A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects
For researchers working on numerical methods for Helmholtz problems, this work offers an improved implementation of a novel method, but it is incremental as it builds on existing Trefftz virtual element methods.
This paper presents implementation details and numerical performance of a nonconforming Trefftz virtual element method for the 2D Helmholtz problem, introducing a strategy to reduce ill-conditioning by filtering basis functions edge by edge, which reduces degrees of freedom. Numerical experiments including h-, p-, and hp-versions and an acoustic scattering application show robust and effective performance compared to other Trefftz methods.
We discuss the implementation details and the numerical performance of the recently introduced nonconforming Trefftz virtual element method for the 2D Helmholtz problem. In particular, we present a strategy to significantly reduce the ill-conditioning of the original method; such a recipe is based on an automatic filtering of the basis functions edge by edge, and therefore allows for a notable reduction of the number of degrees of freedom. A widespread set of numerical experiments, including an application to acoustic scattering, the $h$-, $p$-, and $hp$-versions of the method, is presented. Moreover, a comparison with other Trefftz-based methods for the Helmholtz problem shows that this novel approach results in robust and effective performance.