tolerance;
59 /*
60 * max_inner_tolerance = Maximum error tolerance for residual in inner
61 * iteration. The inner iteration terminates
62 * when the relative linear residual is smaller than inner_tolerance*| F(x_c) |. inner_tolerance is determined
63 * by the modified Eisenstat-Walker formula, if adapt_inner_tolerance is set, otherwise
64 * inner_tolerance = max_inner_tolerance iteration.
65 */
66
67 f=TMPMEMALLOC(n,double);
68 step=TMPMEMALLOC(n,double);
69 if (f==NULL || step ==NULL) {
70 Status=SOLVER_MEMORY_ERROR;
71 } else {
72 /*
73 * initial evaluation of F
74 */
75 Paso_FunctionCall(F,f,x);
76 norm_f=Paso_l2(n,f,F->mpi_info);
77 /*
78 * stoping criterium:
79 */
80 stop_tol=atol + rtol*norm_f;
81 iteration_count=0;
82 if (debug) printf("Start Jacobi-free Newton scheme:\n\ttolerance = %e\n\tstoping tolerance = %e\n",rtol,stop_tol);
83 /*
84 * main iteration loop
85 */
86 while (! (convergeFlag || maxIterFlag || breakFlag)) {
87 /*
88 * keep track of the ratio (reduction_f = norm_f/frnmo) of successive residual norms and
89 * the iteration counter (iteration_count)
90 */
91 iteration_count++;
92 if (debug) printf("iteration step %d: norm of F =%d\n",iteration_count,norm_f);
93 /*
94 * call GMRES to get increment
95 */
96 gmres_iter=lmaxit;
97 gmres_tol=inner_tolerance;
98 if (debug) printf("GMRES called with tolerance = %e (max iter=%d)\n",inner_tolerance,gmres_iter);
99 Status=Paso_Solver_GMRES2(F,f,x,step,&gmres_iter,&gmres_tol,pp);
100 if (debug) printf("GMRES finalized after %d steps (residual = %e)\n",gmres_iter,gmres_tol);
101 iteration_count+=gmres_iter;
102 if ((Status==SOLVER_NO_ERROR) || (Status==SOLVER_MAXITER_REACHED)) {
103 Status=SOLVER_NO_ERROR;
104 /*
105 * update x:
106 */
107 norm_fo=norm_f;
108 Paso_Update(n,1.,x,1.,step);
109 Paso_FunctionCall(F,f,x);
110 iteration_count++;
111 norm_f=Paso_l2(n,f,F->mpi_info);
112 reduction_f=norm_f/norm_fo;
113 /*
114 * adjust inner_tolerance
115 */
116 if (adapt_inner_tolerance) {
117 old_inner_tolerance=inner_tolerance;
118 inner_tolerance=inner_tolerance_safety * reduction_f * reduction_f;
119 rtmp=inner_tolerance_safety * old_inner_tolerance * old_inner_tolerance;
120 if (rtmp>.1) inner_tolerance=MAX(inner_tolerance,rtmp);
121 inner_tolerance=MAX(MIN(inner_tolerance,max_inner_tolerance), .5*stop_tol/norm_f);
122 }
123 convergeFlag = (norm_f <= stop_tol);
124 } else {
125 breakFlag=TRUE;
126 }
127 maxIterFlag = (iteration_count > maxit);
128 }
129 }
130 TMPMEMFREE(f);
131 TMPMEMFREE(step);
132 return Status;
133 }

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