An error minimized pseudospectral penalty direct Poisson solver

This paper presents a direct Poisson solver based on an error minimized Chebyshev pseudospectral penalty formulation for problems defined on rectangular domains. In this study the penalty parameters are determined analytically such that the discrete L2 error is minimized. Numerical experiments are conducted and the results show that the penalty scheme computes numerical solutions with better accuracy, compared to the traditional approach with boundary conditions enforced strongly.