119 lines
3.4 KiB
C++
119 lines
3.4 KiB
C++
#pragma once
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#include <cmath>
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/**
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* User function: f(@p x,@p y)
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @return value for right hand side f(@p x,@p y)
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*/
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double FunctF(double x, double y);
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/**
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* User function: u(@p x,@p y)
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @return value for solution vector u(@p x,@p y)
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*/
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double FunctU(double x, double y);
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/**
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* User function: f(@p x,@p y) = @f$ x^2 \sin(2.5\pi y)@f$.
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @return value f(@p x,@p y)
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*/
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inline
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double fNice(double const x, double const y)
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{
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//return x * x * std::sin(2.5 * M_PI * y); // solution u
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return std::sin(M_PI*2.5*y)*(M_PI*M_PI*2.5*2.5*x*x - 2); // -Laplacian(u)
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}
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/**
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* User function: f(@p x,@p y,@p z).
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @param[in] z z-coordinate of discretization point
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* @return value f(@p x,@p y,@p z)
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*/
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inline
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double fNice(double const x, double const y, double const z)
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{
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return std::sin(M_PI*2.5*y)*(M_PI*M_PI*2.5*2.5*x*x - 2)+z;
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}
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/**
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* User function: f(@p x,@p y) = 0$.
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @return value 0
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*/
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inline
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double f_zero(double const x, double const y)
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//double f_zero(double const /*x*/, double const /*y*/)
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{
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return 0.0 + 0.0*(x+y);
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}
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// ---------------------------------------------------------------------
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/**
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* solution u(@p x,@p y) of -Laplacian.
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @return value u(@p x,@p y)
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* @see rhs_lap2
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*/
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inline
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double sol_lap2(double const x, double const y)
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{
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return x * x * std::sin(2.5 * M_PI * y);
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}
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/**
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* Right hand side f(@p x,@p y) of -Laplacian(u) with the appropriate function u.
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @return value f(@p x,@p y)
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* @see sol_lap2
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*/
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inline
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double rhs_lap2(double const x, double const y)
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{
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return std::sin(M_PI*2.5*y)*(M_PI*M_PI*2.5*2.5*x*x - 2);
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}
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// ---------------------------------------------------------------------
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/**
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* solution u(@p x,@p y,@p z) of -Laplacian.
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @param[in] z z-coordinate of discretization point
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* @return value u(@p x,@p y,@p z)
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* @see rhs_lap3
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*/
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inline
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double sol_lap3(double const x, double const y, double const z)
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{
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//return x*x*std::cos(M_PI*z)*std::sin(M_PI*y);
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return (x*x*(2*x - 3))*std::cos(M_PI*z)*std::cos(M_PI*y);
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}
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/**
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* Right hand side f(@p x,@p y,@p z) of -Laplacian(u) with the appropriate function u.
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* @param[in] x x-coordinate of discretization point
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* @param[in] y y-coordinate of discretization point
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* @param[in] z z-coordinate of discretization point
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* @return value f(@p x,@p y,@p z)
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* @see sol_lap3
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*/
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inline
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double rhs_lap3(double const x, double const y, double const z)
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{
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//return 2.0*std::cos(M_PI*z)*std::sin(M_PI*y)*(M_PI*M_PI*x*x - 1);
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return -2.0*std::cos(M_PI*z)*std::cos(M_PI*y)*(- 2*M_PI*M_PI*x*x*x + 3*M_PI*M_PI*x*x + 6*x - 3);
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}
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// ---------------------------------------------------------------------
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