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hypre/examples/ex13.c

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/*
Example 13
Interface: Semi-Structured interface (SStruct)
Compile with: make ex13
Sample run: mpirun -np 6 ex13 -n 10
To see options: ex13 -help
Description: This code solves the 2D Laplace equation using bilinear
finite element discretization on a mesh with an "enhanced
connectivity" point. Specifically, we solve -Delta u = 1
with zero boundary conditions on a star-shaped domain
consisting of identical rhombic parts each meshed with a
uniform n x n grid. Every part is assigned to a different
processor and all parts meet at the origin, equally
subdividing the 2*pi angle there. The case of six processors
(parts) looks as follows:
+
/ \
/ \
/ \
+--------+ 1 +---------+
\ \ / /
\ 2 \ / 0 /
\ \ / /
+--------+---------+
/ / \ \
/ 3 / \ 5 \
/ / \ \
+--------+ 4 +---------+
\ /
\ /
\ /
+
Note that in this problem we use nodal variables, which are
shared between the different parts. The node at the origin,
for example, belongs to all parts as illustrated below:
.
/ \
. .
/ \ / \
o . *
.---.---o \ / \ / *---.---.
\ \ \ o * / / /
.---.---o \ / *---.---.
\ \ \ x / / /
@---@---x x---z---z
@---@---x x---z---z
/ / / x \ \ \
.---.---a / \ #---.---.
/ / / a # \ \ \
.---.---a / \ / \ #---.---.
a . #
\ / \ /
. .
\ /
.
We recommend viewing the Struct examples before viewing this
and the other SStruct examples. The primary role of this
particular SStruct example is to demonstrate a stencil-based
way to set up finite element problems in SStruct, and
specifically to show how to handle problems with an "enhanced
connectivity" point.
*/
#include <math.h>
#include "_hypre_utilities.h"
#include "HYPRE_sstruct_mv.h"
#include "HYPRE_sstruct_ls.h"
#include "HYPRE.h"
#ifndef M_PI
#define M_PI 3.14159265358979
#endif
/*
This routine computes the bilinear finite element stiffness matrix and
load vector on a rhombus with angle gamma. Specifically, let R be the
rhombus
[3]------[2]
/ /
/ /
[0]------[1]
with sides of length h. The finite element stiffness matrix
S_ij = (grad phi_i,grad phi_j)_R
with bilinear finite element functions {phi_i} has the form
/ 4-k -1 -2+k -1 \
alpha . | -1 4+k -1 -2-k |
| -2+k -1 4-k -1 |
\ -1 -2-k -1 4+k /
where alpha = 1/(6*sin(gamma)) and k = 3*cos(gamma). The load vector
corresponding to a right-hand side of 1 is
F_j = (1,phi_j)_R = h^2/4 * sin(gamma)
*/
void ComputeFEMRhombus (double S[4][4], double F[4], double gamma, double h)
{
int i, j;
double h2_4 = h*h/4;
double sing = sin(gamma);
double alpha = 1/(6*sing);
double k = 3*cos(gamma);
S[0][0] = alpha * (4-k);
S[0][1] = alpha * (-1);
S[0][2] = alpha * (-2+k);
S[0][3] = alpha * (-1);
S[1][1] = alpha * (4+k);
S[1][2] = alpha * (-1);
S[1][3] = alpha * (-2-k);
S[2][2] = alpha * (4-k);
S[2][3] = alpha * (-1);
S[3][3] = alpha * (4+k);
/* The stiffness matrix is symmetric */
for (i = 1; i < 4; i++)
for (j = 0; j < i; j++)
S[i][j] = S[j][i];
for (i = 0; i < 4; i++)
F[i] = h2_4*sing;
}
int main (int argc, char *argv[])
{
int myid, num_procs;
int n;
double gamma, h;
int print_solution;
HYPRE_SStructGrid grid;
HYPRE_SStructGraph graph;
HYPRE_SStructStencil stencil;
HYPRE_SStructMatrix A;
HYPRE_SStructVector b;
HYPRE_SStructVector x;
HYPRE_Solver solver;
/* 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;
/* 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], "-print_solution") == 0 )
{
arg_index++;
print_solution = 1;
}
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(" -print_solution : print the solution vector\n");
printf("\n");
}
if (print_usage)
{
MPI_Finalize();
return (0);
}
}
/* Set the rhombus angle, gamma, and the mesh size, h, depending on the
number of processors np and the given n */
if (num_procs < 3)
{
if (myid ==0) printf("Must run with at least 3 processors!\n");
MPI_Finalize();
exit(1);
}
gamma = 2*M_PI/num_procs;
h = 1.0/n;
/* 1. Set up the grid. We will set up the grid so that processor X owns
part X. Note that each part has its own index space numbering. Later
we relate the parts to each other. */
{
int ndim = 2;
int nparts = num_procs;
/* Create an empty 2D grid object */
HYPRE_SStructGridCreate(MPI_COMM_WORLD, ndim, nparts, &grid);
/* Set the extents of the grid - each processor sets its grid boxes. Each
part has its own relative index space numbering */
{
int part = myid;
int ilower[2] = {1,1}; /* lower-left cell touching the origin */
int iupper[2] = {n,n}; /* upper-right cell */
HYPRE_SStructGridSetExtents(grid, part, ilower, iupper);
}
/* Set the variable type and number of variables on each part. These need
to be set in each part which is neighboring or contains boxes owned by
the processor. */
{
int i;
int nvars = 1;
HYPRE_SStructVariable vartypes[1] = {HYPRE_SSTRUCT_VARIABLE_NODE};
for (i = 0; i < nparts; i++)
HYPRE_SStructGridSetVariables(grid, i, nvars, vartypes);
}
/* Now we need to set the spatial relation between each of the parts.
