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;
}
public Vector getRealU() {
// 4.Weak form
WeakFormLaplace2D weakForm = new WeakFormLaplace2D();
plotFunction(mesh, coef_q, "qReal.dat");
weakForm.setParam(coef_q, 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!");
// 6.Solve linear system
Solver solver = new Solver();
Vector u = solver.solveCG(stiff, load);
System.out.println("u=");
for (int i = 1; i <= u.getDim(); i++) System.out.println(String.format("%.3f", u.get(i)));
plotVector(mesh, u, "uReal.dat");
return u;
}
/**
* 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;
}
public void run() {
// 1.Read in a triangle mesh from an input file with
// format ASCII UCD generated by Gridgen
MeshReader reader = new MeshReader("triangle.grd");
Mesh mesh = reader.read2DMesh();
// Compute geometry relationship of nodes and elements
mesh.computeNodeBelongsToElements();
// 2.Mark border types
HashMap<NodeType, Function> mapNTF = new HashMap<NodeType, Function>();
mapNTF.put(NodeType.Dirichlet, null);
mesh.markBorderNode(mapNTF);
// 3.Use element library to assign degrees of
// freedom (DOF) to element
ElementList eList = mesh.getElementList();
FELinearTriangle feLT = new FELinearTriangle();
for (int i = 1; i <= eList.size(); i++) feLT.assignTo(eList.at(i));
// 4.Weak form
WeakFormLaplace2D weakForm = new WeakFormLaplace2D();
// Right hand side(RHS): f = -2*(x^2+y^2)+36
weakForm.setF(X.M(X).A(Y.M(Y)).M(-2.0).A(36.0));
// 5.Assembly process
AssemblerScalar assembler = new AssemblerScalar(mesh, weakForm);
assembler.assemble();
Matrix stiff = assembler.getStiffnessMatrix();
Vector load = assembler.getLoadVector();
// Boundary condition
assembler.imposeDirichletCondition(C0);
// 6.Solve linear system
SolverJBLAS solver = new SolverJBLAS();
Vector u = solver.solveDGESV(stiff, load);
System.out.println("u=");
for (int i = 1; i <= u.getDim(); i++) System.out.println(String.format("%.3f", u.get(i)));
// 7.Output results to an Techplot format file
MeshWriter writer = new MeshWriter(mesh);
writer.writeTechplot("./tutorial/Laplace2D.dat", u);
this.mesh = mesh;
this.u = u;
}
/**
* 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;
}
public static void adaptiveTestTriangle() {
MeshReader reader = new MeshReader("patch_triangle.grd");
Mesh mesh = reader.read2DMesh();
mesh.computeNodeBelongsToElements();
mesh.computeNeighborNodes();
mesh.computeGlobalEdge();
mesh.computeNeighborElements();
HashMap<NodeType, Function> mapNTF = new HashMap<NodeType, Function>();
mapNTF.put(NodeType.Dirichlet, null);
mesh.markBorderNode(mapNTF);
ElementList eList = mesh.getElementList();
ElementList eToRefine = new ElementList();
// 直接指定需要加密的单元编号
eToRefine.add(eList.at(6));
eToRefine.add(eList.at(16));
eToRefine.add(eList.at(3));
eToRefine.add(eList.at(4));
Refiner.refineOnce(mesh, eToRefine);
mesh.markBorderNode(mapNTF);
// //二次加密
// eToRefine.clear();
// //单元编号的问题该如何处理？
// eToRefine.add(eList.at(17));
// //第一步：新增加的结点赋予全局编号，加入mesh对象
// Refiner.refineOnce(mesh, eToRefine);
// mesh.markBorderNode(mapNTF);
SFLinearLocal2D[] shapeFun = new SFLinearLocal2D[3];
