public NCGrid_Distribution SolveSlow()
{
int m = discretization.Xcount;
int n = discretization.Ycount;
int total_nodes = (m - 2) * (n - 2);
//NCGrid_Distribution dist = new NCGrid_Distribution(boundary_conditions.Bounds, discretization.Xcount, discretization.Ycount);
NCGrid_Distribution dist = discretization.Clone();
dist.ApplyBoundary(boundary_conditions);
Matrix system_matrix = new Matrix(total_nodes, total_nodes);
Matrix RHS = new Matrix(total_nodes, 1);
int neg_y = 0;
int pos_y = 0;
int neg_x = 0;
int pos_x = 0;
int body = 0;
int ll_corner = 0;
int lr_corner = 0;
int ur_corner = 0;
int ul_corner = 0;
List <string> indices = new List <string>();
if (console_output)
{
Console.WriteLine("Populating linear system...");
}
for (int i = 1; i < m - 1; i++)
{
if (console_output && i % (m - 1) / 13 == 0)
{
Console.WriteLine((100 * i / (m - 1)).ToString() + "%");
}
for (int j = 1; j < n - 1; j++)
{
double rhs_here = 0;
indices.Add(i.ToString() + "," + j.ToString());
//for now, assume zero forcing function.
BoundaryCase _case;
bool interior = !isCloseToBoundary(i, j, m, n, out _case);
int surplusi = 1;
int surplusj = 1;
Matrix b = dist.GetTaylorSystemCoeffs(i, j, surplusi, surplusj);
double uijterm = 0;
double ui1jterm = 0;
double uij1term = 0;
double ui_1jterm = 0;
double uij_1term = 0;
double usurplusterm = 0;
int row = (m - 2) * (i - 1) + j - 1;
for (int h = 0; h < 5; h++)
{
ui1jterm += b[h, 0] * lin_operator[h];
uij1term += b[h, 1] * lin_operator[h];
ui_1jterm += b[h, 2] * lin_operator[h];
uij_1term += b[h, 3] * lin_operator[h];
usurplusterm += b[h, 4] * lin_operator[h];
double temp_ij = 0;
for (int k = 0; k < 5; k++)
{
temp_ij += b[h, k];
}
uijterm += lin_operator[h] * temp_ij;
}
switch (_case)
{
case BoundaryCase.NegativeYBoundary:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
uij_1term = 0;
neg_y++;
break;
}
case BoundaryCase.PositiveYBoundary:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
uij1term = 0;
pos_y++;
break;
}
case BoundaryCase.NegativeXBoundary:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
ui_1jterm = 0;
neg_x++;
break;
}
case BoundaryCase.PositiveXBoundary:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
ui1jterm = 0;
pos_x++;
break;
}
case BoundaryCase.ULCorner:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
uij1term = 0;
ui_1jterm = 0;
usurplusterm = 0;
ul_corner++;
break;
}
case BoundaryCase.LLCorner:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i, j - 1].Value * uij_1term;
ui_1jterm = 0;
uij_1term = 0;
ll_corner++;
break;
}
case BoundaryCase.URCorner:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
ui1jterm = 0;
uij1term = 0;
usurplusterm = 0;
ur_corner++;
break;
}
case BoundaryCase.LRCorner:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusj, j + surplusj].Value * usurplusterm;
uij_1term = 0;
ui1jterm = 0;
usurplusterm = 0;
lr_corner++;
break;
}
case BoundaryCase.Body:
{
body++;
break;
}
}
system_matrix[row, map2Dto1D(i - 1, j - 1, m - 1, n - 1)] = -1 * uijterm;
if (ui1jterm != 0)
{
system_matrix[row, map2Dto1D(i, j - 1, m - 1, n - 1)] = ui1jterm;
}
if (uij1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j, m - 1, n - 1)] = uij1term;
}
if (ui_1jterm != 0)
{
system_matrix[row, map2Dto1D(i - 2, j - 1, m - 1, n - 1)] = ui_1jterm;
}
if (uij_1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j - 2, m - 1, n - 1)] = uij_1term;
}
if (usurplusterm != 0)
{
system_matrix[row, map2Dto1D(i - 1 + surplusi, j - 1 + surplusj, m - 1, n - 1)] = usurplusterm;
}
RHS[row] = rhs_here;
}
}
if (console_output)
{
Console.WriteLine("System populated.");
}
Matrix results = Matrix.solve_system(system_matrix, RHS, Matrix.SystemSolvingScheme.Basic, true, true);
for (int i = 0; i < total_nodes; i++)
{
int offset = n - 2;
int J = i % offset;
int I = (i - J) / offset;
dist.assign_value_at(I + 1, J + 1, results[i]);
}
return(dist);
}
private void buildsystem(out Matrix system_matrix, out Matrix RHS)
{
int m = discretization.Xcount;
int n = discretization.Ycount;
int total_nodes = (m - 2) * (n - 2);
NCGrid_Distribution dist = discretization.Clone();
dist.ApplyBoundary(boundary_conditions);
system_matrix = new Matrix(total_nodes, total_nodes);
RHS = new Matrix(total_nodes, 1);
int neg_y = 0;
int pos_y = 0;
int neg_x = 0;
int pos_x = 0;
int body = 0;
int ll_corner = 0;
int lr_corner = 0;
int ur_corner = 0;
int ul_corner = 0;
if (console_output)
{
Console.WriteLine("Populating linear system...");
}
for (int i = 1; i < m - 1; i++)
{
if (console_output && i % (m - 1) / 13 == 0)
{
Console.WriteLine((100 * i / (m - 1)).ToString() + "%");
}
for (int j = 1; j < n - 1; j++)
{
double rhs_here = 0;
//for now, assume zero forcing function.
