A High-Accurate Fast Poisson Solver Based on Harmonic Surface Mapping Algorithm (Communications in Computational Physics, 2021)
Poisson's equations in a cuboid are frequently solved in many scientific andengineering applications such as electric structure calculations, molecular dynamicssimulations and computational astrophysics. In this paper, a fast and highly accuratealgorithm is presented for the solution of the Poisson's equation in a cuboidal domainwith boundary conditions of mixed type. This so-called harmonic surface mappingalgorithm is a meshless algorithm which can achieve a desired order of accuracy byevaluating a body convolution of the source and the free-space Green's function withina sphere containing the cuboid, and another surface integration over the spherical surface. Numerical quadratures are introduced to approximate the integrals, resultingin the solution represented by a summation of point sources in free space, which canbe accelerated by means of the fast multipole algorithm. The complexity of the algorithm is linear to the number of quadrature points, and the convergence rate can bearbitrarily high even when the source term is a piecewise continuous function.