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

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Revision 1476 - (show annotations)
Mon Apr 7 23:38:50 2008 UTC (11 years, 6 months ago) by gross
File MIME type: text/plain
File size: 3878 byte(s)
Jacobian-free Newton method added to Paso
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 #ifdef _OPENMP
33 #include <omp.h>
34 #endif
35 err_t Paso_Solver_NewtonGMRES(
36 Paso_Function *F,
37 double *x,
38 Paso_Options* options,
39 Paso_Performance* pp)
40
41 {
42 const double gamma=.9;
43 dim_t gmres_iter;
44 double stop_tol, fnrm,fnrmo, rat,etaold,etanew, gmres_tol;
45 bool_t convergeFlag=FALSE, maxIterFlag=FALSE, breakFlag=FALSE;
46 double *f=NULL, *step=NULL;
47 err_t Status=SOLVER_NO_ERROR;
48 bool_t debug=options->verbose;
49 dim_t n = n=F->local_n;
50 dim_t itc=0;
51 double atol=options->absolute_tolerance;
52 double rtol=options->tolerance;
53 dim_t maxit=options->iter_max;
54 dim_t lmaxit=options->inner_iter_max;
55 bool_t adapt_eta=options->adapt_inner_tolerance;
56 double etamax=options->inner_tolerance;
57 double eta=etamax;
58 /*
59 * etamax = Maximum error tolerance for residual in inner
60 * iteration. The inner iteration terminates
61 * when the relative linear residual is
62 * smaller than eta*| F(x_c) |. eta is determined
63 * by the modified Eisenstat-Walker formula if etamax > 0.
64 * If etamax < 0, then eta = |etamax| for the entire
65 * iteration.
66 */
67
68 f=TMPMEMALLOC(n,double);
69 step=TMPMEMALLOC(n,double);
70 if (f==NULL || step ==NULL) {
71 Status=SOLVER_MEMORY_ERROR;
72 } else {
73 /*
74 * initial evaluation of F
75 */
76 Paso_FunctionCall(F,f,x);
77 fnrm=Paso_l2(n,f,F->mpi_info);
78 /*
79 * stoping criterium:
80 */
81 stop_tol=atol + rtol*fnrm;
82 itc=0;
83 if (debug) printf("Start Jacobi-free Newton scheme:\n\ttolerance = %e\n\tstoping tolerance = %e\n",rtol,stop_tol);
84 /*
85 * main iteration loop
86 */
87 while (! (convergeFlag || maxIterFlag || breakFlag)) {
88 /*
89 * keep track of the ratio (rat = fnrm/frnmo) of successive residual norms and
90 * the iteration counter (itc)
91 */
92 itc++;
93 if (debug) printf("iteration step %d: norm of F =%d\n",itc,fnrm);
94 /*
95 * call GMRES to get increment
96 */
97 gmres_iter=lmaxit;
98 gmres_tol=eta;
99 if (debug) printf("GMRES called with tolerance = %d\n",eta);
100 Status=Paso_Solver_NLGMRES(F,f,x,step,&gmres_iter,&gmres_tol,pp);
101 itc+=gmres_iter;
102 if ((Status==SOLVER_NO_ERROR) || (Status==SOLVER_MAXITER_REACHED)) {
103 Status==SOLVER_NO_ERROR;
104 /*
105 * update x:
106 */
107 Paso_Update(n,1.,x,1.,step);
108 Paso_FunctionCall(F,f,x);
109 fnrm=Paso_l2(n,f,F->mpi_info);
110 fnrmo=fnrm;
111 rat=fnrm/fnrmo;
112 /*
113 * adjust eta
114 */
115 if (adapt_eta) {
116 etaold=eta;
117 etanew=gamma*rat*rat;
118 if (gamma*etaold*etaold >1.) etanew=MAX(etanew,gamma*etaold*etaold);
119 eta=MAX(MIN(etanew,etamax), .5*stop_tol/fnrm);
120 }
121 } else {
122 breakFlag=TRUE;
123 }
124 maxIterFlag = (itc > maxit);
125 convergeFlag = (fnrm <= stop_tol);
126 }
127 }
128 TMPMEMFREE(f);
129 TMPMEMFREE(step);
130 return Status;
131 }

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