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hypre/examples/ex15big.c
falgout 1217add3b1 Added GraphSetObjectType() calls
2011-09-21 20:32:59 +00:00

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/*
Example 15big
Interface: Semi-Structured interface (SStruct)
Compile with: make ex15big
Sample run: mpirun -np 8 ex15big -n 10
To see options: ex15big -help
Description: This example is a slight modification of Example 15 that
illustrates the 64-bit integer support in hypre needed to
runproblems with more than 2B unknowns.
Specifically, the changes compared to Example 15 are as
follows:
1) All integer arguments to HYPRE functions should be
declared of type HYPRE_Int.
2) Variables of type HYPRE_Int are 64-bit integers, so
they should be printed in the %lld format (not %d).
To enable the 64-bit integer support, you need to build
hypre with the --enable-bigint option of 'configure'.
We recommend comparing this example with Example 15.
*/
#include <math.h>
#include "_hypre_utilities.h"
#include "HYPRE_sstruct_mv.h"
#include "HYPRE_sstruct_ls.h"
#include "_hypre_parcsr_ls.h"
#include "HYPRE.h"
int optionAlpha, optionBeta;
/* Curl-curl coefficient alpha = mu^{-1} */
double alpha(double x, double y, double z)
{
switch (optionAlpha)
{
case 0: /* uniform coefficient */
return 1.0;
case 1: /* smooth coefficient */
return x*x+exp(y)+sin(z);
case 2: /* small outside of an interior cube */
if ((fabs(x-0.5) < 0.25) && (fabs(y-0.5) < 0.25) && (fabs(z-0.5) < 0.25))
return 1.0;
else
return 1.0e-6;
case 3: /* small outside of an interior ball */
if (((x-0.5)*(x-0.5)+(y-0.5)*(y-0.5)+(z-0.5)*(z-0.5)) < 0.0625)
return 1.0;
else
return 1.0e-6;
case 4: /* random coefficient */
return hypre_Rand();
default:
return 1.0;
}
}
/* Mass coefficient beta = sigma */
double beta(double x, double y, double z)
{
switch (optionBeta)
{
case 0: /* uniform coefficient */
return 1.0;
case 1: /* smooth coefficient */
return x*x+exp(y)+sin(z);
case 2:/* small outside of interior cube */
if ((fabs(x-0.5) < 0.25) && (fabs(y-0.5) < 0.25) && (fabs(z-0.5) < 0.25))
return 1.0;
else
return 1.0e-6;
case 3: /* small outside of an interior ball */
if (((x-0.5)*(x-0.5)+(y-0.5)*(y-0.5)+(z-0.5)*(z-0.5)) < 0.0625)
return 1.0;
else
return 1.0e-6;
case 4: /* random coefficient */
return hypre_Rand();
default:
return 1.0;
}
}
/*
This routine computes the lowest order Nedelec, or "edge" finite element
stiffness matrix and load vector on a cube of size h. The 12 edges {e_i}
are numbered in terms of the vertices as follows:
[7]------[6]
/| /| e_0 = 01, e_1 = 12, e_2 = 32, e_3 = 03,
/ | / | e_4 = 45, e_5 = 56, e_6 = 76, e_7 = 47,
[4]------[5] | e_8 = 04, e_9 = 15, e_10 = 26, e_11 = 37.
| [3]----|-[2]
| / | / The edges are oriented from first to the
|/ |/ second vertex, e.g. e_0 is from [0] to [1].
[0]------[1]
We allow for different scaling of the curl-curl and the mass parts of the
matrix with coefficients alpha and beta respectively:
S_ij = alpha (curl phi_i,curl phi_j) + beta (phi_i, phi_j).
The load vector corresponding to a right-hand side of {1,1,1} is
F_j = (1,phi_j) = h^2/4.
