void ISOP2P1::run()
{
/// 初始化.
initialize();
/// 构建 Stokes 系统.
buildStokesSys();
/// 边界条件处理.
boundaryValueStokes();
/// 准备预处理.
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(matrix_vxvx, matrix_vyvy, mat_p_mass);
/// 矩阵求解.
dealii::SolverControl solver_control (4000000, 1e-14, 1);
SolverMinRes<Vector<double> > minres (solver_control);
clock_t t_cost = clock();
minres.solve (matrix, x, rhs, preconditioner);
// minres.solve (matrix, x, rhs, PreconditionIdentity());
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.
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;
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);
/// 数据输出.
outputTecplotP("P0");
outputTecplot("V0");
/// 误差比较.
double error;
RealVx accuracy_vx;
error = Functional::L2Error(v_h[0], accuracy_vx, 2);
std::cout << "|| u - u_h ||_L2 = " << error << std::endl;
error = Functional::H1SemiError(v_h[0], accuracy_vx, 1);
std::cout << "|| u - u_h ||_H1 = " << error << std::endl;
RealVy accuracy_vy;
error = Functional::L2Error(v_h[1], accuracy_vy, 2);
std::cout << "|| v - v_h ||_L2 = " << error << std::endl;
error = Functional::H1SemiError(v_h[1], accuracy_vy, 1);
std::cout << "|| v - v_h ||_H1 = " << error << std::endl;
double p_avg = Functional::meanValue(p_h, 2);
RealP accuracy_p(p_avg);
error = Functional::L2Error(p_h, accuracy_p, 2);
std::cout << "|| p - p_h ||_0 = " << error << std::endl;
};
void ISOP2P1::run()
{
initialize();
std::cout << "Initialize mesh ... " << std::endl;
if (isMoving == 1)
{
double scale_step = 0.2;
scale = scale_step;
do {
// PoiseuilleVx poiseuille_vx(-1.0, 1.0);
// PoiseuilleVy poiseuille_vy;
// Operator::L2Project(poiseuille_vx, v_h[0], Operator::LOCAL_LEAST_SQUARE, 3);
// Operator::L2Project(poiseuille_vy, v_h[1], Operator::LOCAL_LEAST_SQUARE, 3);
buildMatrix();
// stepForwardEuler();
solveStokes();
v_h[0].scale(scale);
v_h[1].scale(scale);
movingMesh();
std::cout << "\r\tscale = " << scale << std::endl;
scale += scale_step;
} while (scale <= 1.0);
/// 重新设置scale 为1.0.
scale = 1.0;
}
// PoiseuilleVx poiseuille_vx(-1.0, 1.0);
// PoiseuilleVy poiseuille_vy;
// Operator::L2Project(poiseuille_vx, v_h[0], Operator::LOCAL_LEAST_SQUARE, 3);
// Operator::L2Project(poiseuille_vy, v_h[1], Operator::LOCAL_LEAST_SQUARE, 3);
// outputSolution();
// v_h[0].reinit(fem_space_v);
// v_h[1].reinit(fem_space_v);
// p_h.reinit(fem_space_p);
solveStokes();
outputTecplotP("P0");
outputTecplot("initial_value0");
getchar();
int steps_before = 0;
int steps_after = 0;
bool isOutput = false;
while (t < t1)
{
/// 准备每步输出一个 tecplot 数据, 注意别把硬盘写爆了!
std::stringstream ss_before;
ss_before << "NS_Euler";
std::stringstream ss_after;
ss_after << "NS_Euler_updateSol";
if (scheme == 1)
{
if(isMoving == 1)
buildMatrix();
stepForwardEuler();
}
else if (scheme == 2)
stepForwardLinearizedEuler();
else
break;
/// 获取时间步长.
time_step();
t += dt;
steps_before++;
ss_before << steps_before;
outputTecplot(ss_before.str());
std::cout << "Data outputed!" << std::endl;
/// 网格移动.
if (isMoving == 1)
movingMesh();
/// 输出一下P网格上的压力,monitor,以及网格移动方向.
outputTecplotP("NS_Euler");
getchar();
/// 输出.
