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// Newton.cc -- solve Theta(h) = 0 via Newton's method
// $Header$
//
// Newton_solve - driver to solve Theta(h) = 0 via Newton's method
//
#include <stdio.h>
#include <assert.h>
#include <math.h>
#include "util_Table.h"
#include "cctk.h"
#include "cctk_Arguments.h"
#include "stl_vector.hh"
#include "config.h"
#include "stdc.h"
#include "../jtutil/util.hh"
#include "../jtutil/array.hh"
#include "../jtutil/cpm_map.hh"
#include "../jtutil/linear_map.hh"
using jtutil::error_exit;
#include "../patch/coords.hh"
#include "../patch/grid.hh"
#include "../patch/fd_grid.hh"
#include "../patch/patch.hh"
#include "../patch/patch_edge.hh"
#include "../patch/patch_interp.hh"
#include "../patch/ghost_zone.hh"
#include "../patch/patch_system.hh"
#include "../elliptic/Jacobian.hh"
#include "../gr/gfns.hh"
#include "../gr/gr.hh"
#include "driver.hh"
//******************************************************************************
//
// This function solves Theta(h) = 0 for h via Newton's method.
//
// Arguments:
// initial_find_flag = true ==> This is the first attempt to find this
// horizon, or this is a subsequent attempt
// and the immediately previous attempt failed.
// false ==> This isn't the first attempt to find this
// horizon, and we found it successfully on
// the immediately previous attempt.
// hn = the horizon number (used only in naming output files)
//
// Results:
// This function returns a success flag: this is true if (and only if)
// it found an h satisfying Theta(h) = 0 to within the error tolerances,
// otherwise it's false.
//
bool Newton_solve(patch_system& ps,
Jacobian& Jac,
const struct cactus_grid_info& cgi,
const struct geometry_info& gi,
const struct Jacobian_info& Jacobian_info,
const struct solver_info& solver_info,
bool initial_find_flag,
const struct IO_info& IO_info,
int hn, const struct verbose_info& verbose_info)
{
const int max_Newton_iterations
= initial_find_flag ? solver_info.max_Newton_iterations__initial
: solver_info.max_Newton_iterations__subsequent;
for (int iteration = 1 ;
iteration <= max_Newton_iterations ;
++iteration)
{
if (verbose_info.print_algorithm_details)
then CCTK_VInfo(CCTK_THORNSTRING,
"Newton iteration %d/%d",
iteration, max_Newton_iterations);
if (solver_info.debugging_output_at_each_Newton_iteration)
then output_gridfn(ps, gfns::gfn__h,
IO_info, IO_info.h_base_file_name,
hn, verbose_info.print_algorithm_details,
iteration);
//
// evaluate the expansion Theta(h)
//
jtutil::norm<fp> Theta_norms;
if (! expansion(ps,
cgi, gi,
true, // yes, we want the Jacobian coeffs
verbose_info.print_algorithm_details,
&Theta_norms))
then return false; // *** ERROR RETURN ***
if (verbose_info.print_algorithm_highlights)
then CCTK_VInfo(CCTK_THORNSTRING,
" iteration %d: Theta ||rms||=%.1e, ||infty||=%.1e",
iteration,
Theta_norms.rms_norm(), Theta_norms.infinity_norm());
if (solver_info.debugging_output_at_each_Newton_iteration)
then output_gridfn(ps, gfns::gfn__Theta,
IO_info, IO_info.Theta_base_file_name,
hn, verbose_info.print_algorithm_details,
iteration);
//
// convergence test on ||Theta||
//
if (Theta_norms.infinity_norm() <= solver_info
.Theta_norm_for_convergence)
then {
if (verbose_info.print_algorithm_details)
then CCTK_VInfo(CCTK_THORNSTRING,
"==> finished (||Theta|| < %g)",