*/
void ComputeFEMND1(double S[12][12], double F[12],
double x, double y, double z, double h)
{
int i, j;
double h2_4 = h*h/4;
double cS1 = alpha(x,y,z)/(6.0*h), cS2 = 2*cS1, cS4 = 2*cS2;
double cM1 = beta(x,y,z)*h/36.0, cM2 = 2*cM1, cM4 = 2*cM2;
S[ 0][ 0] = cS4 + cM4; S[ 0][ 1] = cS2; S[ 0][ 2] = -cS1 + cM2;
S[ 0][ 3] = -cS2; S[ 0][ 4] = -cS1 + cM2; S[ 0][ 5] = cS1;
S[ 0][ 6] = -cS2 + cM1; S[ 0][ 7] = -cS1; S[ 0][ 8] = -cS2;
S[ 0][ 9] = cS2; S[ 0][10] = cS1; S[ 0][11] = -cS1;
S[ 1][ 1] = cS4 + cM4; S[ 1][ 2] = -cS2; S[ 1][ 3] = -cS1 + cM2;
S[ 1][ 4] = cS1; S[ 1][ 5] = -cS1 + cM2; S[ 1][ 6] = -cS1;
S[ 1][ 7] = -cS2 + cM1; S[ 1][ 8] = -cS1; S[ 1][ 9] = -cS2;
S[ 1][10] = cS2; S[ 1][11] = cS1;
S[ 2][ 2] = cS4 + cM4; S[ 2][ 3] = cS2; S[ 2][ 4] = -cS2 + cM1;
S[ 2][ 5] = -cS1; S[ 2][ 6] = -cS1 + cM2; S[ 2][ 7] = cS1;
S[ 2][ 8] = -cS1; S[ 2][ 9] = cS1; S[ 2][10] = cS2;
S[ 2][11] = -cS2;
S[ 3][ 3] = cS4 + cM4; S[ 3][ 4] = -cS1; S[ 3][ 5] = -cS2 + cM1;
S[ 3][ 6] = cS1; S[ 3][ 7] = -cS1 + cM2; S[ 3][ 8] = -cS2;
S[ 3][ 9] = -cS1; S[ 3][10] = cS1; S[ 3][11] = cS2;
S[ 4][ 4] = cS4 + cM4; S[ 4][ 5] = cS2; S[ 4][ 6] = -cS1 + cM2;
S[ 4][ 7] = -cS2; S[ 4][ 8] = cS2; S[ 4][ 9] = -cS2;
S[ 4][10] = -cS1; S[ 4][11] = cS1;
S[ 5][ 5] = cS4 + cM4; S[ 5][ 6] = -cS2; S[ 5][ 7] = -cS1 + cM2;
S[ 5][ 8] = cS1; S[ 5][ 9] = cS2; S[ 5][10] = -cS2;
S[ 5][11] = -cS1;
S[ 6][ 6] = cS4 + cM4; S[ 6][ 7] = cS2; S[ 6][ 8] = cS1;
S[ 6][ 9] = -cS1; S[ 6][10] = -cS2; S[ 6][11] = cS2;
S[ 7][ 7] = cS4 + cM4; S[ 7][ 8] = cS2; S[ 7][ 9] = cS1;
S[ 7][10] = -cS1; S[ 7][11] = -cS2;
S[ 8][ 8] = cS4 + cM4; S[ 8][ 9] = -cS1 + cM2; S[ 8][10] = -cS2 + cM1;
S[ 8][11] = -cS1 + cM2;
S[ 9][ 9] = cS4 + cM4; S[ 9][10] = -cS1 + cM2; S[ 9][11] = -cS2 + cM1;
S[10][10] = cS4 + cM4; S[10][11] = -cS1 + cM2;
S[11][11] = cS4 + cM4;
/* The stiffness matrix is symmetric */
for (i = 1; i < 12; i++)
for (j = 0; j < i; j++)
S[i][j] = S[j][i];
for (i = 0; i < 12; i++)
F[i] = h2_4;
}
int main (int argc, char *argv[])
{
int myid, num_procs;
int n, N, pi, pj, pk;
double h;
int print_solution;
double tol, theta;
int maxit, cycle_type;
int rlx_type, rlx_sweeps, rlx_weight, rlx_omega;
int amg_coarsen_type, amg_agg_levels, amg_rlx_type;
int amg_interp_type, amg_Pmax;
int singular_problem ;
HYPRE_Int time_index;
HYPRE_SStructGrid edge_grid;
HYPRE_SStructGraph A_graph;
HYPRE_SStructMatrix A;
HYPRE_SStructVector b;
HYPRE_SStructVector x;
HYPRE_SStructGrid node_grid;
HYPRE_SStructGraph G_graph;
HYPRE_SStructStencil G_stencil[3];
HYPRE_SStructMatrix G;
HYPRE_SStructVector xcoord, ycoord, zcoord;
HYPRE_Solver solver, precond;
/* Initialize MPI */
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &myid);
MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
/* Set default parameters */
n = 10;
print_solution = 0;
optionAlpha = 0;
optionBeta = 0;
maxit = 100;
tol = 1e-6;
cycle_type = 13;
rlx_type = 2;
rlx_sweeps = 1;
rlx_weight = 1.0;
rlx_omega = 1.0;
amg_coarsen_type = 10;
amg_agg_levels = 1;
amg_rlx_type = 6;
theta = 0.25;
amg_interp_type = 6;
amg_Pmax = 4;
singular_problem = 0;
/* Parse command line */
{
int arg_index = 0;
int print_usage = 0;
while (arg_index < argc)
{
if ( strcmp(argv[arg_index], "-n") == 0 )
{
arg_index++;
n = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-a") == 0 )
{
arg_index++;
optionAlpha = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-b") == 0 )
{
arg_index++;
optionBeta = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-print_solution") == 0 )
{
arg_index++;
print_solution = 1;
}
else if ( strcmp(argv[arg_index], "-maxit") == 0 )
{
arg_index++;
maxit = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-tol") == 0 )
{
