ISOTROPIC FINITE DIFFERENCE DISCRETIZATION OF LAPLACIAN OPERATOR

In this paper, we review and investigate isotropic finite difference discretizations of the two-dimensional (2D) and three-dimensional (3D) Laplacian operators. In particular, we propose benchmark functions to quantitatively evaluate the isotropy of the discrete Laplacian operators in 2D and 3D spaces. The benchmark functions have analytic 2D and 3D Lapla-cian solutions so that we can exactly compute the errors between the numerical and analytic solutions.

Automated summary

In this paper, the authors investigate isotropic finite difference discretizations of the 2D and 3D Laplacian operators and propose benchmark functions for evaluating their isotropy quantitatively. These benchmark functions have analytic solutions for 2D and 3D Laplacian operators, allowing for exact computation of the errors between numerical and analytic solutions.