poisson2Ddirichlet(​F,L,BCl,BCt,BCr,BCb​)

Solves the 2D Poisson equation using spectral method

function U = poisson2Ddirichlet(F,L,BCl,BCt,BCr,BCb)
% POISSON2DDIRICHLET Solves the 2D poisson equation d2UdX2 + dU2dY2 = F
% with zero dirichlet
% boundary conditions
% U = POISSON2DDIRICHLET(F,L,BCl,BCt,BCr,BCb)
%
% F: Right hand side of the equation (N*N Matrix)
% L: Length of the domain (scalar)
% BCl: Left boundary condition (N*1 vector)
% BCt: Top boundary condition (N*1 vector)
% BCr: Right boundary condition (N*1 vector)
% BCb: Bottom boundary condition (N*1 vector)
%
% Please note the the boundaries are added to the matrix F as follows:
% BCl = F(1,:)
% BCt = F(:,end)
% BCr = F(end,:)
% BCb = F(:,1)