arg_index++;
tol = atof(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-type") == 0 )
{
arg_index++;
cycle_type = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-rlx") == 0 )
{
arg_index++;
rlx_type = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-rlxn") == 0 )
{
arg_index++;
rlx_sweeps = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-rlxw") == 0 )
{
arg_index++;
rlx_weight = atof(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-rlxo") == 0 )
{
arg_index++;
rlx_omega = atof(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-ctype") == 0 )
{
arg_index++;
amg_coarsen_type = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-amgrlx") == 0 )
{
arg_index++;
amg_rlx_type = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-agg") == 0 )
{
arg_index++;
amg_agg_levels = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-itype") == 0 )
{
arg_index++;
amg_interp_type = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-pmax") == 0 )
{
arg_index++;
amg_Pmax = atoi(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-sing") == 0 )
{
arg_index++;
singular_problem = 1;
}
else if ( strcmp(argv[arg_index], "-theta") == 0 )
{
arg_index++;
theta = atof(argv[arg_index++]);
}
else if ( strcmp(argv[arg_index], "-help") == 0 )
{
print_usage = 1;
break;
}
else
{
arg_index++;
}
}
if ((print_usage) && (myid == 0))
{
printf("\n");
printf("Usage: %s [<options>]\n", argv[0]);
printf("\n");
printf(" -n <n> : problem size per processor (default: 10)\n");
printf(" -a <alpha_opt> : choice for the curl-curl coefficient (default: 1.0)\n");
printf(" -b <beta_opt> : choice for the mass coefficient (default: 1.0)\n");
printf(" -print_solution : print the solution vector\n");
printf("\n");
printf("PCG-AMS solver options: \n");
printf(" -maxit <num> : maximum number of iterations (100) \n");
printf(" -tol <num> : convergence tolerance (1e-6) \n");
printf(" -type <num> : 3-level cycle type (0-8, 11-14) \n");
printf(" -theta <num> : BoomerAMG threshold (0.25) \n");
printf(" -ctype <num> : BoomerAMG coarsening type \n");
printf(" -agg <num> : Levels of BoomerAMG agg. coarsening \n");
printf(" -amgrlx <num> : BoomerAMG relaxation type \n");
printf(" -itype <num> : BoomerAMG interpolation type \n");
printf(" -pmax <num> : BoomerAMG interpolation truncation \n");
printf(" -rlx <num> : relaxation type \n");
printf(" -rlxn <num> : number of relaxation sweeps \n");
printf(" -rlxw <num> : damping parameter (usually <=1) \n");
printf(" -rlxo <num> : SOR parameter (usually in (0,2)) \n");
printf(" -sing : curl-curl only (singular) problem \n");
printf("\n");
printf("\n");
}
if (print_usage)
{
MPI_Finalize();
return (0);
}
}
/* Figure out the processor grid (N x N x N). The local problem size is n^3,
while pi, pj and pk indicate the position in the processor grid. */
N = pow(num_procs,1.0/3.0) + 0.5;
if (num_procs != N*N*N)
{
if (myid == 0) printf("Can't run on %d processors, try %d.\n",
num_procs, N*N*N);
MPI_Finalize();
exit(1);
}
h = 1.0 / (N*n);
pk = myid / (N*N);
pj = myid/N - pk*N;
pi = myid - pj*N - pk*N*N;
/* Start timing */
time_index = hypre_InitializeTiming("SStruct Setup");
hypre_BeginTiming(time_index);
/* 1. Set up the edge and nodal grids. Note that we do this simultaneously
to make sure that they have the same extends. For simplicity we use
only one part to represent the unit cube. */
{
HYPRE_Int ndim = 3;
HYPRE_Int nparts = 1;
/* Create empty 2D grid objects */
HYPRE_SStructGridCreate(MPI_COMM_WORLD, ndim, nparts, &node_grid);
HYPRE_SStructGridCreate(MPI_COMM_WORLD, ndim, nparts, &edge_grid);
/* Set the extents of the grid - each processor sets its grid boxes. */
{
HYPRE_Int part = 0;