Since we are using nodal variables, we have to use SetSharedPart to
establish the connection at the origin. */
{
/* Relation to the clockwise-previous neighbor part, e.g. 0 and 1 for
the case of 6 parts. Note that we could have used SetNeighborPart
here instead of SetSharedPart. */
{
int part = myid;
/* the box of cells intersecting the boundary in the current part */
int ilower[2] = {1,1}, iupper[2] = {1,n};
/* share all data on the left side of the box */
int offset[2] = {-1,0};
int shared_part = (myid+1) % num_procs;
/* the box of cells intersecting the boundary in the neighbor */
int shared_ilower[2] = {1,1}, shared_iupper[2] = {n,1};
/* share all data on the bottom of the box */
int shared_offset[2] = {0,-1};
/* x/y-direction on the current part is -y/x on the neighbor */
int index_map[2] = {1,0};
int index_dir[2] = {-1,1};
HYPRE_SStructGridSetSharedPart(grid, part, ilower, iupper, offset,
shared_part, shared_ilower,
shared_iupper, shared_offset,
index_map, index_dir);
}
/* Relation to the clockwise-following neighbor part, e.g. 0 and 5 for
the case of 6 parts. Note that we could have used SetNeighborPart
here instead of SetSharedPart. */
{
int part = myid;
/* the box of cells intersecting the boundary in the current part */
int ilower[2] = {1,1}, iupper[2] = {n,1};
/* share all data on the bottom of the box */
int offset[2] = {0,-1};
int shared_part = (myid+num_procs-1) % num_procs;
/* the box of cells intersecting the boundary in the neighbor */
int shared_ilower[2] = {1,1}, shared_iupper[2] = {1,n};
/* share all data on the left side of the box */
int shared_offset[2] = {-1,0};
/* x/y-direction on the current part is y/-x on the neighbor */
int index_map[2] = {1,0};
int index_dir[2] = {1,-1};
HYPRE_SStructGridSetSharedPart(grid, part, ilower, iupper, offset,
shared_part, shared_ilower,
shared_iupper, shared_offset,
index_map, index_dir);
}
/* Relation to all other parts, e.g. 0 and 2,3,4. This can be
described only by SetSharedPart. */
{
int part = myid;
/* the (one cell) box that touches the origin */
int ilower[2] = {1,1}, iupper[2] = {1,1};
/* share all data in the bottom left corner (i.e. the origin) */
int offset[2] = {-1,-1};
int shared_part;
/* the box of one cell that touches the origin */
int shared_ilower[2] = {1,1}, shared_iupper[2] = {1,1};
/* share all data in the bottom left corner (i.e. the origin) */
int shared_offset[2] = {-1,-1};
/* x/y-direction on the current part is -x/-y on the neighbor, but
in this case the arguments are not really important since we are
only sharing a point */
int index_map[2] = {0,1};
int index_dir[2] = {-1,-1};
for (shared_part = 0; shared_part < myid-1; shared_part++)
HYPRE_SStructGridSetSharedPart(grid, part, ilower, iupper, offset,
shared_part, shared_ilower,
shared_iupper, shared_offset,
index_map, index_dir);
for (shared_part = myid+2; shared_part < num_procs; shared_part++)
HYPRE_SStructGridSetSharedPart(grid, part, ilower, iupper, offset,
shared_part, shared_ilower,
shared_iupper, shared_offset,
index_map, index_dir);
}
}
/* Now the grid is ready to be used */
HYPRE_SStructGridAssemble(grid);
}
/* 2. Define the discretization stencils. Since this is a finite element
discretization we define here a full 9-point stencil. We will later
use four sub-stencils for the rows of the local stiffness matrix. */
{
int ndim = 2;
int var = 0;
int entry;
/* Define the geometry of the 9-point stencil */
int stencil_size = 9;
int offsets[9][2] = {{0,0}, /* [8] [4] [7] */
{-1,0}, {1,0}, /* \ | / */
{0,-1}, {0,1}, /* [1]-[0]-[2] */
{-1,-1}, {1,-1}, /* / | \ */
