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A fast multi-resolution lattice Green's function method for elliptic difference equations
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DOI：10.1016/j.jcp.2020.109270.png)
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Abstract
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We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast multipole method in conjunction with fast Fourier transforms to yield linear complexity and decrease timeto-solution. We extend this method to a multi-resolution scheme and allow for locally refined Cartesian blocks embedded in the computational domain. Appropriately chosen interpolation and regularization operators retain consistency between the discrete Laplace operator and its inverse on the unbounded domain. Second-order accuracy and linear complexity are maintained, while significantly reducing the number of degrees of freedom and hence the computational cost. (C) 2020 Elsevier Inc. All rights reserved.
Keywords:
Elliptic difference equation
Poisson problem
Lattice Green's function
Fast multipole method
Mesh refinement
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