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arXiv · 1807.11237

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

L. Mascotto·I. Perugia·A. Pichler
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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 $h$-, $p$-, 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.

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L. Mascotto, I. Perugia, A. Pichler. 2018-07-30. A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects. https://doi.org/10.1016/j.cma.2018.12.039

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