//=============================================================================
int main(int argc, char** argv)
{
srand(time(NULL));
const int size(100);
CPPL::dsymatrix A(size);
for(int i=0; i<size; i++){
for(int j=0; j<=i; j++){
A(i,j) =(double(rand())/double(RAND_MAX))*2.0 -1.0;
}
A(i,i)+=10.;
}
A.write("A.dsymatrix");
CPPL::dcovector x(size);
for(int i=0; i<size; i++){
x(i) =(double(rand())/double(RAND_MAX))*1. -0.5;
}
x.write("answer.dcovector");//solution
std::cerr << "answer=\n" << t(x) << std::endl;
CPPL::dcovector y(size);
y=A*x;
y.write("y.dcovector");
double eps(fabs(damax(y))*1e-6);
//std::cerr << "eps=" << eps << std::endl;
if( minres(A, y, eps) ){
std::cerr << "failed." << std::endl;
exit(1);
}
y.write("solution.dcovector");
std::cout << "solution=\n" << t(y) << std::endl;
return 0;
}
void ISOP2P1::solveStokes()
{
buildStokesSys();
std::cout << "Stokes system builded." << std::endl;
int n_dof_v = fem_space_v.n_dof();
int n_dof_p = fem_space_p.n_dof();
int n_total_dof = 2 * n_dof_v + n_dof_p;
/// 构建系数矩阵和右端项.
/// 这个存放整体的数值解. 没有分割成 u_h[0], u_h[1] 和 p_h.
Vector<double> x(n_total_dof);
/// 将数值解合并一个向量便于边界处理.
for (int i = 0; i < n_dof_v; ++i)
{
x(i) = v_h[0](i);
x(n_dof_v + i) = v_h[1](i);
}
for (int i = 0; i < n_dof_p; ++i)
x(2 * n_dof_v + i) = p_h(i);
rhs.reinit(n_total_dof);
/// 边界条件一起处理了. 修改了matrix, rhs和x.
boundaryValueStokes(x, t);
std::cout << "Stokes boundary applied." << std::endl;
// /// 矩阵求解.
// dealii::SolverControl solver_control (400000, l_tol * rhs.l2_norm(), 1);
// /// 不完全LU分解.
// dealii::SparseILU<double> preconditioner;
// preconditioner.initialize(matrix);
// /// 求解Stokes方程, MinRes要比GMRES求解器要快很多,
// /// 当矩阵规模稍微大点的时候,GMRES会出现不收敛的情况.
// SolverMinRes<Vector<double> > minres (solver_control);
// SolverGMRES<Vector<double> >::AdditionalData para(1000, false, true);
// /// 不用para算不动, 但是均匀网格下可以不用para,算其它的例子也不用para,是不是跟计算区域有关系？
// SolverGMRES<Vector<double> > gmres(solver_control, para);
// // /// 移动网格和时间发展中，这个预处理失效.
// // StokesPreconditioner preconditioner;
// // /// 预处理矩阵.
// // SparseMatrix<double> matrix_vxvx(sp_vxvx);
// // SparseMatrix<double> matrix_vyvy(sp_vyvy);
// // /// 这里从 Stokes 取是因为加了边界条件.
// // for (int i = 0; i < sp_vxvx.n_nonzero_elements(); ++i)
// // matrix_vxvx.global_entry(i) = matrix.global_entry(index_vxvx[i]);
// // for (int i = 0; i < sp_vyvy.n_nonzero_elements(); ++i)
// // matrix_vyvy.global_entry(i) = matrix.global_entry(index_vyvy[i]);
// // preconditioner.initialize(mat_v_stiff, mat_v_stiff, mat_p_mass);
// clock_t t_cost = clock();
// minres.solve (matrix, x, rhs, PreconditionIdentity());
// // gmres.solve(matrix, x, rhs, preconditioner);
// t_cost = clock() - t_cost;
// std::cout << "time cost: " << (((float)t_cost) / CLOCKS_PER_SEC) << std::endl;
// /// 将整体数值解分割成速度和压力.
