392 lines
12 KiB
C
392 lines
12 KiB
C
/*
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* Copyright (C) NHR@FAU, University Erlangen-Nuremberg.
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* All rights reserved. This file is part of nusif-solver.
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* Use of this source code is governed by a MIT style
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* license that can be found in the LICENSE file.
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include "allocate.h"
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#include "solver.h"
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#include "util.h"
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#define FINEST_LEVEL 0
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#define COARSEST_LEVEL (s->levels - 1)
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static void restrictMG(Solver* s, int level, Comm* comm)
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{
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double* r = s->r[level + 1];
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double* old = s->r[level];
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int imaxLocal = comm->imaxLocal;
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int jmaxLocal = comm->jmaxLocal;
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int kmaxLocal = comm->kmaxLocal;
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commExchange(comm, old);
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for (int k = 1; k < comm->kmaxLocal + 1; k++) {
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for (int j = 1; j < comm->jmaxLocal + 1; j++) {
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for (int i = 1; i < comm->imaxLocal + 1; ++i) {
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R(i, j, k) = (OLD(2 * i - 1, 2 * j - 1, 2 * k) +
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OLD(2 * i, 2 * j - 1, 2 * k) * 2 +
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OLD(2 * i + 1, 2 * j - 1, 2 * k) +
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OLD(2 * i - 1, 2 * j, 2 * k) * 2 +
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OLD(2 * i, 2 * j, 2 * k) * 8 +
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OLD(2 * i + 1, 2 * j, 2 * k) * 2 +
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OLD(2 * i - 1, 2 * j + 1, 2 * k) +
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OLD(2 * i, 2 * j + 1, 2 * k) * 2 +
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OLD(2 * i + 1, 2 * j + 1, 2 * k) +
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OLD(2 * i - 1, 2 * j - 1, 2 * k - 1) +
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OLD(2 * i, 2 * j - 1, 2 * k - 1) * 2 +
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OLD(2 * i + 1, 2 * j - 1, 2 * k - 1) +
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OLD(2 * i - 1, 2 * j, 2 * k - 1) * 2 +
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OLD(2 * i, 2 * j, 2 * k - 1) * 4 +
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OLD(2 * i + 1, 2 * j, 2 * k - 1) * 2 +
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OLD(2 * i - 1, 2 * j + 1, 2 * k - 1) +
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OLD(2 * i, 2 * j + 1, 2 * k - 1) * 2 +
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OLD(2 * i + 1, 2 * j + 1, 2 * k - 1) +
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OLD(2 * i - 1, 2 * j - 1, 2 * k + 1) +
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OLD(2 * i, 2 * j - 1, 2 * k + 1) * 2 +
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OLD(2 * i + 1, 2 * j - 1, 2 * k + 1) +
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OLD(2 * i - 1, 2 * j, 2 * k + 1) * 2 +
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OLD(2 * i, 2 * j, 2 * k + 1) * 4 +
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OLD(2 * i + 1, 2 * j, 2 * k + 1) * 2 +
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OLD(2 * i - 1, 2 * j + 1, 2 * k + 1) +
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OLD(2 * i, 2 * j + 1, 2 * k + 1) * 2 +
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OLD(2 * i + 1, 2 * j + 1, 2 * k + 1)) /
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64.0;
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}
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}
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}
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}
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static void prolongate(Solver* s, int level, Comm* comm)
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{
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double* old = s->r[level + 1];
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double* e = s->r[level];
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int imaxLocal = comm->imaxLocal;
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int jmaxLocal = comm->jmaxLocal;
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int kmaxLocal = comm->kmaxLocal;
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for (int k = 2; k < kmaxLocal + 1; k += 2) {
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for (int j = 2; j < jmaxLocal + 1; j += 2) {
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for (int i = 2; i < imaxLocal + 1; i += 2) {
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E(i, j, k) = OLD(i / 2, j / 2, k / 2);
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}
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}
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}
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}
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static void correct(Solver* s, double* p, int level, Comm* comm)
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{
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double* e = s->e[level];
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int imaxLocal = comm->imaxLocal;
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int jmaxLocal = comm->jmaxLocal;
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int kmaxLocal = comm->kmaxLocal;
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for (int k = 1; k < kmaxLocal + 1; ++k) {
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for (int j = 1; j < jmaxLocal + 1; ++j) {
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for (int i = 1; i < imaxLocal + 1; ++i) {
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P(i, j, k) += E(i, j, k);
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}
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}
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}
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}
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static void setBoundaryCondition(
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Solver* s, double* p, int imaxLocal, int jmaxLocal, int kmaxLocal)
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{
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#ifdef _MPI
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if (commIsBoundary(s->comm, FRONT)) {
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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P(i, j, 0) = P(i, j, 1);
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}
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}
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}
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if (commIsBoundary(s->comm, BACK)) {
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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P(i, j, kmaxLocal + 1) = P(i, j, kmaxLocal);
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}
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}
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}
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if (commIsBoundary(s->comm, BOTTOM)) {
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for (int k = 1; k < kmaxLocal + 1; k++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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P(i, 0, k) = P(i, 1, k);
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}
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}
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}
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if (commIsBoundary(s->comm, TOP)) {
