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 -, -, and -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.
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}
}