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

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.

References in corpus (3)

• Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods
• Stability and error analysis for the Helmholtz equation with variable coefficients
• A nonconforming Trefftz virtual element method for the Helmholtz problem

Cited by in corpus (7)

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• Virtual element method for elliptic bulk-surface PDEs in three space dimensions
• Reduced basis stabilization and post-processing for the virtual element method
• A nonconforming Trefftz virtual element method for the Helmholtz problem
• A review on arbitrarily regular conforming virtual element methods for elliptic partial differential equations
• The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation
• Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number