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BytecodeFuncImpFEM.java
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221 lines (200 loc) · 6.62 KB
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package symjava.bytecode;
import static edu.uta.futureye.function.FMath.grad;
import static edu.uta.futureye.function.FMath.pow;
import static edu.uta.futureye.function.FMath.r;
import static edu.uta.futureye.function.FMath.s;
import static edu.uta.futureye.function.FMath.t;
import static edu.uta.futureye.function.FMath.x;
import static edu.uta.futureye.function.FMath.y;
import java.util.HashMap;
import java.util.Map;
import edu.uta.futureye.bytecode.CompiledFunc;
import edu.uta.futureye.core.Element;
import edu.uta.futureye.core.Node;
import edu.uta.futureye.function.basic.FX;
import edu.uta.futureye.function.intf.MathFunc;
import edu.uta.futureye.lib.shapefun.SFLinearLocal2DRS;
import edu.uta.futureye.util.container.NodeList;
public class BytecodeFuncImpFEM implements BytecodeFunc {
public static double eps = 1e-5;
static double[] triW = {
0.06296959,
0.06619708,
0.06296959,
0.06619708,
0.06296959,
0.06619708,
0.11250000
};
static double[] triR = {
0.10128651,
0.47014206,
0.79742699,
0.47014206,
0.10128651,
0.05971587,
0.33333333
};
static double[] triS = {
0.10128651,
0.05971587,
0.10128651,
0.47014206,
0.79742699,
0.47014206,
0.33333333
};
public static void check(String info, double d1, double d2) {
if(Math.abs(d1-d2) < eps) {
System.out.println("pass");
} else {
System.out.println("!!!FAIL!!! "+d1+"!="+d2+" "+info);
}
}
public static double intOnTriangleRefElement(CompiledFunc integrand, double[] params, int paramPos, int order) {
double rlt = 0.0;
if(order == 2) {
params[paramPos] = 0.333333333333333;
params[paramPos+1] = 0.333333333333333;
params[paramPos+2] = 0.333333333333333;
rlt = 0.5*integrand.apply(params);
} else if(order == 3) {
params[paramPos] = 0.5; params[paramPos+1] = 0.5; params[paramPos+2] = 0.0;
double pv1 = integrand.apply(params);
params[paramPos] = 0.0; params[paramPos+1] = 0.5; params[paramPos+2] = 0.5;
double pv2 = integrand.apply(params);
params[paramPos] = 0.5; params[paramPos+1] = 0.0; params[paramPos+2] = 0.5;
double pv3 = integrand.apply(params);
rlt = 0.5*0.333333333333333*(pv1 + pv2 + pv3);
} else if(order == 4) {
double w123 = 25.0/48.0;
double w4 = -27.0/48.0;
params[paramPos] = 0.6; params[paramPos+1] = 0.2; params[paramPos+2] = 0.2;
double pv1 = integrand.apply(params);
params[paramPos] = 0.2; params[paramPos+1] = 0.6; params[paramPos+2] = 0.2;
double pv2 = integrand.apply(params);
params[paramPos] = 0.2; params[paramPos+1] = 0.2; params[paramPos+2] = 0.6;
double pv3 = integrand.apply(params);
params[paramPos] = 0.333333333333333; params[paramPos+1] = 0.333333333333333; params[paramPos+2] = 0.333333333333333;
double pv4 = 0.5*integrand.apply(params);
rlt = 0.5*w123*(pv1 + pv2 + pv3) + w4*pv4;
} else if(order == 5) {
for(int i=0;i<7;i++) {
params[paramPos] = triR[i];
params[paramPos+1] = triS[i];
params[paramPos+2] = 1.0-triR[i]-triS[i];
rlt += triW[i]*integrand.apply(params);
}
}
return rlt;
}
