public static double[] local_fem_1d(int order, double[] node_x, double[] node_v,
int sample_num, double[] sample_x)
//****************************************************************************80
//
// Purpose:
//
// LOCAL_FEM_1D evaluates a local finite element function.
//
// Discussion:
//
// A local finite element function is a finite element function
// defined over a single element.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 19 March 2011
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int ORDER, the order of the element.
// 0 <= ORDER. ORDER = 1 means piecewise linear.
//
// Input, double NODE_X[ORDER], the element nodes.
// These must be distinct. Basis function I is 1 when X = NODE_X(I) and 0
// when X is equal to any other node.
//
// Input, double NODE_V[ORDER], the value of the finite element
// function at each node.
//
// Input, int SAMPLE_NUM, the number of sample points.
//
// Input, double SAMPLE_X[SAMPLE_NUM], the sample points at which
// the local finite element function is to be evaluated.
//
// Output, double LOCAL_FEM_1D[SAMPLE_NUM], the values of the local
// finite element basis functions.
//
{
double[] sample_v = new double[sample_num];
for (int sample = 0; sample < sample_num; sample++)
{
double x = sample_x[sample];
double[] phi = LocalBasis.local_basis_1d(order, node_x, x);
sample_v[sample] = typeMethods.r8vec_dot_product(order, node_v, phi);
}
return(sample_v);
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 verifies LOCAL_BASIS_1D.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 June 2011
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// None
//
{
const int NODE_NUM = 4;
double[] node_x =
{
1.0, 2.0, 4.0, 4.5
}
;
double[] phi;
double[] phi_matrix = new double[NODE_NUM * NODE_NUM];
double x;
Console.WriteLine("");
Console.WriteLine("TEST01:");
Console.WriteLine(" LOCAL_BASIS_1D evaluates the local basis functions");
Console.WriteLine(" for a 1D element.");
Console.WriteLine("");
Console.WriteLine(" Test that the basis functions, evaluated at the nodes,");
Console.WriteLine(" form the identity matrix.");
Console.WriteLine("");
Console.WriteLine(" Number of nodes = " + NODE_NUM + "");
Console.WriteLine("");
Console.WriteLine(" Node coordinates:");
Console.WriteLine("");
for (int j = 0; j < NODE_NUM; j++)
{
Console.WriteLine(" " + j.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + node_x[j].ToString(CultureInfo.InvariantCulture).PadLeft(7) + "");
}
for (int j = 0; j < NODE_NUM; j++)
{
x = node_x[j];
phi = LocalBasis.local_basis_1d(NODE_NUM, node_x, x);
for (int i = 0; i < NODE_NUM; i++)
{
phi_matrix[i + j * NODE_NUM] = phi[i];
}
}
typeMethods.r8mat_print(NODE_NUM, NODE_NUM, phi_matrix, " A(I,J) = PHI(I) at node (J):");
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine(" The PHI functions should sum to 1 at random X values:");
Console.WriteLine("");
Console.WriteLine(" X Sum ( PHI(:)(X) )");
Console.WriteLine("");
for (int j = 1; j <= 5; j++)
{
x = UniformRNG.r8_uniform(1.0, 4.5, ref seed);
phi = LocalBasis.local_basis_1d(NODE_NUM, node_x, x);
double s = typeMethods.r8vec_sum(NODE_NUM, phi);
Console.WriteLine(" " + x.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + s.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}