public static void testSFLinearLocal2D() {
NodeList nodes = new NodeList();
nodes.add(new Node(1, 0.0, 0.0));
nodes.add(new Node(2, 0.2, 0.0));
nodes.add(new Node(3, 0.0, 0.2));
Element e = new Element(nodes);
System.out.println("Test coordinate transform and Jacbian on element " + e);
CoordinateTransform trans = new CoordinateTransform(2);
trans.transformLinear2D(e);
trans.computeJacobianMatrix();
trans.computeJacobian2D();
MathFunc jac = trans.getJacobian();
Variable v = new Variable();
v.set("r", 0);
v.set("s", 0);
check(jac.toString(), jac.apply(v), 0.04);
ScalarShapeFunction[] shapeFun = new ScalarShapeFunction[3];
shapeFun[0] = new SFLinearLocal2DRS(1);
shapeFun[1] = new SFLinearLocal2DRS(2);
shapeFun[2] = new SFLinearLocal2DRS(3);
System.out.println("Test the derivatives of shape function SFLinearLocal2DRS:");
double[] rlt = new double[] {-5, -5, 5, 0, 0, 5};
int j = 0;
for (int i = 0; i < 3; i++) {
System.out.println(shapeFun[i]);
shapeFun[i].assignElement(e);
MathFunc SFdx = shapeFun[i].diff("x");
MathFunc SFdy = shapeFun[i].diff("y");
check("shapeFun[" + i + "].diff(\"x\")", SFdx.apply(), rlt[j++]);
check("shapeFun[" + i + "].diff(\"y\")", SFdy.apply(), rlt[j++]);
}
System.out.println("Test the derivatives of shape function SFLinearLocal2D:");
shapeFun[0] = new SFLinearLocal2D(1);
shapeFun[1] = new SFLinearLocal2D(2);
shapeFun[2] = new SFLinearLocal2D(3);
j = 0;
for (int i = 0; i < 3; i++) {
System.out.println(shapeFun[i]);
shapeFun[i].assignElement(e);
MathFunc SFdx = shapeFun[i].diff("x");
MathFunc SFdy = shapeFun[i].diff("y");
check("shapeFun[" + i + "].diff(\"x\")=" + SFdy, SFdx.apply(v), rlt[j++]);
check("shapeFun[" + i + "].diff(\"y\")=" + SFdy, SFdy.apply(v), rlt[j++]);
}
}
public static void testSFBilinearLocal2D() {
NodeList nodes = new NodeList();
nodes.add(new Node(1, -2.0, -2.0));
nodes.add(new Node(2, 2.0, -2.0));
nodes.add(new Node(3, 2.0, 2.0));
nodes.add(new Node(4, -2.0, 2.0));
Element e = new Element(nodes);
System.out.println("Test coordinate transform and Jacbian on element " + e);
CoordinateTransform trans = new CoordinateTransform(2);
trans.transformLinear2D(e);
trans.computeJacobianMatrix();
trans.computeJacobian2D();
MathFunc jac = trans.getJacobian();
Variable v = new Variable();
v.set("r", 0);
v.set("s", 0);
check(jac.toString(), jac.apply(v), 4.0);
ScalarShapeFunction[] shapeFun = new ScalarShapeFunction[4];
shapeFun[0] = new SFBilinearLocal2D(1);
shapeFun[1] = new SFBilinearLocal2D(2);
shapeFun[2] = new SFBilinearLocal2D(3);
shapeFun[3] = new SFBilinearLocal2D(4);
System.out.println("Test the evaluation of SFBilinearLocal2D:");
double[] args = new double[] {0.1, 0.1};
Variable v0 = new Variable();
v0.set("r", args[0]);
v0.set("s", args[1]);
System.out.println(shapeFun[0]);
check(shapeFun[0].toString(), shapeFun[0].apply(v0), 0.2025);
check(shapeFun[0].toString(), shapeFun[0].apply(args), 0.2025);
check(shapeFun[0].toString(), shapeFun[0].compile().apply(args), 0.2025);
System.out.println("Test the derivatives of shape function SFBilinearLocal2D:");
e.updateJacobin();
double[] rlt = new double[] {-0.125, -0.125, 0.125, -0.125, 0.125, 0.125, -0.125, 0.125};
int j = 0;
for (int i = 0; i < 4; i++) {
System.out.println(shapeFun[i]);
shapeFun[i].assignElement(e);
MathFunc SFdx = shapeFun[i].diff("x");
MathFunc SFdy = shapeFun[i].diff("y");
check("shapeFun[" + i + "].diff(\"x\")=" + SFdy, SFdx.apply(v), rlt[j++]);
check("shapeFun[" + i + "].diff(\"y\")=" + SFdy, SFdy.apply(v), rlt[j++]);
}
}