English

A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects

Numerical Analysis 2019-02-20 v1

Abstract

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 hh-, pp-, and hphp-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.

Keywords

Cite

@article{arxiv.1807.11237,
  title  = {A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects},
  author = {L. Mascotto and I. Perugia and A. Pichler},
  journal= {arXiv preprint arXiv:1807.11237},
  year   = {2019}
}
R2 v1 2026-06-23T03:18:42.072Z