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 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));
}
}
}
}
}
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));
}
}