Interpolation properties of generalized plane waves

Abstract

This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence is shown with respect to the size of the domain considered. The new basis functions are then implemented in a numerical method to solve a scalar wave equation problem with a mixed boundary condition. The order of convergence of the method varies linearly with the one of the interpolation.

Cited by in corpus (12)

• A Survey of Trefftz Methods for the Helmholtz Equation
• Trefftz discontinuous Galerkin methods on unstructured meshes for the wave equation
• A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
• A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media
• Amplitude-based Generalized Plane Waves: new Quasi-Trefftz functions for scalar equations in 2D
• Well-posedness and generalized plane waves simulations of a 2D mode conversion model
• A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media
• A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential
• A geometric optics ansatz-based plane wave method for two dimensional Helmholtz equations with variable wave numbers
• Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number
• A plane wave method based on approximate wave directions for two dimensional Helmholtz equations with large wave numbers
• The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation