private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 carries out test case #3.
//
// Discussion:
//
// Use A3, C3, F3, EXACT3, EXACT_UX3, EXACT_UX3.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 07 July 2014
//
// Author:
//
// John Burkardt
//
{
int i;
int j;
const int nx = 5;
const int ny = 5;
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" Solve - del ( A del U ) + C U = F ");
Console.WriteLine(" on the unit square with zero boundary conditions.");
Console.WriteLine(" A1(X,Y) = 0.0");
Console.WriteLine(" C1(X,Y) = 1.0");
Console.WriteLine(" F1(X,Y) = X * ( 1 - X ) * Y * ( 1 - Y )");
Console.WriteLine(" U1(X,Y) = X * ( 1 - X ) * Y * ( 1 - Y )");
Console.WriteLine("");
Console.WriteLine(" This example is contrived so that the system matrix");
Console.WriteLine(" is the WATHEN matrix.");
Console.WriteLine("");
Console.WriteLine(" Number of X grid values NX = " + nx + "");
Console.WriteLine(" Number of Y grid values NY = " + ny + "");
//
// Geometry definitions.
//
const double x_first = 0.0;
const double x_last = 1.0;
double[] x = typeMethods.r8vec_linspace_new(nx, x_first, x_last);
const double y_first = 0.0;
const double y_last = 1.0;
double[] y = typeMethods.r8vec_linspace_new(ny, y_first, y_last);
double[] u = FEM_2D_BVP_Serene.fem2d_bvp_serene(nx, ny, a3, c3, f3, x, y, true);
switch (nx * ny)
{
case <= 25:
{
Console.WriteLine("");
Console.WriteLine(" I J X Y U Uexact Error");
Console.WriteLine("");
int k = 0;
for (j = 0; j < ny; j++)
{
int inc = (j % 2) switch
{
0 => 1,
_ => 2
};
for (i = 0; i < nx; i += inc)
{
double uexact = exact3(x[i], y[j]);
Console.WriteLine(i.ToString(CultureInfo.InvariantCulture).PadLeft(4) + " "
+ j.ToString(CultureInfo.InvariantCulture).PadLeft(4) + " "
+ x[i].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ y[j].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ u[k].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ uexact.ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ Math.Abs(u[k] - uexact).ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
k += 1;
}
}
break;
}
}
double e1 = FEM_2D_BVP_Serene.fem2d_l1_error_serene(nx, ny, x, y, u, exact3);
double e2 = FEM_2D_BVP_Serene.fem2d_l2_error_serene(nx, ny, x, y, u, exact3);
double h1s = FEM_2D_BVP_Serene.fem2d_h1s_error_serene(nx, ny, x, y, u, exact_ux3, exact_uy3);
Console.WriteLine("");
Console.WriteLine(" l1 norm of error = " + e1 + "");
Console.WriteLine(" L2 norm of error = " + e2 + "");
Console.WriteLine(" Seminorm of error = " + h1s + "");
//
// Pull out the Wathen matrix from MATLAB.
// It will have been multiplied by a random scale factor.
// While my numbering scheme is
// 3 2 1
// 4 8
// 5 6 7
// the numbering scheme used here is
// 1 2 3
// 4 5
// 6 7 8
//
double[] amat = WathenMatrix.wathen(1, 1, 8);
double scale = 0.5 * amat[0 + 2 * 8];
for (j = 0; j < 8; j++)
{
for (i = 0; i < 8; i++)
{
amat[i + j * 8] /= scale;
}
}
typeMethods.r8mat_print(8, 8, amat, " Wathen matrix:");
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 carries out test case #1.
//
// Discussion:
//
// Use A1, C1, F1, EXACT1, EXACT_UX1, EXACT_UX1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 07 July 2014
//
// Author:
//
// John Burkardt
//
{
const int nx = 5;
const int ny = 5;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Solve - del ( A del U ) + C U = F ");
Console.WriteLine(" on the unit square with zero boundary conditions.");
Console.WriteLine(" A1(X,Y) = 1.0");
Console.WriteLine(" C1(X,Y) = 0.0");
Console.WriteLine(" F1(X,Y) = 2*X*(1-X)+2*Y*(1-Y)");
Console.WriteLine(" U1(X,Y) = X * ( 1 - X ) * Y * ( 1 - Y )");
Console.WriteLine("");
Console.WriteLine(" Number of X grid values NX = " + nx + "");
Console.WriteLine(" Number of Y grid values NY = " + ny + "");
//
// Geometry definitions.
//
double x_first = 0.0;
double x_last = 1.0;
double[] x = typeMethods.r8vec_linspace_new(nx, x_first, x_last);
const double y_first = 0.0;
const double y_last = 1.0;
double[] y = typeMethods.r8vec_linspace_new(ny, y_first, y_last);
const bool show11 = false;
double[] u = FEM_2D_BVP_Serene.fem2d_bvp_serene(nx, ny, a1, c1, f1, x, y, show11);
switch (nx * ny)
{
case <= 25:
{
Console.WriteLine("");
Console.WriteLine(" I J X Y U Uexact Error");
Console.WriteLine("");
int k = 0;
int j;
for (j = 0; j < ny; j++)
{
int inc = (j % 2) switch
{
0 => 1,
_ => 2
};
int i;
for (i = 0; i < nx; i += inc)
{
double uexact = exact1(x[i], y[j]);
Console.WriteLine(i.ToString(CultureInfo.InvariantCulture).PadLeft(4) + " "
+ j.ToString(CultureInfo.InvariantCulture).PadLeft(4) + " "
+ x[i].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ y[j].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ u[k].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ uexact.ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ Math.Abs(u[k] - uexact).ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
k += 1;
}
}
break;
}
}
double e1 = FEM_2D_BVP_Serene.fem2d_l1_error_serene(nx, ny, x, y, u, exact1);
double e2 = FEM_2D_BVP_Serene.fem2d_l2_error_serene(nx, ny, x, y, u, exact1);
double h1s = FEM_2D_BVP_Serene.fem2d_h1s_error_serene(nx, ny, x, y, u, exact_ux1, exact_uy1);
Console.WriteLine("");
Console.WriteLine(" l1 norm of error = " + e1 + "");
Console.WriteLine(" L2 norm of error = " + e2 + "");
Console.WriteLine(" Seminorm of error = " + h1s + "");
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 checks the basis functions.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 07 July 2014
//
// Author:
//
// John Burkardt
//
{
int i;
double xq;
double[] xx =
{
2.0, 1.0, 0.0, 0.0, 0.0, 1.0, 2.0, 2.0
}
;
double yq;
double[] yy =
{
5.0, 5.0, 5.0, 4.0, 3.0, 3.0, 3.0, 4.0
}
;
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" Basis function checks.");
//
// Check that V is identity matrix at nodes.
//
Console.WriteLine("");
Console.WriteLine(" The matrix Aij = V(j)(X(i),Y(i)) should be the identity.");
Console.WriteLine("");
double xw = 0.0;
double ys = 3.0;
double xe = 2.0;
double yn = 5.0;
for (i = 0; i < 8; i++)
{
xq = xx[i];
yq = yy[i];
FEM_2D_BVP_Serene.basis_serene(xq, yq, xw, ys, xe, yn, xx, yy);
int j;
for (j = 0; j < 8; j++)
{
}
Console.WriteLine("");
}
//
// Check that VX and VY sum to zero anywhere.
//
Console.WriteLine("");
Console.WriteLine(" The vectors dVdX(1:8)(X,Y) and dVdY(1:8)(X,Y)");
Console.WriteLine(" should both sum to zero for any (X,Y).");
int seed = 123456789;
xq = 2.0 * UniformRNG.r8_uniform_01(ref seed);
yq = 3.0 + 2.0 * UniformRNG.r8_uniform_01(ref seed);
xw = 0.0;
ys = 3.0;
xe = 2.0;
yn = 5.0;
double[] vx = FEM_2D_BVP_Serene.basis_dx_serene(xq, yq, xw, ys, xe, yn, xx, yy);
double[] vy = FEM_2D_BVP_Serene.basis_dy_serene(xq, yq, xw, ys, xe, yn, xx, yy);
Console.WriteLine("");
Console.WriteLine(" Random evaluation point is (" + xq + "," + yq + ")");
Console.WriteLine("");
Console.WriteLine(" dVdX dVdY");
Console.WriteLine("");
for (i = 0; i < 8; i++)
{
Console.WriteLine(i.ToString(CultureInfo.InvariantCulture).PadLeft(6) + " "
+ vx[i].ToString(CultureInfo.InvariantCulture).PadLeft(10) + " "
+ vy[i].ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
}
Console.WriteLine("");
Console.WriteLine(" Sum: "
+ typeMethods.r8vec_sum(8, vx).ToString(CultureInfo.InvariantCulture).PadLeft(10) + " "
+ typeMethods.r8vec_sum(8, vy).ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
}