// if (isOutput)
// {
steps_after++;
ss_after << steps_after;
outputTecplot(ss_after.str());
std::cout << "Data outputed!" << std::endl;
// isOutput = false;
// }
// double t_stop = int((t / 0.01) + 0.5) * 0.01;
// if (t > t_stop - dt && t < t_stop + dt)
// {
// t = t_stop;
// isOutput = true;
// }
// std::cout << "t = " << t << std::endl;
}
}
void ISOP2P1::updateSolution()
{
/// 更新插值点.
fem_space_p.updateDofInterpPoint();
fem_space_v.updateDofInterpPoint();
/// 备份数值解.
FEMFunction<double, DIM> _u_h(v_h[0]);
FEMFunction<double, DIM> _v_h(v_h[1]);
FEMFunction<double, DIM> _p_h(p_h);
const double& msl = moveStepLength();
/// 因为有限元空间插值点变化, 重新构造矩阵.
buildMatrixStruct();
buildMatrix();
/// 因为网格移动量为小量, 因此时间步长可以相对取的大些.
double _dt = 0.1;
int n_dof_v = fem_space_v.n_dof();
int n_dof_p = fem_space_p.n_dof();
int n_total_dof = DIM * n_dof_v + n_dof_p;
int n_total_dof_v = DIM * n_dof_v;
/// 一步Euler.
for (int m = 1; m > 0; --m)
{
/// 系数矩阵直接使用 Stokes 矩阵结构.
SparseMatrix<double> mat_moving;
mat_moving.reinit(sp_stokes);
/// (0, 0)
for (int i = 0; i < sp_vxvx.n_nonzero_elements(); ++i)
mat_moving.global_entry(index_vxvx[i]) = mat_v_mass.global_entry(i);
/// (1, 1) 这两个对角块仅有质量块.
for (int i = 0; i < sp_vyvy.n_nonzero_elements(); ++i)
mat_moving.global_entry(index_vyvy[i]) = mat_v_mass.global_entry(i);
/// (0, 2) 这个不是方阵. 在矩阵结构定义的时候已经直接排除了对角元优
/// 先.
for (int i = 0; i < sp_pvx.n_nonzero_elements(); ++i)
mat_moving.global_entry(index_pvx[i]) = (1.0 / m) * mat_pvx_divT.global_entry(i);
/// (1, 2)
for (int i = 0; i < sp_pvy.n_nonzero_elements(); ++i)
mat_moving.global_entry(index_pvy[i]) = (1.0 / m) * mat_pvy_divT.global_entry(i);
/// (2, 0)
for (int i = 0; i < sp_vxp.n_nonzero_elements(); ++i)
mat_moving.global_entry(index_vxp[i]) = (1.0 / m) * mat_vxp_div.global_entry(i);
/// (2, 1) 这四块直接复制散度矩阵.
for (int i = 0; i < sp_vyp.n_nonzero_elements(); ++i)
mat_moving.global_entry(index_vyp[i]) = (1.0 / m) * mat_vyp_div.global_entry(i);
/// 问题的右端项.
Vector<double> rhs_loc(n_total_dof);
// rhs.reinit(n_total_dof);
FEMSpace<double, DIM>::ElementIterator the_element_v = fem_space_v.beginElement();
FEMSpace<double, DIM>::ElementIterator end_element_v = fem_space_v.endElement();
/// 遍历速度单元, 拼装相关系数矩阵和右端项.
for (the_element_v = fem_space_v.beginElement();
the_element_v != end_element_v; ++the_element_v)
{
/// 当前单元信息.
double volume = the_element_v->templateElement().volume();
/// 积分精度至少为2.
const QuadratureInfo<DIM>& quad_info = the_element_v->findQuadratureInfo(4);
std::vector<double> jacobian = the_element_v->local_to_global_jacobian(quad_info.quadraturePoint());
int n_quadrature_point = quad_info.n_quadraturePoint();
std::vector<Point<DIM> > q_point = the_element_v->local_to_global(quad_info.quadraturePoint());
/// 速度单元信息.
std::vector<std::vector<double> > basis_value_v = the_element_v->basis_function_value(q_point);
std::vector<double> vx_value = _u_h.value(q_point, *the_element_v);
std::vector<double> vy_value = _v_h.value(q_point, *the_element_v);
std::vector<std::vector<double> > vx_gradient = v_h[0].gradient(q_point, *the_element_v);
std::vector<std::vector<double> > vy_gradient = v_h[1].gradient(q_point, *the_element_v);
const std::vector<int>& element_dof_v = the_element_v->dof();
int n_element_dof_v = the_element_v->n_dof();
/// 速度积分点上的移动方向, 注意是速度单元的积分点, 在压力单元上的移动方向.
