/**
* 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 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;
}