// for (int i = 0; i < n_dof_v; ++i)
// {
// v_h[0](i) = x(i);
// v_h[1](i) = x(i + n_dof_v);
// }
// for (int i = 0; i < n_dof_p; ++i)
// p_h(i) = x(i + 2 * n_dof_v);
// /// 计算误差, t为时间参数.
// computeError(t);
// /// debug, 计算惨量的L2 norm。
// Vector<double> res(n_total_dof);
// matrix.vmult(res, x);
// res *= -1;
// res += rhs;
// std::cout << "res_l2norm =" << res.l2_norm() << std::endl;
/// 矩阵求解.
SparseMatrix<double> mat_BTx(sp_pvx);
SparseMatrix<double> mat_BTy(sp_pvy);
SparseMatrix<double> mat_Bx(sp_vxp);
SparseMatrix<double> mat_By(sp_vyp);
SparseMatrix<double> mat_Ax(sp_vxvx);
SparseMatrix<double> mat_Ay(sp_vyvy);
for (int i = 0; i < sp_vxvx.n_nonzero_elements(); ++i)
mat_Ax.global_entry(i) = matrix.global_entry(index_vxvx[i]);
for (int i = 0; i < sp_vyvy.n_nonzero_elements(); ++i)
mat_Ay.global_entry(i) = matrix.global_entry(index_vyvy[i]);
for (int i = 0; i < sp_pvx.n_nonzero_elements(); ++i)
mat_BTx.global_entry(i) = matrix.global_entry(index_pvx[i]);
for (int i = 0; i < sp_pvy.n_nonzero_elements(); ++i)
mat_BTy.global_entry(i) = matrix.global_entry(index_pvy[i]);
for (int i = 0; i < sp_vxp.n_nonzero_elements(); ++i)
mat_Bx.global_entry(i) = matrix.global_entry(index_vxp[i]);
for (int i = 0; i < sp_vyp.n_nonzero_elements(); ++i)
mat_By.global_entry(i) = matrix.global_entry(index_vyp[i]);
/// alp对AMGSolver的初始化影响比较大, 如果取得很小，初始化很快.
double alp = dt * viscosity;
AMGSolver solverQ(mat_Ax, 1.0e-12, 3, 100, 0.382, alp);
// AMGSolver solverQ(mat_Ax);
InverseMatrix AInv(mat_Ax, solverQ);
/// 这里没有对速度质量阵进行边界条件处理.
InverseMatrix QInv(mat_v_mass, solverQ);
SchurComplement schur_complement(mat_BTx, mat_BTy, mat_Bx, mat_By, mat_v_mass, QInv, QInv);
AMGSolver solverP(mat_p_mass);
ApproxSchurComplement asc(mat_p_mass, solverQ);
LSCPreconditioner lsc_preconditioner(mat_BTx, mat_BTy, mat_Bx, mat_By, mat_Ax, mat_Ax, mat_v_mass, schur_complement, asc, QInv,
AInv, AInv);
/// 矩阵求解.
dealii::SolverControl solver_control (400000, l_Euler_tol * rhs.l2_norm(), 0);
SolverMinRes<Vector<double> > minres(solver_control);
minres.solve(matrix, x, rhs, lsc_preconditioner);
/// 将整体数值解分割成速度和压力.
for (int i = 0; i < n_dof_v; ++i)
{
v_h[0](i) = x(i);
v_h[1](i) = x(i + n_dof_v);
}
for (int i = 0; i < n_dof_p; ++i)
p_h(i) = x(i + 2 * n_dof_v);
/// 计算误差, t为时间参数.
computeError(t);
// /// 矩阵求解.