HYPRE_Int ilower[3] = {1 + pi*n, 1 + pj*n, 1 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructGridSetExtents(node_grid, part, ilower, iupper);
HYPRE_SStructGridSetExtents(edge_grid, part, ilower, iupper);
}
/* Set the variable type and number of variables on each grid. */
{
HYPRE_Int i;
HYPRE_Int nnodevars = 1;
HYPRE_Int nedgevars = 3;
HYPRE_SStructVariable nodevars[1] = {HYPRE_SSTRUCT_VARIABLE_NODE};
HYPRE_SStructVariable edgevars[3] = {HYPRE_SSTRUCT_VARIABLE_XEDGE,
HYPRE_SSTRUCT_VARIABLE_YEDGE,
HYPRE_SSTRUCT_VARIABLE_ZEDGE};
for (i = 0; i < nparts; i++)
{
HYPRE_SStructGridSetVariables(node_grid, i, nnodevars, nodevars);
HYPRE_SStructGridSetVariables(edge_grid, i, nedgevars, edgevars);
}
}
/* Since there is only one part, there is no need to call the
SetNeighborPart or SetSharedPart functions, which determine the spatial
relation between the parts. See Examples 12, 13 and 14 for
illustrations of these calls. */
/* Now the grids are ready to be used */
HYPRE_SStructGridAssemble(node_grid);
HYPRE_SStructGridAssemble(edge_grid);
}
/* 2. Create the finite element stiffness matrix A and load vector b. */
{
HYPRE_Int part = 0; /* this problem has only one part */
/* Set the ordering of the variables in the finite element problem. This
is done by listing the variable offset directions relative to the
element's center. See the Reference Manual for more details. */
{
HYPRE_Int ordering[48] = { 0, 0, -1, -1, /* x-edge [0]-[1] */
1, +1, 0, -1, /* y-edge [1]-[2] */
/* [7]------[6] */ 0, 0, +1, -1, /* x-edge [3]-[2] */
/* /| /| */ 1, -1, 0, -1, /* y-edge [0]-[3] */
/* / | / | */ 0, 0, -1, +1, /* x-edge [4]-[5] */
/* [4]------[5] | */ 1, +1, 0, +1, /* y-edge [5]-[6] */
/* | [3]----|-[2] */ 0, 0, +1, +1, /* x-edge [7]-[6] */
/* | / | / */ 1, -1, 0, +1, /* y-edge [4]-[7] */
/* |/ |/ */ 2, -1, -1, 0, /* z-edge [0]-[4] */
/* [0]------[1] */ 2, +1, -1, 0, /* z-edge [1]-[5] */
2, +1, +1, 0, /* z-edge [2]-[6] */
2, -1, +1, 0 }; /* z-edge [3]-[7] */
HYPRE_SStructGridSetFEMOrdering(edge_grid, part, ordering);
}
/* Set up the Graph - this determines the non-zero structure of the
matrix. */
{
HYPRE_Int part = 0;
/* Create the graph object */
HYPRE_SStructGraphCreate(MPI_COMM_WORLD, edge_grid, &A_graph);
/* See MatrixSetObjectType below */
HYPRE_SStructGraphSetObjectType(A_graph, HYPRE_PARCSR);
/* Indicate that this problem uses finite element stiffness matrices and
load vectors, instead of stencils. */
HYPRE_SStructGraphSetFEM(A_graph, part);
/* The edge finite element matrix is full, so there is no need to call the
HYPRE_SStructGraphSetFEMSparsity() function. */
/* Assemble the graph */
HYPRE_SStructGraphAssemble(A_graph);
}
/* Set up the SStruct Matrix and right-hand side vector */
{
/* Create the matrix object */
HYPRE_SStructMatrixCreate(MPI_COMM_WORLD, A_graph, &A);
/* Use a ParCSR storage */
HYPRE_SStructMatrixSetObjectType(A, HYPRE_PARCSR);
/* Indicate that the matrix coefficients are ready to be set */
HYPRE_SStructMatrixInitialize(A);
/* Create an empty vector object */
HYPRE_SStructVectorCreate(MPI_COMM_WORLD, edge_grid, &b);
/* Use a ParCSR storage */
HYPRE_SStructVectorSetObjectType(b, HYPRE_PARCSR);
/* Indicate that the vector coefficients are ready to be set */
HYPRE_SStructVectorInitialize(b);
}
/* Set the matrix and vector entries by finite element assembly */
{
/* local stiffness matrix and load vector */
double S[12][12], F[12];
int i, j, k;
HYPRE_Int index[3];
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
for (k = 1; k <= n; k++)
{
/* Compute the FEM matrix and r.h.s. for cell (i,j,k) with
coefficients evaluated at the cell center. */
index[0] = i + pi*n; index[1] = j + pj*n; index[2] = k + pk*n;
