public SparseMatrix getC(Vector uk) {
// 4.Weak form: (\nabla{\phi},dq\nabla{uk})
WeakFormGCM weakForm = new WeakFormGCM();
Function fuk = new Vector2Function(uk, mesh, "x", "y");
Function u_x = fuk._d("x");
Function u_y = fuk._d("y");
plotFunction(mesh, u_x, "u_x.dat");
plotFunction(mesh, u_y, "u_y.dat");
weakForm.setParam(FC.C0, FC.C0, u_x, u_y);
// Right hand side(RHS): f(x) = 0
weakForm.setF(FC.C0);
// 5.Assembly process
AssemblerScalar assembler = new AssemblerScalar(mesh, weakForm);
System.out.println("Begin Assemble...");
assembler.assemble();
SparseMatrix stiff = assembler.getStiffnessMatrix();
// Boundary condition
// 边界条件需要在大矩阵中设置
// assembler.imposeDirichletCondition(FC.c0);
System.out.println("Assemble done!");
return stiff;
}
@Override
public double integrate(Element e, Function fun) {
if (fun == null) return 0.0;
if (e.dim() == 2) {
if (e.vertices().size() == 3) {
// 三角形单元
return FOIntegrate.intOnTriangleRefElement(fun.M(e.getJacobin()), 2);
} else if (e.vertices().size() == 4) {
// 四边形单元
return FOIntegrate.intOnRectangleRefElement(
fun.M(e.getJacobin()), 5 // TODO
);
}
} else if (e.dim() == 3) {
if (e.vertices().size() == 4) {
// 四面体单元
return FOIntegrate.intOnTetrahedraRefElement(fun.M(e.getJacobin()), 2);
} else if (e.vertices().size() == 8) {
// 六面体单元
return FOIntegrate.intOnHexahedraRefElement(fun.M(e.getJacobin()), 2);
}
} else if (e.dim() == 1) {
// 一维单元
return FOIntegrate.intOnLinearRefElement(fun.M(e.getJacobin()), 5);
} else {
throw new FutureyeException("Can NOT integrate on e" + e.vertices());
}
throw new FutureyeException("Error");
}
/**
* Adjoint equation L_{u} := (q\nabla{\psi},\nabla{\lambda}) + (u-z,\psi)
*
* @return
*/
public SparseVector getResLu(Vector u, Vector lambda, Vector q) {
// 4.Weak form
WeakFormLaplace2D weakForm = new WeakFormLaplace2D();
Function fq = new Vector2Function(q);
weakForm.setParam(fq, FC.C0, null, null);
// Right hand side(RHS): f(x) = - (u - z)
Function z_u = z.S(new Vector2Function(u));
plotFunction(mesh, z_u, String.format("z_u%02d.dat", this.iterNum));
weakForm.setF(z_u);
// 5.Assembly process
AssemblerScalar assembler = new AssemblerScalar(mesh, weakForm);
System.out.println("Begin Assemble...");
assembler.assemble();
SparseMatrix stiff = assembler.getStiffnessMatrix();
SparseVector load = assembler.getLoadVector();
// Boundary condition
assembler.imposeDirichletCondition(FC.C0);
System.out.println("Assemble done!");
if (debug) {
// 6.Solve linear system
Solver solver = new Solver();
Vector lmd_solve = solver.solveCGS(stiff, load);
plotVector(mesh, lmd_solve, "lambda_solve.dat");
}
// Residual
SparseVector res = new SparseVectorHashMap(lambda.getDim());
stiff.mult(lambda, res);
res.add(-1.0, load);
plotVector(mesh, res, "Res_Lu.dat");
return res;
}
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 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 Vector solveAdjointEquation(Vector u, Vector q) {
// 4.Weak form
WeakFormLaplace2D weakForm = new WeakFormLaplace2D();
Function fq = new Vector2Function(q);
weakForm.setParam(fq, FC.C0, null, null);
// Right hand side(RHS): f(x) = - (u - z)
weakForm.setF(z.S(new Vector2Function(u)));
// 5.Assembly process
AssemblerScalar assembler = new AssemblerScalar(mesh, weakForm);
System.out.println("Begin Assemble...");
assembler.assemble();
SparseMatrix stiff = assembler.getStiffnessMatrix();
SparseVector load = assembler.getLoadVector();
// Boundary condition
assembler.imposeDirichletCondition(FC.C0);
System.out.println("Assemble done!");
// 6.Solve linear system
Solver solver = new Solver();
Vector lmd_solve = solver.solveCGS(stiff, load);
return lmd_solve;
}