{1,1}, {-1,1}}; /* [5] [3] [6] */
HYPRE_SStructStencilCreate(ndim, stencil_size, &stencil);
for (entry = 0; entry < stencil_size; entry++)
HYPRE_SStructStencilSetEntry(stencil, entry, offsets[entry], var);
}
/* 3. Set up the Graph - this determines the non-zero structure of the
matrix. */
{
int part;
int var = 0;
/* Create the graph object */
HYPRE_SStructGraphCreate(MPI_COMM_WORLD, grid, &graph);
/* Now we need to tell the graph which stencil to use for each
variable on each part (we only have one variable) */
for (part = 0; part < num_procs; part++)
HYPRE_SStructGraphSetStencil(graph, part, var, stencil);
/* Assemble the graph */
HYPRE_SStructGraphAssemble(graph);
}
/* 4. Set up the SStruct Matrix and right-hand side vector */
{
int part = myid;
int var = 0;
/* Create the matrix object */
HYPRE_SStructMatrixCreate(MPI_COMM_WORLD, 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, 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 stifness matrix and load vector */
double S[4][4], F[4];
/* The index of the local nodes 0-3 relative to the cell index,
i.e. node k in cell (i,j) is in the upper-right corner of the
cell (i,j) + node_index_offset[k]. */
int node_index_offset[4][2] = {{-1,-1},{0,-1},{0,0},{-1,0}};
/* The cell sub-stencils of nodes 0-3 indexed from the full stencil,
i.e. we take the full stencil in each node of a fixed cell, and
restrict it to that as is done in the finite element stiffness
matrix:
[4] [7] [8] [4] [1]-[0] [0]-[2]
| / \ | / | | \
[0]-[2] , [1]-[0] , [5] [3] , [3] [6]
Note that the ordering of the local nodes remains fixed, and
therefore the above sub-stencil at node k corresponds to the kth row
of the local stiffness matrix and the kth entry of the local load
vector. */
int node_stencil[4][4] = {{0,2,7,4},{1,0,4,8},{5,3,0,1},{3,6,2,0}};
int i, j, k;
int index[2];
int nentries = 4;
/* set the values in the interior cells */
{
ComputeFEMRhombus(S, F, gamma, h);
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
for (k = 0; k < 4; k++) /* node k in cell (i,j) */
{
index[0] = i + node_index_offset[k][0];
index[1] = j + node_index_offset[k][1];
HYPRE_SStructMatrixAddToValues(A, part, index, var,
nentries, node_stencil[k],
&S[k][0]);
HYPRE_SStructVectorAddToValues(b, part, index, var, &F[k]);
}
}
/* cells having nodes 1,2 on the domain boundary */
{
ComputeFEMRhombus(S, F, gamma, h);
/* eliminate nodes 1,2 from S and F */
for (k = 0; k < 4; k++)
{
S[1][k] = S[k][1] = 0.0;
S[2][k] = S[k][2] = 0.0;
}
S[1][1] = 1.0;
S[2][2] = 1.0;
F[1] = 0.0;
F[2] = 0.0;
for (i = n; i <= n; i++)
for (j = 1; j <= n; j++)
for (k = 0; k < 4; k++) /* node k in cell (n,j) */
{
index[0] = i + node_index_offset[k][0];
index[1] = j + node_index_offset[k][1];
HYPRE_SStructMatrixAddToValues(A, part, index, var,
nentries, node_stencil[k],
&S[k][0]);
HYPRE_SStructVectorAddToValues(b, part, index, var, &F[k]);
}
}
/* cells having nodes 2,3 on the domain boundary */
{
ComputeFEMRhombus(S, F, gamma, h);
/* eliminate nodes 2,3 from S and F */
for (k = 0; k < 4; k++)
{
S[2][k] = S[k][2] = 0.0;
S[3][k] = S[k][3] = 0.0;
}
S[2][2] = 1.0;
S[3][3] = 1.0;
F[2] = 0.0;
F[3] = 0.0;
for (i = 1; i <= n; i++)
for (j = n; j <= n; j++)
for (k = 0; k < 4; k++) /* node k in cell (i,n) */
{
index[0] = i + node_index_offset[k][0];
index[1] = j + node_index_offset[k][1];
HYPRE_SStructMatrixAddToValues(A, part, index, var,
nentries, node_stencil[k],
&S[k][0]);
HYPRE_SStructVectorAddToValues(b, part, index, var, &F[k]);
}
}
/* cells having nodes 1,2,3 on the domain boundary */
{
ComputeFEMRhombus(S, F, gamma, h);