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for (int k = 1; k < kmaxLocal + 1; k++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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P(i, jmaxLocal + 1, k) = P(i, jmaxLocal, k);
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}
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}
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}
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if (commIsBoundary(s->comm, LEFT)) {
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for (int k = 1; k < kmaxLocal + 1; k++) {
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for (int j = 1; j < jmaxLocal + 1; j++) {
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P(0, j, k) = P(1, j, k);
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}
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}
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}
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if (commIsBoundary(s->comm, RIGHT)) {
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for (int k = 1; k < kmaxLocal + 1; k++) {
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for (int j = 1; j < jmaxLocal + 1; j++) {
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P(imaxLocal + 1, j, k) = P(imaxLocal, j, k);
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}
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}
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}
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#else
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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P(i, j, 0) = P(i, j, 1);
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P(i, j, kmaxLocal + 1) = P(i, j, kmaxLocal);
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}
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}
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for (int k = 1; k < kmaxLocal + 1; k++) {
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for (int i = 1; i < imaxLocal + 1; i++) {
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P(i, 0, k) = P(i, 1, k);
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P(i, jmaxLocal + 1, k) = P(i, jmaxLocal, k);
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}
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}
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for (int k = 1; k < kmaxLocal + 1; k++) {
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for (int j = 1; j < jmaxLocal + 1; j++) {
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P(0, j, k) = P(1, j, k);
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P(imaxLocal + 1, j, k) = P(imaxLocal, j, k);
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}
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}
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#endif
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}
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static void smooth(Solver* s, double* p, double* rhs, int level, Comm* comm)
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{
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int imaxLocal = comm->imaxLocal;
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int jmaxLocal = comm->jmaxLocal;
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int kmaxLocal = comm->kmaxLocal;
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double eps = s->eps;
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int itermax = s->itermax;
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double dx2 = s->grid->dx * s->grid->dx;
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double dy2 = s->grid->dy * s->grid->dy;
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double dz2 = s->grid->dz * s->grid->dz;
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double idx2 = 1.0 / dx2;
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double idy2 = 1.0 / dy2;
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double idz2 = 1.0 / dz2;
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double factor = s->omega * 0.5 * (dx2 * dy2 * dz2) /
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(dy2 * dz2 + dx2 * dz2 + dx2 * dy2);
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double* r = s->r[level];
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double epssq = eps * eps;
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int it = 0;
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int pass, ksw, jsw, isw;
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double res = 1.0;
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ksw = 1;
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for (pass = 0; pass < 2; pass++) {
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jsw = ksw;
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commExchange(comm, p);
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for (int k = 1; k < kmaxLocal + 1; k++) {
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isw = jsw;
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = isw; i < imaxLocal + 1; i += 2) {
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P(i, j, k) -=
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factor *
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(RHS(i, j, k) -
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((P(i + 1, j, k) - 2.0 * P(i, j, k) + P(i - 1, j, k)) * idx2 +
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(P(i, j + 1, k) - 2.0 * P(i, j, k) + P(i, j - 1, k)) *
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idy2 +
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(P(i, j, k + 1) - 2.0 * P(i, j, k) + P(i, j, k - 1)) *
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idz2));
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}
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isw = 3 - isw;
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}
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jsw = 3 - jsw;
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}
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ksw = 3 - ksw;
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}
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}
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static double calculateResidual(Solver* s, double* p, double* rhs, int level, Comm* comm)
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{
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int imaxLocal = comm->imaxLocal;
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int jmaxLocal = comm->jmaxLocal;
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int kmaxLocal = comm->kmaxLocal;
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double eps = s->eps;
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int itermax = s->itermax;
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double dx2 = s->grid->dx * s->grid->dx;
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double dy2 = s->grid->dy * s->grid->dy;
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double dz2 = s->grid->dz * s->grid->dz;
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double idx2 = 1.0 / dx2;
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double idy2 = 1.0 / dy2;
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double idz2 = 1.0 / dz2;
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double factor = s->omega * 0.5 * (dx2 * dy2 * dz2) /
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(dy2 * dz2 + dx2 * dz2 + dx2 * dy2);
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double* r = s->r[level];
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double epssq = eps * eps;
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int it = 0;
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int pass, ksw, jsw, isw;
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double res = 1.0;
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ksw = 1;
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for (pass = 0; pass < 2; pass++) {
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jsw = ksw;
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commExchange(comm, p);
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for (int k = 1; k < kmaxLocal + 1; k++) {
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isw = jsw;
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for (int j = 1; j < jmaxLocal + 1; j++) {
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for (int i = isw; i < imaxLocal + 1; i += 2) {
