public NCGrid_Distribution solve_iterative_morph(int max_morph_count, double size)
{
NCGrid_Distribution soln = Solve();
for (int i = 0; i < max_morph_count - 1; i++)
{
soln.QuickSketch("soln-" + i.ToString());
soln.ApplyMeshMorphGA(size);
discretization = soln.Clone();
soln = Solve();
}
return(soln);
}
public static NCGrid_Distribution MakeMagnitude(NCGrid_Distribution A, NCGrid_Distribution B)
{
NCGrid_Distribution output = A.Clone();
for (int i = 0; i < A.Xcount; i++)
{
for (int j = 0; j < B.Ycount; j++)
{
double x = A[i, j].Value;
double y = B[i, j].Value;
output.assign_value_at(i, j, Math.Sqrt((x * x) + (y * y)));
}
}
output.force_extrema_update();
return(output);
}
public NCGrid_Distribution Solve()
{
int m = discretization.Xcount;
int n = discretization.Ycount;
int total_nodes = (m - 2) * (n - 2);
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;
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.");
}
Matrix results = RunExteriorSolve(system_matrix, RHS);
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);
}
static void testfunction()
{
Console.WriteLine("Press enter to begin, or enter \"c\" to clear repos.");
if (Console.ReadLine() == "c")
{
RepoManagement.ClearRepo(Paths.DistributionRepo, Paths.ImageRepo);
}
DateTime then = DateTime.Now;
Console.WriteLine("Solving...");
double L = 10;
double H = 10;
int n = 38;
RBounds2D bounds = new RBounds2D(0, L, 0, H);
NCGrid_Distribution dist = new NCGrid_Distribution(bounds, n, n);
BoundaryConditions conditions = new BoundaryConditions(bounds, n, n, BoundaryConditions.BoundaryConditionType.Dirichlet);
double dx = L / (n - 1);
double max = 5;
string fxn = string.Format("{0}*Sin({1}*x/{2})*(Exp({1}*y/{2}) - Exp(-1*{1}*y/{2}))/(Exp({1}*{3}/{2}) - Exp(-1*{1}*{3}/{2}))", max, Math.PI, L, H);
conditions.SetConstant(0, BoundaryConditions.Direction.Negative_X);
conditions.SetConstant(0, BoundaryConditions.Direction.Negative_Y);
conditions.SetConstant(0, BoundaryConditions.Direction.Positive_Y);
for (int i = 0; i < n; i++)
{
double x = i * dx;
double z = max * Math.Sin(Math.PI * x / L);
conditions[i, BoundaryConditions.Direction.Positive_Y] = z;
}
int solcount = 50;
double[] errors = new double[solcount];
double[] iteration = new double[solcount];
DistributionSketchSettings S = DistributionSketchSettings.Fancy();
S.SetFigureTitle("Temperature Distribution");
for (int i = 0; i < solcount; i++)
{
Console.WriteLine(i.ToString() + " of " + solcount.ToString() + " iterations processed.");
iteration[i] = i;
BVPLinear2D problem = new BVPLinear2D(conditions, LinearOperatorOrder2.Laplace, dist);
problem.EnableConsoleOutput();
NCGrid_Distribution soln = problem.Solve(Matrix.SystemSolvingScheme.Kaczmarz);
NCGrid_Distribution analytic = ExactFunctionGeneratorVB2D.GenerateFunctionToGrid(fxn, soln);
soln.ApplyMeshMorphGA(15);
errors[i] = ErrorEstimation.NormDifference(soln, analytic);
string title = "iterative-" + i.ToString();
soln.WriteToFile(title);
DistributionSketch2D sketch = new DistributionSketch2D(soln, S);
dist = soln.Clone();
sketch.CreateSketch(true);
sketch.SaveImage(title + "-plot", false);
}
List <string> filestuff = new List <string>();
for (int i = 0; i < iteration.Length; i++)
{
filestuff.Add(iteration[i].ToString() + "," + errors[i].ToString());
}
File.WriteAllLines(@"C:\Users\Will\Desktop\Folders\MATH435\repo\curves-1d\errors-temp.csv", filestuff.ToArray());
Console.WriteLine("Done.");
Console.ReadLine();
}
static void testfunction3()
{
Console.WriteLine("Press enter to begin, or enter \"c\" to clear repos.");
if (Console.ReadLine() == "c")
{
RepoManagement.ClearRepo(Paths.DistributionRepo, Paths.ImageRepo);
}
DateTime then = DateTime.Now;
Console.WriteLine("Solving...");
double L = 10;
double H = 10;
int n = 26;
RBounds2D bounds = new RBounds2D(0, L, 0, H);
NCGrid_Distribution dist = new NCGrid_Distribution(bounds, n, n);
BoundaryConditions conditions = new BoundaryConditions(bounds, n, n, BoundaryConditions.BoundaryConditionType.Dirichlet);
double dx = L / (n - 1);
double omega = 4;
double max = 8;
conditions.SetConstant(0, BoundaryConditions.Direction.Negative_X);
conditions.SetConstant(0, BoundaryConditions.Direction.Negative_Y);
for (int i = 0; i < n; i++)
{
double x = i * dx;
double y = i * dx;
double ybound = max / (1 + Math.Exp(-1 * (omega * x / L)));
double xbound = max / (1 + Math.Exp(-1 * (omega * y / H)));
conditions[i, BoundaryConditions.Direction.Positive_Y] = ybound;
conditions[i, BoundaryConditions.Direction.Positive_X] = xbound;
}
int solcount = 15;
LinearOperatorOrder2 op = LinearOperatorOrder2.Laplace;
DistributionSketchSettings S = DistributionSketchSettings.Fancy();
S.SetFigureTitle("Double Logistic Boundary");
for (int i = 0; i < solcount; i++)
{
Console.WriteLine(i.ToString() + " of " + solcount.ToString() + " iterations processed.");
BVPLinear2D problem = new BVPLinear2D(conditions, op, dist);
problem.EnableConsoleOutput();
NCGrid_Distribution soln = problem.SolveSRDD();
string title = "iterative-" + i.ToString();
soln.WriteToFile(title);
DistributionSketch2D sketch = new DistributionSketch2D(soln, S);
dist = soln.Clone();
sketch.CreateSketch(true);
sketch.SaveImage(title + "-plot", false);
//dist.ApplyMeshMorphGA(2, 0.0019);
Random R = new Random();
for (int h = 1; h < dist.Xcount - 1; h++)
{
for (int k = 1; k < dist.Ycount - 1; k++)
{
double ddx = (0.5 - R.NextDouble()) * dx * 0.6;
double ddy = (0.5 - R.NextDouble()) * dx * 0.6;
Vector3 move = new Vector3(ddx, ddy, 0);
dist[h, k] = dist[h, k] + move;
}
}
}
Console.WriteLine("Done.");
Console.ReadLine();
}