/* eliminate nodes 2,3 from S and F */
for (k = 0; k < 4; k++)
{
S[1][k] = S[k][1] = 0.0;
S[2][k] = S[k][2] = 0.0;
S[3][k] = S[k][3] = 0.0;
}
S[1][1] = 1.0;
S[2][2] = 1.0;
S[3][3] = 1.0;
F[1] = 0.0;
F[2] = 0.0;
F[3] = 0.0;
for (i = n; i <= n; i++)
for (j = n; j <= n; j++)
for (k = 0; k < 4; k++) /* node k in cell (n,n) */
{
index[0] = i + node_index_offset[k][0];
index[1] = j + node_index_offset[k][1];
HYPRE_SStructMatrixAddToValues(A, part, index, var,
nentries, node_stencil[k],
&S[k][0]);
HYPRE_SStructVectorAddToValues(b, part, index, var, &F[k]);
}
}
}
}
/* Collective calls finalizing the matrix and vector assembly */
HYPRE_SStructMatrixAssemble(A);
HYPRE_SStructVectorAssemble(b);
/* 5. Set up SStruct Vector for the solution vector x */
{
int part = myid;
int var = 0;
int nvalues = (n+1)*(n+1);
double *values;
/* Since the SetBoxValues() calls below set the values of the nodes in
the upper-right corners of the cells, the nodal box should start
from (0,0) instead of (1,1). */
int ilower[2] = {0,0};
int iupper[2] = {n,n};
values = calloc(nvalues, sizeof(double));
/* Create an empty vector object */
HYPRE_SStructVectorCreate(MPI_COMM_WORLD, 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 */
HYPRE_SStructVectorSetBoxValues(x, part, ilower, iupper, var, values);
free(values);
/* Finalize the vector assembly */
HYPRE_SStructVectorAssemble(x);
}
/* 6. Set up and call the solver (Solver options can be found in the
Reference Manual.) */
{
double final_res_norm;
int its;
HYPRE_ParCSRMatrix par_A;
HYPRE_ParVector par_b;
HYPRE_ParVector par_x;
/* 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);
/* Here we construct a BoomerAMG solver. See the other SStruct examples
as well as the Reference manual for additional solver choices. */
HYPRE_BoomerAMGCreate(&solver);
HYPRE_BoomerAMGSetCoarsenType(solver, 6);
HYPRE_BoomerAMGSetStrongThreshold(solver, 0.25);
HYPRE_BoomerAMGSetTol(solver, 1e-6);
HYPRE_BoomerAMGSetPrintLevel(solver, 2);
HYPRE_BoomerAMGSetMaxIter(solver, 50);
/* call the setup */
HYPRE_BoomerAMGSetup(solver, par_A, par_b, par_x);
/* call the solve */
HYPRE_BoomerAMGSolve(solver, par_A, par_b, par_x);
/* get some info */
HYPRE_BoomerAMGGetNumIterations(solver, &its);
HYPRE_BoomerAMGGetFinalRelativeResidualNorm(solver,
&final_res_norm);
/* clean up */
HYPRE_BoomerAMGDestroy(solver);
/* Gather the solution vector */
HYPRE_SStructVectorGather(x);
/* Print the solution with replicated shared data */
if (print_solution)
{
FILE *file;
char filename[255];
int i, part = myid, var = 0;
int nvalues = (n+1)*(n+1);
double *values;
int ilower[2] = {0,0};
int iupper[2] = {n,n};
values = calloc(nvalues, sizeof(double));
/* get all local data (including a local copy of the shared values) */
HYPRE_SStructVectorGetBoxValues(x, part, ilower, iupper,
var, values);
sprintf(filename, "sstruct.out.x.00.00.%05d", part);
if ((file = fopen(filename, "w")) == NULL)
{
printf("Error: can't open output file %s\n", filename);
MPI_Finalize();
exit(1);
}
for (i = 0; i < nvalues; i++)
fprintf(file, "%.14e\n", values[i]);
fflush(file);
fclose(file);
free(values);
}
if (myid == 0)
{
printf("\n");
printf("Iterations = %d\n", its);
printf("Final Relative Residual Norm = %g\n", final_res_norm);
printf("\n");
}
}
/* Free memory */
HYPRE_SStructGridDestroy(grid);
HYPRE_SStructStencilDestroy(stencil);
HYPRE_SStructGraphDestroy(graph);
HYPRE_SStructMatrixDestroy(A);
HYPRE_SStructVectorDestroy(b);
HYPRE_SStructVectorDestroy(x);
/* Finalize MPI */
MPI_Finalize();
return 0;
}
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