ComputeFEMND1(S,F,(pi*n+i)*h-h/2,(pj*n+j)*h-h/2,(pk*n+k)*h-h/2,h);
/* Eliminate boundary conditions on x = 0 */
if (index[0] == 1)
{
int ii, jj, bc_edges[4] = { 3, 11, 7, 8 };
for (ii = 0; ii < 4; ii++)
{
for (jj = 0; jj < 12; jj++)
S[bc_edges[ii]][jj] = S[jj][bc_edges[ii]] = 0.0;
S[bc_edges[ii]][bc_edges[ii]] = 1.0;
F[bc_edges[ii]] = 0.0;
}
}
/* Eliminate boundary conditions on y = 0 */
if (index[1] == 1)
{
int ii, jj, bc_edges[4] = { 0, 9, 4, 8 };
for (ii = 0; ii < 4; ii++)
{
for (jj = 0; jj < 12; jj++)
S[bc_edges[ii]][jj] = S[jj][bc_edges[ii]] = 0.0;
S[bc_edges[ii]][bc_edges[ii]] = 1.0;
F[bc_edges[ii]] = 0.0;
}
}
/* Eliminate boundary conditions on z = 0 */
if (index[2] == 1)
{
int ii, jj, bc_edges[4] = { 0, 1, 2, 3 };
for (ii = 0; ii < 4; ii++)
{
for (jj = 0; jj < 12; jj++)
S[bc_edges[ii]][jj] = S[jj][bc_edges[ii]] = 0.0;
S[bc_edges[ii]][bc_edges[ii]] = 1.0;
F[bc_edges[ii]] = 0.0;
}
}
/* Eliminate boundary conditions on x = 1 */
if (index[0] == N*n)
{
int ii, jj, bc_edges[4] = { 1, 10, 5, 9 };
for (ii = 0; ii < 4; ii++)
{
for (jj = 0; jj < 12; jj++)
S[bc_edges[ii]][jj] = S[jj][bc_edges[ii]] = 0.0;
S[bc_edges[ii]][bc_edges[ii]] = 1.0;
F[bc_edges[ii]] = 0.0;
}
}
/* Eliminate boundary conditions on y = 1 */
if (index[1] == N*n)
{
int ii, jj, bc_edges[4] = { 2, 10, 6, 11 };
for (ii = 0; ii < 4; ii++)
{
for (jj = 0; jj < 12; jj++)
S[bc_edges[ii]][jj] = S[jj][bc_edges[ii]] = 0.0;
S[bc_edges[ii]][bc_edges[ii]] = 1.0;
F[bc_edges[ii]] = 0.0;
}
}
/* Eliminate boundary conditions on z = 1 */
if (index[2] == N*n)
{
int ii, jj, bc_edges[4] = { 4, 5, 6, 7 };
for (ii = 0; ii < 4; ii++)
{
for (jj = 0; jj < 12; jj++)
S[bc_edges[ii]][jj] = S[jj][bc_edges[ii]] = 0.0;
S[bc_edges[ii]][bc_edges[ii]] = 1.0;
F[bc_edges[ii]] = 0.0;
}
}
/* Assemble the matrix */
HYPRE_SStructMatrixAddFEMValues(A, part, index, &S[0][0]);
/* Assemble the vector */
HYPRE_SStructVectorAddFEMValues(b, part, index, F);
}
}
/* Collective calls finalizing the matrix and vector assembly */
HYPRE_SStructMatrixAssemble(A);
HYPRE_SStructVectorAssemble(b);
}
/* 3. Create the discrete gradient matrix G, which is needed in AMS. */
{
HYPRE_Int part = 0;
HYPRE_Int stencil_size = 2;
/* Define the discretization stencil relating the edges and nodes of the
grid. */
{
HYPRE_Int ndim = 3;
HYPRE_Int entry;
HYPRE_Int var = 0; /* the node variable */
/* The discrete gradient stencils connect edge to node variables. */
HYPRE_Int Gx_offsets[2][3] = {{-1,0,0},{0,0,0}}; /* x-edge [7]-[6] */
HYPRE_Int Gy_offsets[2][3] = {{0,-1,0},{0,0,0}}; /* y-edge [5]-[6] */
HYPRE_Int Gz_offsets[2][3] = {{0,0,-1},{0,0,0}}; /* z-edge [2]-[6] */
HYPRE_SStructStencilCreate(ndim, stencil_size, &G_stencil[0]);
HYPRE_SStructStencilCreate(ndim, stencil_size, &G_stencil[1]);
HYPRE_SStructStencilCreate(ndim, stencil_size, &G_stencil[2]);
for (entry = 0; entry < stencil_size; entry++)
{
HYPRE_SStructStencilSetEntry(G_stencil[0], entry, Gx_offsets[entry], var);
HYPRE_SStructStencilSetEntry(G_stencil[1], entry, Gy_offsets[entry], var);
HYPRE_SStructStencilSetEntry(G_stencil[2], entry, Gz_offsets[entry], var);
}
}
/* Set up the Graph - this determines the non-zero structure of the
matrix. */
{
HYPRE_Int nvars = 3;
HYPRE_Int var; /* the edge variables */
/* Create the discrete gradient graph object */
HYPRE_SStructGraphCreate(MPI_COMM_WORLD, edge_grid, &G_graph);
/* See MatrixSetObjectType below */
HYPRE_SStructGraphSetObjectType(G_graph, HYPRE_PARCSR);
/* Since the discrete gradient relates edge and nodal variables (it is a
rectangular matrix), we have to specify the domain (column) grid. */
HYPRE_SStructGraphSetDomainGrid(G_graph, node_grid);
