115 lines
3.8 KiB
C
115 lines
3.8 KiB
C
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#pragma once
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#include <functional>
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#include "Matrix.h"
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/** Stencil
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*/
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struct Stencil {
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const double C; /*< Center */
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const double B; /*< Bottom */
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const double L; /*< Left */
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const double U; /*< Up */
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const double R; /*< Right */
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};
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class Solver {
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public:
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Solver(const size_t nx, const size_t ny, const double h, const double k,
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std::function<double(double, double)> fun,
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std::function<double(double)> gN,
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std::function<double(double)> gE,
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std::function<double(double)> gS,
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std::function<double(double)> gW
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) :
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_iter{0},
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_nx{nx},
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_ny{ny},
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_stencil{ 4.0 / (h * h) + 4.0 * k * k, /* Center */
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-1.0 / (h * h), /* Bottom */
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-1.0 / (h * h), /* Left */
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-1.0 / (h * h), /* Up */
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-1.0 / (h * h)}, /* Right */
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_rhs(nx, ny),
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_sol(nx, ny, 0.0),
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_tmp(nx, ny)
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{
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// Initialize Right Hand Size _rhs(x, y) = f(X(x), Y(y))
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// Note that the correspondence usual matrix indexing sceeme as
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// row/colums indices lead to an missplaces representation if the matrix
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// is printed in the usual format (x <-> rows, y <-> negative columns).
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// If this in entierly ignored and only considured in the case of
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// printing the matrix, everything is fine.
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for (size_t x = 0; x < nx; ++x) {
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for (size_t y = 0; y < ny; ++y) {
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_rhs(x, y) = fun(X(x), Y(y));
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}
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}
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// Set Dirichlet boundary conditions
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// North
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for (size_t x = 0; x < nx; ++x) { _sol(x, -1) = _tmp(x, -1) = gN(X(x)); }
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// East
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for (size_t y = 0; y < ny; ++y) { _sol(-1, y) = _tmp(-1, y) = gE(Y(y)); }
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// South
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for (size_t x = 0; x < nx; ++x) { _sol(x, 0) = _tmp(x, 0) = gS(X(x)); }
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// West
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for (size_t y = 0; y < ny; ++y) { _sol(0, y) = _tmp(0, y) = gW(Y(y)); }
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};
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/* Maps x/y index to x/y position in the [0, 1] x [0, 1] domain */
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double X(size_t x) const {
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return static_cast<double>(x) / static_cast<double>(_nx - 1);
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}
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double Y(size_t y) const {
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return static_cast<double>(y) / static_cast<double>(_ny - 1);
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}
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enum class Dir {
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North, East, South, West,
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N = North, E = East, S = South, W = West
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};
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MatrixView<double> boundary(enum Dir dir) {
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switch (dir) {
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case Dir::North:
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return Col<double>(_sol, -1);
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case Dir::East:
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return Row<double>(_sol, -1);
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case Dir::South:
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return Col<double>(_sol, 0);
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default: // Dir::West
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return Row<double>(_sol, 0);
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}
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};
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/**
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* Performs a single Jacobian Iteration
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*/
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void iterate() {
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double s = 1.0 / _stencil.C;
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for (size_t y = 1; y < _ny - 1; ++y) {
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for (size_t x = 1; x < _nx - 1; ++x) {
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_tmp(x, y) = s * (_rhs(x, y) - (_stencil.B * _sol(x, y - 1) +
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_stencil.L * _sol(x - 1, y) +
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_stencil.U * _sol(x, y + 1) +
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_stencil.R * _sol(x + 1, y)));
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}
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}
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std::swap(_tmp, _sol);
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_iter++;
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};
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private:
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size_t _iter; /*< Iteration count */
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const size_t _nx; /*< Number of X-axis grid points */
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const size_t _ny; /*< Number of Y-axis grid points */
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const Stencil _stencil; /*< Simple, + shaped stencil */
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Matrix<double> _rhs; /*< Grid evaluated RHS of the PDE = f(x, y) */
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Matrix<double> _sol; /*< Solution after _iter iterations */
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Matrix<double> _tmp; /*< Temp. datablock, used in iterate() */
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};
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