for (int i = 0; i < 3; i++) shapeFun[i] = new SFLinearLocal2D(i + 1);
SFLinearLocal2D[] shapeFun2 = new SFLinearLocal2D[3];
for (int i = 0; i < 3; i++) {
shapeFun2[i] = new SFLinearLocal2D(i + 1, 0.5);
}
// Asign degree of freedom to element
for (int i = 1; i <= mesh.getElementList().size(); i++) {
Element e = mesh.getElementList().at(i);
int nDofLocalIndexCounter = 0;
for (int j = 1; j <= e.nodes.size(); j++) {
// Asign shape function to DOF
if (e.nodes.at(j) instanceof NodeRefined) {
NodeRefined nRefined = (NodeRefined) e.nodes.at(j);
if (nRefined.isHangingNode()) {
DOF dof =
new DOF(
++nDofLocalIndexCounter,
nRefined.constrainNodes.at(1).globalIndex,
shapeFun2[j - 1]);
e.addNodeDOF(j, dof);
DOF dof2 =
new DOF(
++nDofLocalIndexCounter,
nRefined.constrainNodes.at(2).globalIndex,
shapeFun2[j - 1]);
e.addNodeDOF(j, dof2);
} else {
DOF dof = new DOF(++nDofLocalIndexCounter, e.nodes.at(j).globalIndex, shapeFun[j - 1]);
e.addNodeDOF(j, dof);
}
} else {
DOF dof = new DOF(++nDofLocalIndexCounter, e.nodes.at(j).globalIndex, shapeFun[j - 1]);
e.addNodeDOF(j, dof);
}
}
}
// User defined weak form of PDE (including bounder conditions)
WeakFormLaplace2D weakForm = new WeakFormLaplace2D();
// -\Delta{u} = f
// u(x,y)=0, (x,y)\in\partial{\Omega}
// \Omega = [0,10]*[0,10]
// u=[(x-5)^2-25]*[(y-5)^2-25]
// f=-2*( (x-5)^2 + (y-5)^2 ) + 100
Function fxm5 = new FAxpb("x", 1.0, -5.0);
Function fym5 = new FAxpb("y", 1.0, -5.0);
weakForm.setF(
FC.c(-2.0)
.M(FMath.pow(fxm5, new FC(2.0)))
.A(FC.c(-2.0).M(FMath.pow(fym5, new FC(2.0))))
.A(FC.c(100.0)));
AssemblerScalar assembler = new AssemblerScalar(mesh, weakForm);
System.out.println("Begin Assemble...");
assembler.assemble();
Matrix stiff = assembler.getStiffnessMatrix();
Vector load = assembler.getLoadVector();
assembler.imposeDirichletCondition(new FC(0.0));
System.out.println("Assemble done!");
SolverJBLAS solver = new SolverJBLAS();
Vector u = solver.solveDGESV(stiff, load);
// hanging node赋值
for (int i = 1; i <= mesh.getElementList().size(); i++) {
Element e = mesh.getElementList().at(i);
for (int j = 1; j <= e.nodes.size(); j++) {
if (e.nodes.at(j) instanceof NodeRefined) {
NodeRefined nRefined = (NodeRefined) e.nodes.at(j);
if (nRefined.isHangingNode()) {
double hnValue =
(u.get(nRefined.constrainNodes.at(1).globalIndex)
+ u.get(nRefined.constrainNodes.at(2).globalIndex))
/ 2.0;
u.set(nRefined.globalIndex, hnValue);
}
}
}
}
System.out.println("u=");
for (int i = 1; i <= u.getDim(); i++) System.out.println(String.format("%.3f", u.get(i)));
MeshWriter writer = new MeshWriter(mesh);
writer.writeTechplot("patch_triangle.dat", u);
}
public static void beforeRefinement() {
// MeshReader reader = new MeshReader("patch_rectangle.grd");
MeshReader reader = new MeshReader("patch_rectangle2.grd");
// MeshReader reader = new MeshReader("patch_rectangle_refine.grd");
Mesh mesh = reader.read2DMesh();
mesh.computeNodeBelongsToElements();
mesh.computeNeighborNodes();
mesh.computeGlobalEdge();
mesh.computeNeighborElements();
HashMap<NodeType, Function> mapNTF = new HashMap<NodeType, Function>();