/* Tell the graph which stencil to use for each edge variable on each
part (we only have one part). */
for (var = 0; var < nvars; var++)
HYPRE_SStructGraphSetStencil(G_graph, part, var, G_stencil[var]);
/* Assemble the graph */
HYPRE_SStructGraphAssemble(G_graph);
}
/* Set up the SStruct Matrix */
{
/* Create the matrix object */
HYPRE_SStructMatrixCreate(MPI_COMM_WORLD, G_graph, &G);
/* Use a ParCSR storage */
HYPRE_SStructMatrixSetObjectType(G, HYPRE_PARCSR);
/* Indicate that the matrix coefficients are ready to be set */
HYPRE_SStructMatrixInitialize(G);
}
/* Set the discrete gradient values, assuming a "natural" orientation of
the edges (i.e. one in agreement with the coordinate directions). */
{
int i;
int nedges = n*(n+1)*(n+1);
double *values;
HYPRE_Int stencil_indices[2] = {0,1}; /* the nodes of each edge */
values = calloc(2*nedges, sizeof(double));
/* The edge orientation is fixed: from first to second node */
for (i = 0; i < nedges; i++)
{
values[2*i] = -1.0;
values[2*i+1] = 1.0;
}
/* Set the values in the discrete gradient x-edges */
{
HYPRE_Int var = 0;
HYPRE_Int ilower[3] = {1 + pi*n, 0 + pj*n, 0 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructMatrixSetBoxValues(G, part, ilower, iupper, var,
stencil_size, stencil_indices,
values);
}
/* Set the values in the discrete gradient y-edges */
{
HYPRE_Int var = 1;
HYPRE_Int ilower[3] = {0 + pi*n, 1 + pj*n, 0 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructMatrixSetBoxValues(G, part, ilower, iupper, var,
stencil_size, stencil_indices,
values);
}
/* Set the values in the discrete gradient z-edges */
{
HYPRE_Int var = 2;
HYPRE_Int ilower[3] = {0 + pi*n, 0 + pj*n, 1 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructMatrixSetBoxValues(G, part, ilower, iupper, var,
stencil_size, stencil_indices,
values);
}
free(values);
}
/* Finalize the matrix assembly */
HYPRE_SStructMatrixAssemble(G);
}
/* 4. Create the vectors of nodal coordinates xcoord, ycoord and zcoord,
which are needed in AMS. */
{
int i, j, k;
HYPRE_Int part = 0;
HYPRE_Int var = 0; /* the node variable */
HYPRE_Int index[3];
double xval, yval, zval;
/* Create empty vector objects */
HYPRE_SStructVectorCreate(MPI_COMM_WORLD, node_grid, &xcoord);
HYPRE_SStructVectorCreate(MPI_COMM_WORLD, node_grid, &ycoord);
HYPRE_SStructVectorCreate(MPI_COMM_WORLD, node_grid, &zcoord);
/* Set the object type to ParCSR */
HYPRE_SStructVectorSetObjectType(xcoord, HYPRE_PARCSR);
HYPRE_SStructVectorSetObjectType(ycoord, HYPRE_PARCSR);
HYPRE_SStructVectorSetObjectType(zcoord, HYPRE_PARCSR);
/* Indicate that the vector coefficients are ready to be set */
HYPRE_SStructVectorInitialize(xcoord);
HYPRE_SStructVectorInitialize(ycoord);
HYPRE_SStructVectorInitialize(zcoord);
/* Compute and set the coordinates of the nodes */
for (i = 0; i <= n; i++)
for (j = 0; j <= n; j++)
for (k = 0; k <= n; k++)
{
index[0] = i + pi*n; index[1] = j + pj*n; index[2] = k + pk*n;
xval = index[0]*h;
yval = index[1]*h;
zval = index[2]*h;
HYPRE_SStructVectorSetValues(xcoord, part, index, var, &xval);
HYPRE_SStructVectorSetValues(ycoord, part, index, var, &yval);
HYPRE_SStructVectorSetValues(zcoord, part, index, var, &zval);
}
/* Finalize the vector assembly */
HYPRE_SStructVectorAssemble(xcoord);
HYPRE_SStructVectorAssemble(ycoord);
HYPRE_SStructVectorAssemble(zcoord);
}
/* 5. Set up a SStruct Vector for the solution vector x */
{
HYPRE_Int part = 0;
int nvalues = n*(n+1)*(n+1);
double *values;
values = calloc(nvalues, sizeof(double));
/* Create an empty vector object */
HYPRE_SStructVectorCreate(MPI_COMM_WORLD, edge_grid, &x);
/* Set the object type to ParCSR */
HYPRE_SStructVectorSetObjectType(x, HYPRE_PARCSR);
