A Sparse Grid Wavelet Galerkin Method for 3-D Static Piezoelectric Equations

Abstract

The 3-D static piezoelectric equations with four unknowns are fundamental in studying physical behavior of piezoelectric materials. It is very challenging to numerically solve the equations efficiently due to the so-called “curse of dimensionality”. In this paper, we propose a sparse grid wavelet Galerkin method to overcome the difficulty, by combining the wavelet Galerkin method and the sparse grid technique. The error analysis is also developed in detail. Both the theoretical analysis and numerical results show the previous method outperforms the usual finite element method.