public Vector solveStateEquation(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) = -4.0
weakForm.setF(FC.c(-4.0));
// 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(diri); // ???给定一个初始猜测q,边界条件是什么？
System.out.println("Assemble done!");
// 6.Solve linear system
Solver solver = new Solver();
Vector u_solve = solver.solveCGS(stiff, load);
return u_solve;
}
/**
* 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;
}
/**
* State equation L_{\lambda} := (q\nabla{u},\nabla{\phi})-(f,\phi)=0
*
* <p>获取状态方程的余量
*
* @return
*/
public SparseVector getResLlmd(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) = -4.0
weakForm.setF(FC.c(-4.0));
// 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(diri);
System.out.println("Assemble done!");
if (debug) {
// 6.Solve linear system
Solver solver = new Solver();
Vector u_solve = solver.solveCGS(stiff, load);
plotVector(mesh, u_solve, "u_solve.dat");
}
// Residual
SparseVector res = new SparseVectorHashMap(u.getDim());
stiff.mult(u, res);
res.add(-1.0, load);
plotVector(mesh, res, "Res_Llambda.dat");
return res;
}
/**
* Parameter regularization L_{q} := \beta(q-\overline{q},\chi) + (\chi\nabla{u},\nabla{\lambda})
*
* @param u
* @param lambda
* @param q
* @return
*/
public SparseVector getResLq(Vector u, Vector lambda, Vector q) {
// 4.Weak form
WeakFormL22D weakForm = new WeakFormL22D();
weakForm.setParam(FC.C0, FC.C1);
// Right hand side(RHS): f(x) = -(1.0/\beta)\nabla{u}\cdot\nabla{v}
Function fu = new Vector2Function(u, mesh, "x", "y");
Function flmd = new Vector2Function(lambda, mesh, "x", "y");
Function f = FMath.grad(fu).dot(FMath.grad(flmd));
plotFunction(mesh, f, String.format("Grad(u)Grad(lmd)%02d.dat", this.iterNum));
Function f2 = FC.c(-1.0 / beta).M(f).A(qBar);
plotFunction(mesh, f2, String.format("LqRHS%02d.dat", this.iterNum));
weakForm.setF(f2);
// 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.c(8.0));
System.out.println("Assemble done!");
if (debug) {
// 6.Solve linear system
Solver solver = new Solver();
Vector q_solve = solver.solveCGS(stiff, load);
plotVector(mesh, q_solve, "q_solve.dat");
}
// Residual
SparseVector res = new SparseVectorHashMap(q.getDim());
stiff.mult(q, res);
res.add(-1.0, load);
plotVector(mesh, res, "Res_Lq.dat");
return res;
}