diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..9ba7d3e --- /dev/null +++ b/Makefile @@ -0,0 +1,22 @@ +CC= gcc +RM= rm -vf +CFLAGS= -Wall -g -std=c99 +OPENMPFLAG= -fopenmp +LIBS= -lrt -lm + +PROGFILES= mg + +main: serial_mg.o parallel_mg.o helpers.o main.c + $(CC) $(CFLAGS) $(OPENMPFLAG) serial_mg.o parallel_mg.o helpers.o main.c -o mg $(LIBS) + +serial_mg.o: serial_mg.c serial_mg.h + $(CC) $(CFLAGS) -c serial_mg.c $(LIBS) + +parallel_mg.o: parallel_mg.c parallel_mg.h + $(CC) $(CFLAGS) $(OPENMPFLAG) -c parallel_mg.c $(LIBS) + +helpers.o: helpers.c helpers.h + $(CC) $(CFLAGS) $(OPENMPFLAG) -c helpers.c $(LIBS) + +clean: + $(RM) *.o $(PROGFILES) diff --git a/helpers.c b/helpers.c new file mode 100644 index 0000000..073a805 --- /dev/null +++ b/helpers.c @@ -0,0 +1,3 @@ +#include "helpers.h" + +int getIndex(int x, int y, int width) { return x*width + y; } diff --git a/helpers.h b/helpers.h new file mode 100644 index 0000000..3a9f298 --- /dev/null +++ b/helpers.h @@ -0,0 +1,18 @@ +#ifndef HELPERS_H +#define HELPERS_H + +#include +#include +#include + +typedef struct{ + int N; + int Lmax; + int size[20]; + double a[20]; + double alpha;; +} param_t; + +int getIndex(int x, int y, int width); + +#endif diff --git a/main.c b/main.c new file mode 100644 index 0000000..f70e3ca --- /dev/null +++ b/main.c @@ -0,0 +1,100 @@ +/*====================================================================================== +Rich Brower Sat May 28 00:23:17 EDT 2011 + +C program based on simple FMV code of S. F. McCormick, Multigrid Methods, Frontiers in Applied! Mathematics, +vol. 3, SIAM Books, Philadelphia, 1987.The code is intentionally put into a single file with no input parameters +to keep is concise. Of course a full code may have more traditional C structures! + +We solve the 2-d Laplace problem: A phi = b + + (A phi)((x,y) = [4 phi(x,y) - phi(x+1,y) - phi(x-1,y) - phi(x,y+1) -phi(x,y+1)]/a^2 + m^2 phi(x,y) = b(x,y) + + Multiply by scale = 1/(4 + a^2 m^2) + + phi = (1 - scale*A) phi + scale*b = phi + res + = scale * (phi(x+1,y) + phi(x-1,y) + phi(x,y+1) + phi(x,y+1)) + a^2 scale*b(x,y) + +where we use rescaled: res = a^2 scale b - scale* A phi + +with scale(lev) = 1/(4 + pow(2,lev)^2 m^2) or the lattice spacing is a(lev) = pow(2,lev) + +So the code is really sovling the new matrix iteration: + + phi(x,y) = [(1- scale(lev) * A)phi](x,y) + res(x,y) + + = scale(lev) * (phi(x+1,y) + phi(x-1,y) + phi(x,y+1) + phi(x,y+1)) + res + +At present relex iteration uses Jacobi method. +======================================================================================*/ + +#include +#include +#include +#include +#include "helpers.h" +#include "serial_mg.h" +#include "parallel_mg.h" +#include + +double const_func(int x); +double sin_func(int x); +struct timespec diff(struct timespec start, struct timespec end); +int main(int argc, char **argv) +{ +// struct timespec time1, time2, total; + + // NON-PARALLEL + printf("Running Non-Parallelized Multigrid\n"); + // clock_gettime(CLOCK_MONOTONIC, &time1); + double t1, t2; + double duration; + t1 = omp_get_wtime(); + multigrid(7, sin_func); + //clock_gettime(CLOCK_MONOTONIC, &time2); + t2 = omp_get_wtime(); + duration = (t2 - t1); + printf(" Total time: %f seconds\n", duration); + + // PARALLEL + printf("Running Parallelized Multigrid\n"); + // clock_gettime(CLOCK_MONOTONIC, &time1); + t1 = omp_get_wtime(); + parallel_multigrid(7, sin_func); + //clock_gettime(CLOCK_MONOTONIC, &time2); + t2 = omp_get_wtime(); + duration = (t2 - t1); + printf(" Total time: %f seconds\n", duration); + + // NON-PARALLEL + // printf("Running Serial Multigrid\n"); + // clock_gettime(CLOCK_MONOTONIC, &time1); + // serial_multigrid(7); + // clock_gettime(CLOCK_MONOTONIC, &time2); + // total = diff(time1, time2); + // printf(" Serial Total time: %ld.