// SparseMatrix<double> mat_BTx(sp_pvx);
// SparseMatrix<double> mat_BTy(sp_pvy);
// SparseMatrix<double> mat_Bx(sp_vxp);
// SparseMatrix<double> mat_By(sp_vyp);
// SparseMatrix<double> mat_Ax(sp_vxvx);
// SparseMatrix<double> mat_Ay(sp_vyvy);
// for (int i = 0; i < sp_vxvx.n_nonzero_elements(); ++i)
// mat_Ax.global_entry(i) = matrix.global_entry(index_vxvx[i]);
// for (int i = 0; i < sp_vyvy.n_nonzero_elements(); ++i)
// mat_Ay.global_entry(i) = matrix.global_entry(index_vyvy[i]);
// for (int i = 0; i < sp_pvx.n_nonzero_elements(); ++i)
// mat_BTx.global_entry(i) = matrix.global_entry(index_pvx[i]);
// for (int i = 0; i < sp_pvy.n_nonzero_elements(); ++i)
// mat_BTy.global_entry(i) = matrix.global_entry(index_pvy[i]);
// for (int i = 0; i < sp_vxp.n_nonzero_elements(); ++i)
// mat_Bx.global_entry(i) = matrix.global_entry(index_vxp[i]);
// for (int i = 0; i < sp_vyp.n_nonzero_elements(); ++i)
// mat_By.global_entry(i) = matrix.global_entry(index_vyp[i]);
// Vector<double> tmp1(n_dof_v);
// Vector<double> tmp2(n_dof_v);
// Vector<double> rhs_vx(n_dof_v);
// Vector<double> rhs_vy(n_dof_v);
// Vector<double> rhs_p(n_dof_p);
// for (int i = 0; i < n_dof_v; ++i)
// {
// rhs_vx(i) = rhs(i);
// v_h[0](i) = x(i);
// rhs_vy(i) = rhs(n_dof_v + i);
// v_h[1](i) = x(n_dof_v + i);
// }
// for (int i = 0; i < n_dof_p; ++i)
// {
// rhs_p(i) = rhs(2 * n_dof_v + i);
// p_h(i) = x(2 * n_dof_v + i);
// }
// Vector<double> schur_rhs (n_dof_p);
// AMGSolver solverQ(mat_Ax);
// InverseMatrix M(mat_Ax, solverQ);
// M.vmult (tmp1, rhs_vx);
// M.vmult (tmp2, rhs_vy);
// mat_Bx.vmult(schur_rhs, tmp1);
// mat_By.vmult_add(schur_rhs, tmp2);
// schur_rhs -= rhs_p;
// SchurComplement schur_complement(mat_BTx, mat_BTy, mat_Bx, mat_By, mat_v_mass, M, M, dt);
// SolverControl solver_control_cg (n_dof_p * 2,
// 1e-12*schur_rhs.l2_norm());
// SolverCG<> cg (solver_control_cg);
// AMGSolver AQ(mat_p_mass);
// ApproxSchurComplement asc(mat_p_mass, AQ);
// cg.solve (schur_complement, p_h, schur_rhs, asc);
// // cg.solve (schur_complement, p_h, schur_rhs, PreconditionIdentity());
// std::cout << solver_control_cg.last_step()
// << " CG Schur complement iterations to obtain convergence."
// << std::endl;
// mat_BTx.vmult(tmp1, *dynamic_cast<const Vector<double>* >(&p_h));
// mat_BTy.vmult(tmp2, *dynamic_cast<const Vector<double>* >(&p_h));
// tmp1 *= -1;
// tmp2 *= -1;
// tmp1 += rhs_vx;
// tmp2 += rhs_vy;
// M.vmult(v_h[0], tmp1);
// M.vmult(v_h[1], tmp2);
// std::cout << "Stokes system solved." << std::endl;
// /// 计算误差, t为时间参数.
// computeError(t);
// /// debug, 计算惨量的L2 norm。
// Vector<double> res(n_total_dof);
// matrix.vmult(res, x);
// res *= -1;
// res += rhs;
// std::cout << "res_l2norm =" << res.l2_norm() << std::endl;
};