/* Indicate that the vector coefficients are ready to be set */
HYPRE_SStructVectorInitialize(x);
/* Set the values for the initial guess x-edge */
{
HYPRE_Int var = 0;
HYPRE_Int ilower[3] = {1 + pi*n, 0 + pj*n, 0 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructVectorSetBoxValues(x, part, ilower, iupper, var, values);
}
/* Set the values for the initial guess y-edge */
{
HYPRE_Int var = 1;
HYPRE_Int ilower[3] = {0 + pi*n, 1 + pj*n, 0 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructVectorSetBoxValues(x, part, ilower, iupper, var, values);
}
/* Set the values for the initial guess z-edge */
{
HYPRE_Int var = 2;
HYPRE_Int ilower[3] = {0 + pi*n, 0 + pj*n, 1 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructVectorSetBoxValues(x, part, ilower, iupper, var, values);
}
free(values);
/* Finalize the vector assembly */
HYPRE_SStructVectorAssemble(x);
}
/* Finalize current timing */
hypre_EndTiming(time_index);
hypre_PrintTiming("SStruct phase times", MPI_COMM_WORLD);
hypre_FinalizeTiming(time_index);
hypre_ClearTiming();
/* 6. Set up and call the PCG-AMS solver (Solver options can be found in the
Reference Manual.) */
{
double final_res_norm;
HYPRE_Int its;
HYPRE_ParCSRMatrix par_A;
HYPRE_ParVector par_b;
HYPRE_ParVector par_x;
HYPRE_ParCSRMatrix par_G;
HYPRE_ParVector par_xcoord;
HYPRE_ParVector par_ycoord;
HYPRE_ParVector par_zcoord;
/* Extract the ParCSR objects needed in the solver */
HYPRE_SStructMatrixGetObject(A, (void **) &par_A);
HYPRE_SStructVectorGetObject(b, (void **) &par_b);
HYPRE_SStructVectorGetObject(x, (void **) &par_x);
HYPRE_SStructMatrixGetObject(G, (void **) &par_G);
HYPRE_SStructVectorGetObject(xcoord, (void **) &par_xcoord);
HYPRE_SStructVectorGetObject(ycoord, (void **) &par_ycoord);
HYPRE_SStructVectorGetObject(zcoord, (void **) &par_zcoord);
if (myid == 0)
printf("Problem size: %lld\n\n",
hypre_ParCSRMatrixGlobalNumRows((hypre_ParCSRMatrix*)par_A));
/* Start timing */
time_index = hypre_InitializeTiming("AMS Setup");
hypre_BeginTiming(time_index);
/* Create solver */
HYPRE_ParCSRPCGCreate(MPI_COMM_WORLD, &solver);
/* Set some parameters (See Reference Manual for more parameters) */
HYPRE_PCGSetMaxIter(solver, maxit); /* max iterations */
HYPRE_PCGSetTol(solver, tol); /* conv. tolerance */
HYPRE_PCGSetTwoNorm(solver, 0); /* use the two norm as the stopping criteria */
HYPRE_PCGSetPrintLevel(solver, 2); /* print solve info */
HYPRE_PCGSetLogging(solver, 1); /* needed to get run info later */
/* Create AMS preconditioner */
HYPRE_AMSCreate(&precond);
/* Set AMS parameters */
HYPRE_AMSSetMaxIter(precond, 1);
HYPRE_AMSSetTol(precond, 0.0);
HYPRE_AMSSetCycleType(precond, cycle_type);
HYPRE_AMSSetPrintLevel(precond, 1);
/* Set discrete gradient */
HYPRE_AMSSetDiscreteGradient(precond, par_G);
/* Set vertex coordinates */
HYPRE_AMSSetCoordinateVectors(precond,
par_xcoord, par_ycoord, par_zcoord);
if (singular_problem)
HYPRE_AMSSetBetaPoissonMatrix(precond, NULL);
/* Smoothing and AMG options */
HYPRE_AMSSetSmoothingOptions(precond,
rlx_type, rlx_sweeps,
rlx_weight, rlx_omega);
HYPRE_AMSSetAlphaAMGOptions(precond,
amg_coarsen_type, amg_agg_levels,
amg_rlx_type, theta, amg_interp_type,
amg_Pmax);
HYPRE_AMSSetBetaAMGOptions(precond,
amg_coarsen_type, amg_agg_levels,
amg_rlx_type, theta, amg_interp_type,
amg_Pmax);
/* Set the PCG preconditioner */
HYPRE_PCGSetPrecond(solver,
(HYPRE_PtrToSolverFcn) HYPRE_AMSSolve,
(HYPRE_PtrToSolverFcn) HYPRE_AMSSetup,
precond);
/* Call the setup */
HYPRE_ParCSRPCGSetup(solver, par_A, par_b, par_x);
/* Finalize current timing */
hypre_EndTiming(time_index);
hypre_PrintTiming("Setup phase times", MPI_COMM_WORLD);
hypre_FinalizeTiming(time_index);