mapNTF.put(NodeType.Dirichlet, null);
mesh.markBorderNode(mapNTF);
SFBilinearLocal2D[] shapeFun = new SFBilinearLocal2D[4];
for (int i = 0; i < 4; i++) shapeFun[i] = new SFBilinearLocal2D(i + 1);
// Asign degree of freedom to element
for (int i = 1; i <= mesh.getElementList().size(); i++) {
Element e = mesh.getElementList().at(i);
int nDofLocalIndexCounter = 0;
for (int j = 1; j <= e.nodes.size(); j++) {
// Asign shape function to DOF
DOF dof = new DOF(++nDofLocalIndexCounter, e.nodes.at(j).globalIndex, shapeFun[j - 1]);
e.addNodeDOF(j, dof);
}
}
// User defined weak form of PDE (including bounder conditions)
WeakFormLaplace2D weakForm = new WeakFormLaplace2D();
// -\Delta{u} = f
// u(x,y)=0, (x,y)\in\partial{\Omega}
// \Omega = [0,10]*[0,10]
// u=[(x-5)^2-25]*[(y-5)^2-25]
// f=-2*( (x-5)^2 + (y-5)^2 ) + 100
Function fxm5 = new FAxpb("x", 1.0, -5.0);
Function fym5 = new FAxpb("y", 1.0, -5.0);
weakForm.setF(
FC.c(-2.0)
.M(FMath.pow(fxm5, new FC(2.0)))
.A(FC.c(-2.0).M(FMath.pow(fym5, new FC(2.0))))
.A(FC.c(100.0)));
AssemblerScalar assembler = new AssemblerScalar(mesh, weakForm);
System.out.println("Begin Assemble...");
assembler.assemble();
Matrix stiff = assembler.getStiffnessMatrix();
Vector load = assembler.getLoadVector();
assembler.imposeDirichletCondition(new FC(0.0));
System.out.println("Assemble done!");
stiff.print();
SolverJBLAS solver = new SolverJBLAS();
Vector u = solver.solveDGESV(stiff, load);
System.out.println("u=");
for (int i = 1; i <= u.getDim(); i++) System.out.println(String.format("%.3f", u.get(i)));
MeshWriter writer = new MeshWriter(mesh);
writer.writeTechplot("patch_rectangle_before_refine.dat", u);
writer.writeTechplot("patch_rectangle_before_refine_load.dat", load);
}
public static void adaptiveTestRectangle() {
// MeshReader reader = new MeshReader("patch_rectangle.grd");
MeshReader reader = new MeshReader("patch_rectangle2.grd");
// MeshReader reader = new MeshReader("patch_rectangle_refine.grd");
Mesh mesh = reader.read2DMesh();
HashMap<NodeType, Function> mapNTF = new HashMap<NodeType, Function>();
// 验证边界结点加密后是自由的，而不是hanging node
// mapNTF.put(NodeType.Robin, new AbstractFunction("x","y"){
// @Override
// public double value(Variable v) {
// if(Math.abs(v.get("x"))<0.01)
// return 1.0;
// else
// return -1.0;
// }
// });
mapNTF.put(NodeType.Dirichlet, null);
mesh.computeNodeBelongsToElements();
mesh.computeNeighborNodes();
mesh.markBorderNode(mapNTF);
mesh.computeGlobalEdge();
mesh.computeNeighborElements();
ElementList eList = mesh.getElementList();
ElementList eToRefine = new ElementList();
eToRefine.add(eList.at(6));
eToRefine.add(eList.at(7));
eToRefine.add(eList.at(10));
eToRefine.add(eList.at(11));
Refiner.refineOnce(mesh, eToRefine);
mesh.markBorderNode(mapNTF);
mesh.printMeshInfo();
Tools.plotFunction(mesh, "", "patch_rectangle_test1.dat", FC.C0);
// 二次加密
eToRefine.clear();
// 单元编号的问题该如何处理？
eToRefine.add(eList.at(17));
eToRefine.add(eList.at(18));
// 第一步：新增加的结点赋予全局编号，加入mesh对象
Refiner.refineOnce(mesh, eToRefine);
mesh.markBorderNode(mapNTF);
mesh.printMeshInfo();
