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A nonconforming Trefftz virtual element method for the Helmholtz problem: Numerical aspects
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DOI：10.1016/j.cma.2018.12.039.png)
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Abstract
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We discuss the implementation details and the numerical performance of the recently introduced nonconforming Trefftz virtual element method (Mascotto et al., 2018) 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. (C) 2018 Elsevier B.V. All rights reserved.
Keywords:
Helmholtz equation
Virtual element method
Polygonal meshes
Plane waves
Ill-conditioning
Nonconforming spaces
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