Summary
A direct method is developed for the discrete solution of Poisson's equation on a rectangle. The algorithm proposed is of the class of marching methods. The idea is to generalize the classical Cramer's method using Chebyshev matrix polynomials formalism. This results in the solution ofN independent diagonal system of linear equations in the eigenvector coordinate system. An elementary transformation to the original coordinate system is then carried out.
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Onana, A., Kwankam, S.Y. & Zoue, E. A fast Poisson solver. Period Math Hung 28, 89–101 (1994). https://doi.org/10.1007/BF01876899
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DOI: https://doi.org/10.1007/BF01876899