Title

The closed-form particular solutions for the Laplace operator using oscillatory radial basis functions in 2D

Authors

Anup Lamichhane, Ohio Northern UniversityFollow
B. Ghamire, Alabama State University
Yu Wakayama, Ohio Northern University
Alex T. Sube, Ohio Northern University

Document Type

Article

Recommended Citation

Lamichhane, Anup, B. Ghamire, Yu Wakayama, and Alex T. Sube. "The closed-form particular solutions for the Laplace operator using oscillatory radial basis functions in 2D." Engineering Analysis with Boundary Elements 96 (Nov 2018): 187-193. doi: 10.1016/j.enganabound.2018.09.002.

Abstract

The closed-form particular solutions of the radial basis functions (RBFs) are essential for the implementation of several numerical methods to solve various partial differential equations (PDEs). Recently, a new class of oscillatory RBFs has been introduced. In this paper, we derive the closed-form particular solutions of the oscillatory RBFs for the Laplace operator in 2D so that it can be applied to particular solutions based numerical methods. We have successfully implemented the newly derived particular solutions in the method of particular solutions (MPS) for solving Poisson’s equation as well as elliptic PDEs with variable coefficients.

Publication Date

11-2018