/// 所以下面一行程序, 仔细算过, 没有问题.
std::vector<std::vector<double> > move_vector = moveDirection(q_point, index_v2p[the_element_v->index()]);
for (int l = 0; l < n_quadrature_point; ++l)
{
double Jxw = quad_info.weight(l) * jacobian[l] * volume;
for (int i = 0; i < n_element_dof_v; ++i)
{
double rhs_cont = (vx_value[l] + (1.0 / m) * msl * innerProduct(move_vector[l], vx_gradient[l])) * basis_value_v[i][l];
rhs_cont *= Jxw;
rhs_loc(element_dof_v[i]) += rhs_cont;
rhs_cont = (vy_value[l] + (1.0 / m) * msl * innerProduct(move_vector[l], vy_gradient[l])) * basis_value_v[i][l];
rhs_cont *= Jxw;
rhs_loc(n_dof_v + element_dof_v[i]) += rhs_cont;
}
}
}
/// 构建系数矩阵和右端项.
Vector<double> x(n_total_dof);
// PoiseuilleVx real_vx (-1.0, 1.0);
// PoiseuilleVy real_vy;
// Operator::L2Project(real_vx, v_h[0], Operator::LOCAL_LEAST_SQUARE, 3);
// Operator::L2Project(real_vy, v_h[1], Operator::LOCAL_LEAST_SQUARE, 3);
// /// 边界处理.
const std::size_t * rowstart = sp_stokes.get_rowstart_indices();
const unsigned int * colnum = sp_stokes.get_column_numbers();
/// 遍历全部维度的速度节点.
for (unsigned int i = 0; i < n_total_dof_v; ++i)
{
/// 边界标志.
int bm = -1;
/// 判断一下是 x 方向还是 y 方向. 分别读取标志.
if (i < n_dof_v)
bm = fem_space_v.dofInfo(i).boundary_mark;
else
bm = fem_space_v.dofInfo(i - n_dof_v).boundary_mark;
if (bm == 0)
continue;
/// 方腔流边界条件.
if (bm == 1 || bm == 2 || bm == 4 || bm == 5)
x(i) = 0.0;
if (bm == 3)
if (i < n_dof_v)
{
/// 不包括顶端的两个端点,称为watertight cavity.
// x(i) = scale * 1.0;
Regularized regularize;
x(i) = scale * regularize.value(fem_space_v.dofInfo(i).interp_point);
}
else
x(i) = 0.0;
// /// poiseuille flow边界条件.
// if (bm == 1 || bm == 2 || bm == 4 || bm == 5)
// if (i < n_dof_v)
// x(i) = scale * real_vx.value(fem_space_v.dofInfo(i).interp_point);
// else
// x(i) = scale * real_vy.value(fem_space_v.dofInfo(i - n_dof_v).interp_point);
/// 右端项这样改, 如果该行和列其余元素均为零, 则在迭代中确
/// 保该数值解和边界一致.
if (bm == 1 || bm == 2 || bm == 3 || bm == 4 || bm == 5)
// if (bm == 1 || bm == 2 || bm == 4 || bm == 5)
{
rhs_loc(i) = mat_moving.diag_element(i) * x(i);
/// 遍历 i 行.
for (unsigned int j = rowstart[i] + 1; j < rowstart[i + 1]; ++j)
{
/// 第 j 个元素消成零(不是第 j 列!). 注意避开了对角元.
mat_moving.global_entry(j) -= mat_moving.global_entry(j);
/// 第 j 个元素是第 k 列.
unsigned int k = colnum[j];
/// 看看第 k 行的 i 列是否为零元.
