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

DOI10.1016/j.cma.2018.12.039zbMath1440.65251arXiv1807.11237OpenAlexW2883324933MaRDI QIDQ1987821

Lorenzo Mascotto, Alexander Pichler, Ilaria Perugia

Publication date: 16 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.11237

zbMATH Keywords

plane wavesHelmholtz equationill-conditioningvirtual element methodpolygonal meshesnonconforming spaces

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Wave scattering in solid mechanics (74J20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (15)

Local strategies for improving the conditioning of the plane-wave ultra-weak variational formulation ⋮ Stabilization of the nonconforming virtual element method ⋮ Virtual element method for elliptic bulk‐surface PDEs in three space dimensions ⋮ Rapid calculation of large-scale acoustic scattering from complex targets by a dual-level fast direct solver ⋮ Relationship between the vertex-centered linearity-preserving scheme and the lowest-order virtual element method for diffusion problems on star-shaped polygons ⋮ Reduced basis stabilization and post-processing for the virtual element method ⋮ Virtual element method for solving an inhomogeneous Brusselator model with and without cross-diffusion in pattern formation ⋮ Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number ⋮ An enhanced VEM formulation for plane elasticity ⋮ A virtual element method for the miscible displacement of incompressible fluids in porous media ⋮ A nonconforming Trefftz virtual element method for the Helmholtz problem ⋮ A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes ⋮ Virtual Elements for the Transmission Eigenvalue Problem on Polytopal Meshes ⋮ The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation ⋮ A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations

Uses Software

• PolyMesher

Cites Work

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