@Override
public double apply(Variable v) {
double r = v.get(VN.r);
double s = v.get(VN.s);
double t = v.get(VN.t);
return (vt[funIndex][0] * r + 1.0)
* (vt[funIndex][1] * s + 1.0)
* (vt[funIndex][2] * t + 1.0)
/ 8.0;
}
public static void plotFunction(Mesh mesh, Function fun, String fileName) {
NodeList list = mesh.getNodeList();
int nNode = list.size();
Variable var = new Variable();
Vector v = new SparseVectorHashMap(nNode);
for (int i = 1; i <= nNode; i++) {
Node node = list.at(i);
var.setIndex(node.globalIndex);
var.set("x", node.coord(1));
var.set("y", node.coord(2));
v.set(i, fun.value(var));
}
plotVector(mesh, v, fileName);
}
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++]);
}
}
@Override
public double apply(Variable v) {
double r = v.get(VN.r);
double s = v.get(VN.s);
double t = v.get(VN.t);
double cr = vt[funIndex][0];
double cs = vt[funIndex][1];
double ct = vt[funIndex][2];
if ("r".equals(var)) return cr * (cs * s + 1.0) * (ct * t + 1.0) / 8.0;
else if ("s".equals(var)) return (cr * r + 1.0) * cs * (ct * t + 1.0) / 8.0;
else if ("t".equals(var)) return (cr * r + 1.0) * (cs * s + 1.0) * ct / 8.0;
else throw new FutureyeException("");
}
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++]);
}
}
@Override
public double value(Variable v) {
double x = v.get("x");
double y = v.get("y");
if (Math.sqrt(x * x + y * y) < 0.5) return 1.0;
else return 8.0;
}
public void imposeDirichletCondition(SparseBlockMatrix BM, SparseBlockVector BV, Function diri) {
ElementList eList = mesh.getElementList();
int nNode = mesh.getNodeList().size();
for (int i = 1; i <= eList.size(); i++) {
Element e = eList.at(i);
DOFList DOFs = e.getAllDOFList(DOFOrder.NEFV);
for (int j = 1; j <= DOFs.size(); j++) {
DOF dof = DOFs.at(j);
GeoEntity ge = dof.getOwner();
if (ge instanceof Node) {
Node n = (Node) ge;
if (n.getNodeType() == NodeType.Dirichlet) {
Variable v = Variable.createFrom(diri, n, 0);
setDirichlet(BM, BV, dof.getGlobalIndex(), diri.value(v));
setDirichlet(BM, BV, nNode + dof.getGlobalIndex(), diri.value(v));
setDirichlet(BM, BV, nNode * 2 + dof.getGlobalIndex(), diri.value(v));
}
}
}
}
}
@Override
public double value(Variable v) {
double x = v.get("x");
double y = v.get("y");
return (x * x + y * y) / 8.0 + 7.0 / 32.0;
}
public void gaussNewtonIterate() {
// 初值
NodeList nodes = mesh.getNodeList();
// 初始q=q0
Vector q0 = new SparseVectorHashMap(nodes.size());
Vector q00 = new SparseVectorHashMap(nodes.size());
for (int i = 1; i <= nodes.size(); i++) {
Node node = nodes.at(i);
if (node.getNodeType() == NodeType.Dirichlet)
q0.set(i, this.coef_q.value(Variable.createFrom(coef_q, node, 0)));
else {
// q0.set(i,this.coef_q.value(Variable.createFrom(coef_q, node, 0))+1.0+Math.random()*0.9);
// q0.set(i,1.0+Math.random()*0.9);
double x = node.coord(1);
double y = node.coord(2);
if (Math.sqrt((x) * (x) + (y) * (y)) < 0.5) {
q0.set(i, 3.0);
// =1的圆位置偏移
// if(Math.sqrt((x-0.3)*(x-0.3)+(y)*(y))<0.5) {
// q0.set(i,1.0);
} else {
q0.set(i, 8.0);
}
}
q00.set(
i, this.coef_q.value(Variable.createFrom(coef_q, node, 0)) + 1.0 + Math.random() * 0.9);
}
plotVector(mesh, q0, "q0.dat");
plotVector(mesh, q00, "q00.dat");
// 初始u=u0, lambda=lambda0，从q00计算而来
Vector u0 = this.solveStateEquation(q0); // q00
plotVector(mesh, u0, "u0.dat");
Vector lambda0 = this.solveAdjointEquation(u0, q0); // q00
plotVector(mesh, lambda0, "lambda0.dat");
// 强制u0=0,lambda0=0
// q0 = new SparseVectorHashMap(nodes.size(),1.0);
// u0 = new SparseVectorHashMap(nodes.size(),0.0);
// lambda0 = new SparseVectorHashMap(nodes.size(),0.0);
SparseBlockVector f = new SparseBlockVector(3);
// 迭代求解
for (int iter = 0; iter < 50; iter++) {
iterNum = iter;
SparseBlockMatrix BM = this.getSearchDirectionMatrix(u0, q0);
f.setBlock(1, this.getResLu(u0, lambda0, q0).scale(-1.0));
f.setBlock(2, this.getResLlmd(u0, q0).scale(-1.0)); // bugfix lambda0->q0
f.setBlock(3, this.getResLq(u0, lambda0, q0).scale(-1.0));
// 设置边界条件并求解
// 需要交换矩阵BM的第1, 2列，然后设置边界条件，这样使得矩阵A, A'可逆
// BlockMatrix newBM = this.changeBlockColumn(BM, 1, 2);
// this.imposeDirichletCondition(newBM, f, FC.c0);
// SchurComplementLagrangianSolver solver =
// new SchurComplementLagrangianSolver(BM, f,mesh);
// BlockVector x = solver.solve();
this.imposeDirichletCondition(BM, f, FC.C0);
SolverJBLAS sol = new SolverJBLAS();
SparseBlockVector x = sol.solveDGESV(BM, f);
plotVector(mesh, x.getBlock(1), String.format("delta_u%02d.dat", iter));
plotVector(mesh, x.getBlock(2), String.format("delta_lambda%02d.dat", iter));
plotVector(mesh, x.getBlock(3), String.format("delta_q%02d.dat", iter));
// 待定，与beta选取有关
// double stepLength = 0.01;
// double stepLength = 0.3;
// double stepLength = 0.00005;
double stepLength = 0.0001;
u0.add(stepLength, x.getBlock(1));
lambda0.add(stepLength, x.getBlock(2));
q0.add(stepLength, x.getBlock(3));
plotVector(mesh, u0, String.format("rlt_u%02d.dat", iter));
plotVector(mesh, lambda0, String.format("rlt_lambda%02d.dat", iter));
plotVector(mesh, q0, String.format("rlt_q%02d.dat", iter));
}
}
@Override
public double apply(Variable v) {
return v.get(varNames[funIndex]);
}