Reducing Dispersion of Linear Triangular Elements for the Helmholtz Equation

Abstract

The Galerkin/least squares (GLS) modification improves the performance of finite-element computations of time-harmonic acoustics at high wave numbers. The design of the GLS resolution-dependent method parameter for two-dimensional computation in previous work was based on dispersion analysis of one-dimensional and square bilinear elements. We analyze the dispersion of linear triangular finite elements, and define method parameters that eliminate dispersion on a hexagonal patch. Numerical tests compare the performance of the proposed method with established techniques on structured and unstructured triangular meshes. Based on this work, we propose a method parameter that may be used for computation with both linear triangular and bilinear quadrilateral elements.