double(solver_info
.Theta_norm_for_convergence));
return true; // *** NORMAL RETURN ***
}
//
// compute the Newton step
//
if (! expansion_Jacobian(ps, Jac,
cgi, gi, Jacobian_info,
verbose_info.print_algorithm_details))
then return false; // *** ERROR RETURN ***
if (verbose_info.print_algorithm_details)
then CCTK_VInfo(CCTK_THORNSTRING,
"solving linear system for Delta_h (%d unknowns)",
Jac.NN());
const fp rcond = Jac.solve_linear_system(gfns::gfn__Theta,
gfns::gfn__Delta_h);
if (rcond == 0.0)
then {
CCTK_VWarn(1, __LINE__, __FILE__, CCTK_THORNSTRING,
"Newton_solve: Jacobian matrix is numerically singular!");
return false; // *** ERROR RETURN ***
}
if (verbose_info.print_algorithm_details)
then {
if (rcond > 0.0)
then CCTK_VInfo(CCTK_THORNSTRING,
"done solving linear system (condition number %.1e)",
double(rcond));
else CCTK_VInfo(CCTK_THORNSTRING,
"done solving linear system");
}
if (solver_info.debugging_output_at_each_Newton_iteration)
then output_gridfn(ps, gfns::gfn__Delta_h,
IO_info, IO_info.Delta_h_base_file_name,
hn, verbose_info.print_algorithm_details,
iteration);
//
// if the Newton step is too large, scale it down
//
jtutil::norm<fp> h_norms;
ps.ghosted_gridfn_norms(gfns::gfn__h, h_norms);
const fp max_allowable_Delta_h
= solver_info.max_Delta_h_over_h * h_norms.mean();
jtutil::norm<fp> Delta_h_norms;
ps.gridfn_norms(gfns::gfn__Delta_h, Delta_h_norms);
const fp max_Delta_h = Delta_h_norms.infinity_norm();
const fp scale = (max_Delta_h > max_allowable_Delta_h)
? max_allowable_Delta_h / max_Delta_h
: 1.0;
//
// take the Newton step (scaled if need be)
//
for (int pn = 0 ; pn < ps.N_patches() ; ++pn)
{
patch& p = ps.ith_patch(pn);
for (int irho = p.min_irho() ;
irho <= p.max_irho() ;
++irho)
{
for (int isigma = p.min_isigma() ;
isigma <= p.max_isigma() ;
++isigma)
{
p.ghosted_gridfn(gfns::gfn__h, irho,isigma)
-= scale * p.gridfn(gfns::gfn__Delta_h, irho,isigma);
}
}
}
if (verbose_info.print_algorithm_details)
then {
if (scale == 1.0)
then CCTK_VInfo(CCTK_THORNSTRING,
"h += Delta_h (rms-norm=%.1e, infinity-norm=%.1e)",
Delta_h_norms.rms_norm(),
Delta_h_norms.infinity_norm());
else CCTK_VInfo(CCTK_THORNSTRING,
"h += %g * Delta_h (infinity-norm clamped to %.2g)",
scale,
scale * Delta_h_norms.infinity_norm());
}
//
// convergence test on ||Delta_h||
//
if ( scale * Delta_h_norms.infinity_norm()
<= solver_info.Delta_h_norm_for_convergence )
then {
if (verbose_info.print_algorithm_details)
then CCTK_VInfo(CCTK_THORNSTRING,
"==> finished (||Delta_h|| < %g)",
double(solver_info
.Delta_h_norm_for_convergence));
if (solver_info.final_Theta_update_if_Delta_h_converged)
then {
if (verbose_info.print_algorithm_details)
then CCTK_VInfo(CCTK_THORNSTRING,
" doing final Theta(h) evaluation");
if (! expansion(ps,
cgi, gi,
false, // no Jacobian coeffs
verbose_info.print_algorithm_details))
then return false; // *** ERROR RETURN ***
}
return true; // *** NORMAL RETURN ***
}
}
if (solver_info.final_Theta_update_if_Delta_h_converged)
then {
if (verbose_info.print_algorithm_details)
then CCTK_VInfo(CCTK_THORNSTRING,
" doing final Theta(h) evaluation");
if (! expansion(ps,
cgi, gi,
false, // no Jacobian coeffs
verbose_info.print_algorithm_details))
then return false; // *** ERROR RETURN ***
}
return false; // *** ERROR RETURN ***
}
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