BoundaryCase _case;
bool interior = !isCloseToBoundary(i, j, m, n, out _case);
int surplusi = 1;
int surplusj = 1;
Matrix b = dist.GetTaylorSystemCoeffs(i, j, surplusi, surplusj);
double uijterm = 0;
double ui1jterm = 0;
double uij1term = 0;
double ui_1jterm = 0;
double uij_1term = 0;
double usurplusterm = 0;
int row = (m - 2) * (i - 1) + j - 1;
for (int h = 0; h < 5; h++)
{
ui1jterm += b[h, 0] * lin_operator[h];
uij1term += b[h, 1] * lin_operator[h];
ui_1jterm += b[h, 2] * lin_operator[h];
uij_1term += b[h, 3] * lin_operator[h];
usurplusterm += b[h, 4] * lin_operator[h];
double temp_ij = 0;
for (int k = 0; k < 5; k++)
{
temp_ij += b[h, k];
}
uijterm += lin_operator[h] * temp_ij;
}
switch (_case)
{
case BoundaryCase.NegativeYBoundary:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
uij_1term = 0;
neg_y++;
break;
}
case BoundaryCase.PositiveYBoundary:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
uij1term = 0;
pos_y++;
break;
}
case BoundaryCase.NegativeXBoundary:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
ui_1jterm = 0;
neg_x++;
break;
}
case BoundaryCase.PositiveXBoundary:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
ui1jterm = 0;
pos_x++;
break;
}
case BoundaryCase.ULCorner:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
uij1term = 0;
ui_1jterm = 0;
usurplusterm = 0;
ul_corner++;
break;
}
case BoundaryCase.LLCorner:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i, j - 1].Value * uij_1term;
ui_1jterm = 0;
uij_1term = 0;
ll_corner++;
break;
}
case BoundaryCase.URCorner:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
ui1jterm = 0;
uij1term = 0;
usurplusterm = 0;
ur_corner++;
break;
}
case BoundaryCase.LRCorner:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusj, j + surplusj].Value * usurplusterm;
uij_1term = 0;
ui1jterm = 0;
usurplusterm = 0;
lr_corner++;
break;
}
case BoundaryCase.Body:
{
body++;
break;
}
}
system_matrix[row, map2Dto1D(i - 1, j - 1, m - 1, n - 1)] = -1 * uijterm;
if (ui1jterm != 0)
{
system_matrix[row, map2Dto1D(i, j - 1, m - 1, n - 1)] = ui1jterm;
}
if (uij1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j, m - 1, n - 1)] = uij1term;
}
if (ui_1jterm != 0)
{
system_matrix[row, map2Dto1D(i - 2, j - 1, m - 1, n - 1)] = ui_1jterm;
}
if (uij_1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j - 2, m - 1, n - 1)] = uij_1term;
}
if (usurplusterm != 0)
{
system_matrix[row, map2Dto1D(i - 1 + surplusi, j - 1 + surplusj, m - 1, n - 1)] = usurplusterm;
}
RHS[row] = rhs_here;
}
}
if (console_output)
{
Console.WriteLine("System populated.");
}
}