Tools.plotFunction(mesh, "", "patch_rectangle_test2.dat", FC.C0);
SFBilinearLocal2D[] shapeFun = new SFBilinearLocal2D[4];
for (int i = 0; i < 4; i++) shapeFun[i] = new SFBilinearLocal2D(i + 1);
SFBilinearLocal2D[] shapeFun2 = new SFBilinearLocal2D[4];
for (int i = 0; i < 4; i++) {
shapeFun2[i] = new SFBilinearLocal2D(i + 1, 0.5);
}
// Asign degree of freedom to element
for (int i = 1; i <= mesh.getElementList().size(); i++) {
Element e = mesh.getElementList().at(i);
int nDofLocalIndexCounter = 0;
for (int j = 1; j <= e.nodes.size(); j++) {
// Asign shape function to DOF
if (e.nodes.at(j) instanceof NodeRefined) {
NodeRefined nRefined = (NodeRefined) e.nodes.at(j);
if (nRefined.isHangingNode()) {
DOF dof =
new DOF(
++nDofLocalIndexCounter,
nRefined.constrainNodes.at(1).globalIndex,
shapeFun2[j - 1]);
e.addNodeDOF(j, dof);
DOF dof2 =
new DOF(
++nDofLocalIndexCounter,
nRefined.constrainNodes.at(2).globalIndex,
shapeFun2[j - 1]);
e.addNodeDOF(j, dof2);
} else {
DOF dof = new DOF(++nDofLocalIndexCounter, e.nodes.at(j).globalIndex, shapeFun[j - 1]);
e.addNodeDOF(j, dof);
}
} else {
DOF dof = new DOF(++nDofLocalIndexCounter, e.nodes.at(j).globalIndex, shapeFun[j - 1]);
e.addNodeDOF(j, dof);
}
}
}
// User defined weak form of PDE (including bounder conditions)
WeakFormLaplace2D weakForm = new WeakFormLaplace2D();
// -\Delta{u} = f
// u(x,y)=0, (x,y)\in\partial{\Omega}
// \Omega = [0,10]*[0,10]
// u=[(x-5)^2-25]*[(y-5)^2-25]
// f=-2*( (x-5)^2 + (y-5)^2 ) + 100
Function fxm5 = new FAxpb("x", 1.0, -5.0);
Function fym5 = new FAxpb("y", 1.0, -5.0);
weakForm.setF(
FC.c(-2.0)
.M(FMath.pow(fxm5, new FC(2.0)))
.A(FC.c(-2.0).M(FMath.pow(fym5, new FC(2.0))))
.A(FC.c(100.0)));
AssemblerScalar assembler = new AssemblerScalar(mesh, weakForm);
System.out.println("Begin Assemble...");
assembler.assemble();
Matrix stiff = assembler.getStiffnessMatrix();
Vector load = assembler.getLoadVector();
assembler.imposeDirichletCondition(new FC(0.0));
System.out.println("Assemble done!");
stiff.print();
load.print();
SolverJBLAS solver = new SolverJBLAS();
Vector u = solver.solveDGESV(stiff, load);
// //hanging node赋值
// for(int i=1;i<=mesh.getElementList().size();i++) {
// Element e = mesh.getElementList().at(i);
// for(int j=1;j<=e.nodes.size();j++) {
// if(e.nodes.at(j) instanceof NodeRefined) {
// NodeRefined nRefined = (NodeRefined)e.nodes.at(j);
// if(nRefined.isHangingNode()) {
// double hnValue =
// (u.get(nRefined.constrainNodes.at(1).globalIndex)+
// u.get(nRefined.constrainNodes.at(2).globalIndex))/2.0;
//
// u.set(nRefined.globalIndex, hnValue);
// }
// }
// }
// }
System.out.println("u=");
for (int i = 1; i <= u.getDim(); i++) System.out.println(String.format("%.3f", u.get(i)));
MeshWriter writer = new MeshWriter(mesh);
writer.writeTechplot("patch_rectangle.dat", u);
Vector res = new SparseVectorHashMap(u.getDim());
stiff.mult(u, res);
res.add(-1.0, load);
writer.writeTechplot("patch_rectangle_res.dat", res);
writer.writeTechplot("patch_rectangle_load.dat", load);
connectSells(mesh, load);
writer.writeTechplot("patch_rectangle_load_connectSells.dat", load);
}