A Sparse Grid Wavelet Galerkin Method for 3-D Static Piezoelectric Equations (Communications in Computational Physics, 2024)
The 3-D static piezoelectric equations with four unknowns are fundamentalin 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. Theerror analysis is also developed in detail. Both the theoretical analysis and numericalresults show the previous method outperforms the usual finite element method.