Trefftz difference schemes on irregular stencils

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Tsukerman, Igor

关键词: Flexible local approximation;    Finite difference schemes;    Trefftz functions;    Electrostatics;    Wave propagation;    Wave scattering;    Electromagnetic waves;    Multiparticle problems;    Long-range interactions;    Irregular stencils;    Meshless methods;    Least squares approximation;   

DOI  :  10.1016/j.jcp.2009.12.025

来源: Elsevier

【 摘 要 】

The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions - local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed recently by Pinheiro and Webb: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of that, FLAME schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions. The accuracy of the method is preserved but its robustness is improved. For demonstration, the paper presents a number of numerical examples in 2D and 313: electrostatic (magnetostatic) particle interactions, scattering of electromagnetic (acoustic) waves, and wave propagation in a photonic crystal. The examples explore the role of the grid and stencil size, of the number of approximating functions, and of the irregularity of the stencils. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free