__forceinline__ __device__ float sourceTermWest(float (&U)[height][width],
float (&B)[height][width],
float (&RUx)[height][width],
float (&RBx)[height][width],
unsigned int p, unsigned int q) {
float bx;
float h;
h = U[q][p]-RUx[q][p]-RBx[q][p];
bx = RBx[q][p+1]-RBx[q][p];
return sourceTerm(h, bx);
}
__forceinline__ __device__ float sourceTermSouth(float (&U)[height][width],
float (&B)[height][width],
float (&RUy)[height][width],
float (&RBy)[height][width],
unsigned int p, unsigned int q) {
float bx;
float h;
h = U[q][p]-RUy[q][p]-RBy[q][p];
bx = RBy[q+1][p]-RBy[q][p];
return sourceTerm(h, bx);
}
Domain CN( Domain T )
{
cout << endl << "Iterating domain using CN method..."<<endl;
for( int it = 0; it < T.settings.nsteps; it++)
{
// Starting timer...
clock_t start, end;
double cpu_time_used;
start = clock();
T.updateBC( it );
cout << endl;
cout << "t = " << it << endl;
show_sample( T );
double C = T.settings.dt * T.settings.alpha / 2;
double diag = 1 + 2*C / pow(T.settings.dx, 2) + 2*C / pow(T.settings.dy,2) + 2*C/pow(T.settings.dz,2);
double xdiag = - C / pow(T.settings.dx,2);
double ydiag = - C / pow(T.settings.dy,2);
double zdiag = - C / pow(T.settings.dz,2);
int xs;
int ys;
int zs;
int length = (T.settings.p_x) * (T.settings.p_y) * (T.settings.p_z);
// Creation of A
vector<vector<double> > A;
A.resize(length);
for( int i = 0; i < length; i++ )
{
A[i].resize(length);
for( int j = 0; j < length; j++ )
{
// Main diagonal
if( i == j )
A[i][j] = diag;
// Z diagonals
else if( j == i - 9 )
{
if( i < T.settings.p_x * T.settings.p_y )
A[i][j] = 0;
else
A[i][j] = zdiag;
}
else if( j == i + 9 )
{
if( i > length - T.settings.p_z )
A[i][j] = 0;
else
A[i][j] = zdiag;
}
// Y diagonals
else if( j == i - 3 )
{
if( ( i / T.settings.p_x ) % T.settings.p_y == 0 )
A[i][j] = 0;
else
A[i][j] = ydiag;
}
else if( j == i + 3 )
{
if( ( i / T.settings.p_x ) % T.settings.p_y == T.settings.p_y - 1 )
A[i][j] = 0 ;
else
A[i][j] = ydiag;
}
// X diagonals
else if( j == i - 1 )
{
if( i % T.settings.p_x == 0 )
A[i][j] = 0;
else
A[i][j] = xdiag;
}
else if( j == i + 1 )
{
if( i % T.settings.p_x == T.settings.p_x - 1 )
A[i][j] = 0;
else
A[i][j] = xdiag;
}
else
A[i][j] = 0;
}
}
// Initialization of x
vector<double> x;
x.resize(length);
/*
// print upper left of A
for( int i = 0; i < 20; i++ )
{
if( i % 10 == 0)
cout << endl;
for( int j = 0; j < 20; j++ )
{
if( j % 10 == 0 )
cout << " ";
cout << setw(9) << A[i][j] <<" ";
}
cout << endl;
}
*/
// Initialization / Update of b
vector<double> b;
b.resize(length+1);
for( int i = 0; i < length; i++ )
{
xs = i % T.settings.p_x + 1;
ys = ( i / T.settings.p_x ) % T.settings.p_y + 1;
zs = ( ( i / T.settings.p_x ) / T.settings.p_y ) % T.settings.p_z + 1;
double term1 = C / pow(T.settings.dx,2) * (T.m[xs+1][ys][zs] - 2*T.m[xs][ys][zs] + T.m[xs-1][ys][zs]);
double term2 = C / pow(T.settings.dy,2) * (T.m[xs][ys+1][zs] - 2*T.m[xs][ys][zs] + T.m[xs][ys-1][zs]);
double term3 = C / pow(T.settings.dz,2) * (T.m[xs][ys][zs+1] - 2*T.m[xs][ys][zs] + T.m[xs][ys][zs-1]);
b[i] = T.m[xs][ys][zs] + term1 + term2 + term3 + sourceTerm(xs, ys, zs);
}
// GAUSSIAN ELIMINATION
// GE - upper-triangulate
double scale;
for (int j=0;j<length;++j) /* loop over columns */
for (int i=j+1;i<length;++i) /* loop over rows beneath pivot */
{
if (A[i][j] != 0)
{
scale = A[i][j]/A[j][j]; /* zero out based on pivot */
for (int k=0;k<length;++k)
A[i][k] = A[i][k] - A[j][k]*scale;
b[i] = b[i] - b[j]*scale; /* same for b */
}
}
// GE - Back substitution
x[length-1] = b[length-1]/A[length-1][length-1];
for (int i=length-2;i>=0;--i)
{
x[i] = b[i];
for (int j=i+1;j<length;++j)
{
x[i] -= A[i][j]*x[j];
}
x[i]/=A[i][i];
}
// SOLUTION CALCULATED - stored in x vector.
// loads solution vector (x) back into the 3-D Domain
for( int i = 0; i < length ; i++ )
{
xs = i % T.settings.p_x + 1;
ys = ( i / T.settings.p_x ) % T.settings.p_y + 1;
zs = ( ( i / T.settings.p_x ) / T.settings.p_y ) % T.settings.p_z + 1;
T.m[xs][ys][zs] = x[i];
}
// Ending timer...
end = clock();
cpu_time_used = ( (double) (end - start ) ) / CLOCKS_PER_SEC;
cout << "Iterating Domain of dimension "<<T.settings.p_x<<"x";
cout << T.settings.p_y<<"x"<<T.settings.p_z<<" took ";
cout << cpu_time_used<<" seconds."<<endl;
}
return T;
}