hypre_ClearTiming();
/* Start timing again */
time_index = hypre_InitializeTiming("AMS Solve");
hypre_BeginTiming(time_index);
/* Call the solve */
HYPRE_ParCSRPCGSolve(solver, par_A, par_b, par_x);
/* Finalize current timing */
hypre_EndTiming(time_index);
hypre_PrintTiming("Solve phase times", MPI_COMM_WORLD);
hypre_FinalizeTiming(time_index);
hypre_ClearTiming();
/* Get some info */
HYPRE_PCGGetNumIterations(solver, &its);
HYPRE_PCGGetFinalRelativeResidualNorm(solver, &final_res_norm);
/* Clean up */
HYPRE_AMSDestroy(precond);
HYPRE_ParCSRPCGDestroy(solver);
/* Gather the solution vector */
HYPRE_SStructVectorGather(x);
/* Print the solution with replicated shared data */
if (print_solution)
{
FILE *file;
char filename[255];
HYPRE_Int part = 0;
int nvalues = n*(n+1)*(n+1);
double *xvalues, *yvalues, *zvalues;
xvalues = calloc(nvalues, sizeof(double));
yvalues = calloc(nvalues, sizeof(double));
zvalues = calloc(nvalues, sizeof(double));
/* Get local solution in the x-edges */
{
HYPRE_Int var = 0;
HYPRE_Int ilower[3] = {1 + pi*n, 0 + pj*n, 0 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructVectorGetBoxValues(x, part, ilower, iupper,
var, xvalues);
}
/* Get local solution in the y-edges */
{
HYPRE_Int var = 1;
HYPRE_Int ilower[3] = {0 + pi*n, 1 + pj*n, 0 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructVectorGetBoxValues(x, part, ilower, iupper,
var, yvalues);
}
/* Get local solution in the z-edges */
{
HYPRE_Int var = 2;
HYPRE_Int ilower[3] = {0 + pi*n, 0 + pj*n, 1 + pk*n};
HYPRE_Int iupper[3] = {n + pi*n, n + pj*n, n + pk*n};
HYPRE_SStructVectorGetBoxValues(x, part, ilower, iupper,
var, zvalues);
}
sprintf(filename, "sstruct.out.x.00.00.%05d", myid);
if ((file = fopen(filename, "w")) == NULL)
{
printf("Error: can't open output file %s\n", filename);
MPI_Finalize();
exit(1);
}
/* Save the edge values, element by element, using the same numbering
as the local finite element degrees of freedom. */
{
int i, j, k, s;
/* Initial x-, y- and z-edge indices in the values arrays */
int oi[4] = { 0, n, n*(n+1), n*(n+1)+n }; /* e_0, e_2, e_4, e_6 */
int oj[4] = { 0, 1, n*(n+1), n*(n+1)+1 }; /* e_3, e_1, e_7, e_5 */
int ok[4] = { 0, 1, n+1, n+2 }; /* e_8, e_9, e_11, e_10 */
/* Loop over the cells while updating the above offsets */
for (k = 0; k < n; k++)
{
for (j = 0; j < n; j++)
{
for (i = 0; i < n; i++)
{
fprintf(file,
"%.14e\n%.14e\n%.14e\n%.14e\n"
"%.14e\n%.14e\n%.14e\n%.14e\n"
"%.14e\n%.14e\n%.14e\n%.14e\n",
xvalues[oi[0]], yvalues[oj[1]], xvalues[oi[1]], yvalues[oj[0]],
xvalues[oi[2]], yvalues[oj[3]], xvalues[oi[3]], yvalues[oj[2]],
zvalues[ok[0]], zvalues[ok[1]], zvalues[ok[3]], zvalues[ok[2]]);
for (s=0; s<4; s++) oi[s]++, oj[s]++, ok[s]++;
}
for (s=0; s<4; s++) oj[s]++, ok[s]++;
}
for (s=0; s<4; s++) oi[s]+=n, ok[s]+=n+1;
}
}
fflush(file);
fclose(file);
free(xvalues);
free(yvalues);
free(zvalues);
}
if (myid == 0)
{
printf("\n");
printf("Iterations = %lld\n", its);
printf("Final Relative Residual Norm = %g\n", final_res_norm);
printf("\n");
}
}
/* Free memory */
HYPRE_SStructGridDestroy(edge_grid);
HYPRE_SStructGraphDestroy(A_graph);
HYPRE_SStructMatrixDestroy(A);
HYPRE_SStructVectorDestroy(b);
HYPRE_SStructVectorDestroy(x);
HYPRE_SStructGridDestroy(node_grid);
HYPRE_SStructGraphDestroy(G_graph);
HYPRE_SStructStencilDestroy(G_stencil[0]);
HYPRE_SStructStencilDestroy(G_stencil[1]);
HYPRE_SStructStencilDestroy(G_stencil[2]);
HYPRE_SStructMatrixDestroy(G);
HYPRE_SStructVectorDestroy(xcoord);
HYPRE_SStructVectorDestroy(ycoord);
HYPRE_SStructVectorDestroy(zcoord);
/* Finalize MPI */
MPI_Finalize();
return 0;
}
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