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R(i,
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j,
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k) = (RHS(i, j, k) -
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((P(i + 1, j, k) - 2.0 * P(i, j, k) + P(i - 1, j, k)) *
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idx2 +
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(P(i, j + 1, k) - 2.0 * P(i, j, k) + P(i, j - 1, k)) *
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idy2 +
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(P(i, j, k + 1) - 2.0 * P(i, j, k) + P(i, j, k - 1)) *
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idz2));
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res += (R(i, j, k) * R(i, j, k));
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}
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isw = 3 - isw;
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}
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jsw = 3 - jsw;
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}
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ksw = 3 - ksw;
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}
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commReduction(&res, SUM);
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res = res / (double)(imaxLocal * jmaxLocal * kmaxLocal);
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#ifdef DEBUG
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if (commIsMaster(s->comm)) {
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printf("%d Residuum: %e\n", it, res);
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}
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#endif
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return res;
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}
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static double multiGrid(Solver* s, double* p, double* rhs, int level, Comm* comm)
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{
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int imaxLocal = comm->imaxLocal;
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int jmaxLocal = comm->jmaxLocal;
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int kmaxLocal = comm->kmaxLocal;
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double res = 0.0;
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// coarsest level
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if (level == COARSEST_LEVEL) {
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for (int i = 0; i < 5; i++) {
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smooth(s, p, rhs, level, comm);
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}
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return res;
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}
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// pre-smoothing
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for (int i = 0; i < s->presmooth; i++) {
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smooth(s, p, rhs, level, comm);
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if (level == FINEST_LEVEL)
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setBoundaryCondition(s, p, imaxLocal, jmaxLocal, kmaxLocal);
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}
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res = calculateResidual(s, p, rhs, level, comm);
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// restrict
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restrictMG(s, level, comm);
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// Create a new comm object withupdated imaxLocal and jmaxLocal
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// along with their updated bufferTypes, sdispls, rdispls
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Comm newcomm;
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commUpdateDatatypes(s->comm, &newcomm, imaxLocal, jmaxLocal, kmaxLocal);
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// MGSolver on residual and error.
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multiGrid(s, s->e[level + 1], s->r[level + 1], level + 1, &newcomm);
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commFreeCommunicator(&newcomm);
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// prolongate
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prolongate(s, level, comm);
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// correct p on finer level using residual
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correct(s, p, level, comm);
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if (level == FINEST_LEVEL)
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setBoundaryCondition(s, p, imaxLocal, jmaxLocal, kmaxLocal);
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// post-smoothing
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for (int i = 0; i < s->postsmooth; i++) {
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smooth(s, p, rhs, level, comm);
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if (level == FINEST_LEVEL)
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setBoundaryCondition(s, p, imaxLocal, jmaxLocal, kmaxLocal);
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}
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return res;
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}
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void initSolver(Solver* s, Discretization* d, Parameter* p)
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{
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s->eps = p->eps;
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s->omega = p->omg;
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s->itermax = p->itermax;
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s->levels = p->levels;
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s->grid = &d->grid;
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s->presmooth = p->presmooth;
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s->postsmooth = p->postsmooth;
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s->comm = &d->comm;
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s->problem = p->name;
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int imax = s->grid->imax;
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int jmax = s->grid->jmax;
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int kmax = s->grid->kmax;
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int levels = s->levels;
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if (commIsMaster(s->comm)) printf("Using Multigrid solver with %d levels\n", levels);
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s->r = malloc(levels * sizeof(double*));
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s->e = malloc(levels * sizeof(double*));
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size_t size = (imax + 2) * (jmax + 2) * (kmax + 2);
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for (int j = 0; j < levels; j++) {
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s->r[j] = allocate(64, size * sizeof(double));
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s->e[j] = allocate(64, size * sizeof(double));
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for (size_t i = 0; i < size; i++) {
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s->r[j][i] = 0.0;
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s->e[j][i] = 0.0;
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}
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}
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}
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double solve(Solver* s, double* p, double* rhs)
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{
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double res = multiGrid(s, p, rhs, 0, s->comm);
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#ifdef VERBOSE
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if (commIsMaster(s->comm)) {
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printf("Residuum: %.6f\n", res);
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}
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#endif
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return res;
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}
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