The Power of Trefftz Approximations: Finite Difference, Boundary Difference and Discontinuous Galerkin Methods; Nonreflecting Conditions and Non-Asymptotic Homogenization
DOI10.1007/978-3-319-20239-6_5zbMath1359.65205OpenAlexW1414259359MaRDI QIDQ2942186
Vadim A. Markel, Herbert Egger, Igor Tsukerman, Farzad Ahmadi, Nabil Nowak, Fritz Kretzschmar, Sascha M. Schnepp
Publication date: 20 August 2015
Published in: Finite Difference Methods,Theory and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-20239-6_5
wave propagationMaxwell equationsfinite difference schemesdiscontinuous Galerkin methodsnonreflecting boundary conditionsmetamaterialsTrefftz functionseffective medium theoryboundary difference schemes
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Non-dissipative space-time \(hp\)-discontinuous Galerkin method for the time-dependent Maxwell equations
- A general approach for high order absorbing boundary conditions for the Helmholtz equation
- Discretization of the wave equation using continuous elements in time and a hybridizable discontinuous Galerkin method in space
- Transparent boundary conditions for a discontinuous Galerkin Trefftz method
- Boundary integral equations
- Trefftz difference schemes on irregular stencils
- Numerical solution of problems on unbounded domains. A review
- A formulation of asymptotic and exact boundary conditions using local operators
- On the definition of surface potentials for finite-difference operators
- High-order nonreflecting boundary conditions for the dispersive shallow water equations.
- Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
- Plane wave approximation of homogeneous Helmholtz solutions
- Optimizing the perfectly matched layer
- A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
- High-order local non-reflecting boundary conditions: a review
- A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems
- Further results on controlling the false discovery proportion
- Discontinuous Galerkin methods with Trefftz approximations
- Modelling of periodic electromagnetic structures bianisotropic materials with memory effects
- A class of difference schemes with flexible local approximation
- Method of Difference Potentials and Its Applications
- Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
- The Theory of Distributions
- A space-time discontinuous Galerkin method for the solution of the wave equation in the time domain
- Simulation of Diffraction in Periodic Media with a Coupled Finite Element and Plane Wave Approach
- Boundary algebraic equations for lattice problems
- Absorbing Boundary Conditions for Difference Approximations to the Multi-Dimensional Wave Equation
- Numerical Absorbing Boundary Conditions for the Wave Equation
- Radiation boundary conditions for wave-like equations
- Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions
- The Theory of Composites
- A Singularity-Free Boundary Equation Method for Wave Scattering
- A Boundary Difference Method for Electromagnetic Scattering Problems With Perfect Conductors and Corners
- Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
- High-order nonreflecting boundary conditions without high-order derivatives
This page was built for publication: The Power of Trefftz Approximations: Finite Difference, Boundary Difference and Discontinuous Galerkin Methods; Nonreflecting Conditions and Non-Asymptotic Homogenization