%ld seconds\n", total.tv_sec, total.tv_nsec); + + return 0; +} + +double const_func(int x) { + return 4.0; +} + +double sin_func(int x) { + return sin( ( (double)(2.0 * 3.14) /256 ) * x ); +} + +/* +struct timespec diff(struct timespec start, struct timespec end) +{ + struct timespec temp; + if ((end.tv_nsec-start.tv_nsec)<0) { + temp.tv_sec = end.tv_sec-start.tv_sec-1; + temp.tv_nsec = 1000000000+end.tv_nsec-start.tv_nsec; + } else { + temp.tv_sec = end.tv_sec-start.tv_sec; + temp.tv_nsec = end.tv_nsec-start.tv_nsec; + } + return temp; +} +*/ diff --git a/parallel_data.dat b/parallel_data.dat new file mode 100644 index 0000000..ccd817b --- /dev/null +++ b/parallel_data.dat @@ -0,0 +1,65536 @@ +0 0 -0.027713 +0 1 -0.052224 +0 2 -0.076704 +0 3 -0.101137 +0 4 -0.125510 +0 5 -0.149807 +0 6 -0.174014 +0 7 -0.198116 +0 8 -0.222099 +0 9 -0.245948 +0 10 -0.269650 +0 11 -0.293189 +0 12 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+255 255 -0.027713 diff --git a/parallel_mg.c b/parallel_mg.c new file mode 100644 index 0000000..6190648 --- /dev/null +++ b/parallel_mg.c @@ -0,0 +1,268 @@ +#include +#include "parallel_mg.h" +#include "helpers.h" + +void relax_parallel(double *phi, double *res, int lev, int niter, param_t p); +void proj_res_parallel(double *res_c, double *rec_f, double *phi_f, int lev,param_t p); +void inter_add_parallel(double *phi_f, double *phi_c, int lev, param_t p); +double GetResRoot_parallel(double *phi, double *res, int lev, param_t p); + +int parallel_multigrid(int Lmax, double (*boundary_func)(int)) { + double *phi[20], *res[20]; + param_t p; + int nlev; + int i,j,lev; + + //set parameters________________________________________ + p.Lmax = Lmax; // max number of levels + p.N = 2*(int)pow(2,p.Lmax); // MUST BE POWER OF 2 +// p.m = 0.01; + nlev = 2; // NUMBER OF LEVELS: nlev = 0 give top level alone + if(nlev > p.Lmax){ + printf(" ERROR: More levels than available in lattice! \n"); + return 1; + } + + double resmag = 1.0; // not rescaled. + int ncycle = 0; + int n_per_lev = 10; + + printf(" V cycle for %d by %d lattice with nlev = %d out of max %d \n", p.N, p.N, nlev, p.Lmax); + + // initialize arrays__________________________________ + p.size[0] = p.N; + p.a[0] = 1.0; + p.alpha = 1.0; + for(lev = 1;lev< p.Lmax+1; lev++) { + p.size[lev] = (p.size[lev-1])/2; + p.a[lev] = 2.0 * p.a[lev-1]; + // p.scale[lev] = 1.0/(4.0 + p.m*p.m*p.a[lev]*p.a[lev]); + } + + for(lev = 0;lev< p.Lmax+1; lev++) { + phi[lev] = (double *) malloc(p.size[lev]*p.size[lev] * sizeof(double)); + res[lev] = (double *) malloc(p.size[lev]*p.size[lev] * sizeof(double)); + for(i = 0; i < p.size[lev]*p.size[lev]; i++) { + phi[lev][i] = 0.0; + res[lev][i] = 0.0; + } + } + + // set up the boundary conditions + for (i=0; i 0.00001 && ncycle < 10000) + while(resmag > 0.00001) { + ncycle +=1; + for(lev = 0;lev= 0; lev--) { //come up + relax_parallel(phi[lev],res[lev],lev, n_per_lev,p); // lev = nlev -1, ... 0; + if(lev > 0) inter_add_parallel(phi[lev-1], phi[lev], lev, p); // phi[lev-1] += error = P phi[lev] and set phi[lev] = 0; + } + resmag = GetResRoot_parallel(phi[0],res[0],0,p); + if (ncycle % 100 == 0) printf(" At the %d cycle the mag residue is %g \n", ncycle, resmag); + } + + FILE *file = fopen("parallel_data.dat", "w+"); + for (i=0; i p.Lmax){ + printf(" ERROR: More levels than available in lattice! \n"); + return 1; + } + + double resmag = 1.0; // not rescaled. + int ncycle = 0; + int n_per_lev = 10; + + printf(" V cycle for %d by %d lattice with nlev = %d out of max %d \n", p.N, p.N, nlev, p.Lmax); + + // initialize arrays__________________________________ + p.size[0] = p.N; + p.a[0] = 1.0; + p.alpha = 1.0; + for(lev = 1;lev< p.Lmax+1; lev++) { + p.size[lev] = (p.size[lev-1])/2; + p.a[lev] = 2.0 * p.a[lev-1]; + // p.scale[lev] = 1.0/(4.0 + p.m*p.m*p.a[lev]*p.a[lev]); + } + + for(lev = 0;lev< p.Lmax+1; lev++) { + phi[lev] = (double *) malloc(p.size[lev]*p.size[lev] * sizeof(double)); + res[lev] = (double *) malloc(p.size[lev]*p.size[lev] * sizeof(double)); + for(i = 0; i < p.size[lev]*p.size[lev]; i++) { + phi[lev][i] = 0.0; + res[lev][i] = 0.0; + } + } +/* + // set up the boundary conditions + for (i=0; i 0.00001 && ncycle < 10000) + while(resmag > 0.00001) { + ncycle +=1; + for(lev = 0;lev= 0; lev--) { //come up + relax(phi[lev],res[lev],lev, n_per_lev,p); // lev = nlev -1, ... 0; + if(lev > 0) inter_add(phi[lev-1], phi[lev], lev, p); // phi[lev-1] += error = P phi[lev] and set phi[lev] = 0; + } + resmag = GetResRoot(phi[0],res[0],0,p); + if (ncycle % 100 == 0) printf(" At the %d cycle the mag residue is %g \n", ncycle, resmag); + } + + FILE *file = fopen("serial.dat", "w+"); + for (i=0; i