public static void solveLaplace(double[] nodesData) {
int nEle = (int)nodesData[0];
NodeList nodes = new NodeList();
/**
* |\
* | \
* ----
*/
nodes.add(new Node(1, 1.0,1.0));
nodes.add(new Node(2, 2.0,1.0));
nodes.add(new Node(3, 1.0,2.0));
Element e = new Element(nodes);
e.updateJacobin();
MathFunc jac = e.getJacobin();
System.out.println(jac.compile().apply());
System.out.println(jac.apply());
SFLinearLocal2DRS[] sf = new SFLinearLocal2DRS[3];
sf[0] = new SFLinearLocal2DRS(1);
sf[1] = new SFLinearLocal2DRS(2);
sf[2] = new SFLinearLocal2DRS(3);
for(int i=0; i<3; i++)
sf[i].assignElement(e);
//Construct a function with the coordinate of points in an element as parameters
String[] argsOrder = new String[]{"x1","x2","x3","y1","y2","y3","r","s","t"};
FX x1 = new FX("x1");
FX x2 = new FX("x2");
FX x3 = new FX("x3");
FX y1 = new FX("y1");
FX y2 = new FX("y2");
FX y3 = new FX("y3");
MathFunc fx = x1*r + x2*s + x3*t;
MathFunc fy = y1*r + y2*s + y3*t;
// MathFunc ff = fx*fy;
// MathFunc f = sin(PI*x)*sin(PI*y)*pow(E, -0.2);
MathFunc f = 4*pow(x,4)*pow(y,4);
// MathFunc f = 4*(x*x*x*x + y*y*y*y);
Map<String, MathFunc> map = new HashMap<String, MathFunc>();
map.put("x", fx);
map.put("y", fy);
MathFunc ff = f.compose(map);
MathFunc[][] lhs = new MathFunc[3][3];
MathFunc[] rhs = new MathFunc[3];
for(int j=0; j<3; j++) {
MathFunc v = sf[j];
for(int i=0; i<3; i++) {
MathFunc u = sf[i];
//lhs[j][i] = (u.diff("x")*v.diff("x")+u.diff("y")*v.diff("y") + u*v)*jac;
lhs[j][i] = (grad(u,"x","y").dot(grad(v,"x","y")) + u*v)*jac;
}
rhs[j] = v*ff*jac;
rhs[j].setName("RHS"+j);
}
CompiledFunc[][] clhs = new CompiledFunc[3][3];
CompiledFunc[] crhs = new CompiledFunc[3];
for(int j=0; j<3; j++) {
for(int i=0; i<3; i++) {
clhs[j][i] = lhs[j][i].compile(argsOrder);
}
crhs[j] = rhs[j].compile(argsOrder);
}
double[][] A = new double[3][3];
double[] b = new double[3];
double[] params = new double[9];
double[] coords = e.getNodeCoords();
System.arraycopy(coords, 0, params, 0, coords.length);
long start = System.currentTimeMillis();
for(int k=0; k<nEle; k++) {
for(int j=0; j<3; j++) {
for(int i=0; i<3; i++) {
A[j][i] += intOnTriangleRefElement(clhs[j][i], params, coords.length, 3);
}
b[j] += intOnTriangleRefElement(crhs[j], params, coords.length, 3);
}
}
System.out.println(System.currentTimeMillis()-start);
for(int j=0; j<3; j++) {
for(int i=0; i<3; i++) {
System.out.print(A[j][i]+" ");
}
System.out.println();
}
for(int j=0; j<3; j++) {
System.out.println(b[j]);
}
/*
*
* 1.4999999999999984 0.0 -1.4999999999999984
0.0 0.9999999999999989 -0.9999999999999989
-1.4999999999999984 -0.9999999999999989 2.4999999999999973
0.8749999999999991
0.8749999999999991
-1.7499999999999982
Correct: (add setArgIdx() in FComposite)
1.0833333333333321 -0.45833333333333287 -0.45833333333333287
-0.45833333333333287 0.5833333333333327 0.04166666666666662
-0.45833333333333287 0.04166666666666662 0.5833333333333327
0.24999999999999972
0.31249999999999967
0.31249999999999967
*/
}
public static void main(String[] args) {
solveLaplace(new double[]{100});
}
@Override
public double apply(double... args) {
solveLaplace(args);
return args[0];
}
}