const unsigned int *p = std::find(&colnum[rowstart[k] + 1],
&colnum[rowstart[k + 1]],
i);
/// 如果是非零元. 则需要将这一项移动到右端项. 因为第 i 个未知量已知.
if (p != &colnum[rowstart[k + 1]])
{
/// 计算 k 行 i 列的存储位置.
unsigned int l = p - &colnum[rowstart[0]];
/// 移动到右端项. 等价于 r(k) = r(k) - x(i) * A(k, i).
rhs_loc(k) -= mat_moving.global_entry(l) * x(i);
/// 移完此项自然是零.
mat_moving.global_entry(l) -= mat_moving.global_entry(l);
}
}
}
}
std::cout << "boundary values for updateSolution OK!" << std::endl;
// /// debug 边界条件处理部分,已经测试过, 边界处理正确.
// RegularMesh<DIM> &mesh_v = irregular_mesh_v->regularMesh();
// for (int i = 0; i < mesh_v.n_geometry(0); ++i)
// {
// Point<DIM> &p= mesh_v.point(i);
// if (fabs(1 - p[1]) < eps || fabs(1 - p[0]) < eps || fabs(-1 - p[1]) < eps || fabs(-1 - p[0]) < eps)
// {
// std::cout << "point(" << i << ") = (" << p[0] << "," << p[1] << ");" << std::endl;
// std::cout << "uh(" << i << ") = " << v_h[0](i) << std::endl;
// std::cout << "vh(" << i << ") = " << v_h[1](i) << std::endl;
// }
// }
// getchar();
// /// debug
clock_t t_cost = clock();
/// 预处理矩阵.
/// 不完全LU分解.
dealii::SparseILU <double> preconditioner;
preconditioner.initialize(mat_moving);
/// 矩阵求解.
dealii::SolverControl solver_control (4000000, l_tol, check);
SolverMinRes<Vector<double> > minres (solver_control);
minres.solve (mat_moving, x, rhs_loc, PreconditionIdentity());
t_cost = clock() - t_cost;
std::cout << "time cost: " << (((float)t_cost) / CLOCKS_PER_SEC) << std::endl;
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);
/// debug
std::ofstream mat_deb;
// rowstart = sp_pvx.get_rowstart_indices();
// colnum = sp_pvx.get_column_numbers();
mat_deb.open("mat.m", std::ofstream::out);
mat_deb.setf(std::ios::fixed);
mat_deb.precision(20);
for (int i = 0; i < n_total_dof; ++i)
{
for (int j = rowstart[i]; j < rowstart[i + 1]; ++j)
{
mat_deb << "A(" << i + 1 << ", " << colnum[j] + 1 << ")="
<< mat_moving.global_entry(j) << ";" << std::endl;
}
mat_deb << "x(" << i + 1<< ") = " << x(i) << ";" << std::endl;
mat_deb << "rhs(" << i + 1 << ") = " << rhs_loc(i) << ";" << std::endl;
}
// for(int i = 0; i < n_dof_p; ++i)
// mat_deb << "x(" << i + 1<< ") = " << p_h(i) << ";" << std::endl;
mat_deb.close();
std::cout << "mat output" << std::endl;
Vector<double> res(n_total_dof);
mat_moving.vmult(res, x);
res *= -1;
res += rhs_loc;
std::cout << "res_l2norm =" << res.l2_norm() << std::endl;
// double error;
// error = Functional::L2Error(v_h[0], real_vx, 3);
// std::cout << "|| u - u_h ||_L2 = " << error << std::endl;
// error = Functional::H1SemiError(v_h[0], real_vx, 3);
// std::cout << "|| u - u_h ||_H1 = " << error << std::endl;
/// debug
RegularMesh<DIM> &mesh_p = irregular_mesh_p->regularMesh();
for (int i = 0; i < mesh_p.n_geometry(0); ++i)
{
(*mesh_p.h_geometry<0>(i))[0] += moveDirection(i)[0];
(*mesh_p.h_geometry<0>(i))[1] += moveDirection(i)[1];
}
/// 输出一下.
outputTecplotP("NS_Euler");
getchar();
}
};