Trefftz approximations in complex media: accuracy and applications
DOI10.1016/j.camwa.2018.08.065zbMath1442.65408arXiv1801.09355OpenAlexW2963992848MaRDI QIDQ2203886
Shampy Mansha, Vadim A. Markel, Yi Dong Chong, Igor Tsukerman
Publication date: 2 October 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.09355
homogenizationMaxwell's equationsfinite difference schemeswave scatteringphotonic devicesTrefftz approximations
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Wave scattering in solid mechanics (74J20) Diffraction, scattering (78A45)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(S^{4}\): a free electromagnetic solver for layered periodic structures
- Characteristic vectors of bordered matrices with infinite dimensions
- Interpolation properties of generalized plane waves
- The least singular value of a random square matrix is O\((n ^{- 1/2})\)
- Trefftz difference schemes on irregular stencils
- Random matrices: The distribution of the smallest singular values
- Some polynomial approximation operators
- The partition of unity finite element method: basic theory and applications
- The wave based method: an overview of 15 years of research
- Wave interpolation finite elements for Helmholtz problems with jumps in the wave speed
- Operator adapted spectral element methods. I: Harmonic and generalized harmonic polynomials
- A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
- The generalized finite element method for Helmholtz equation: theory, computation, and open problems
- Plane wave decomposition in the unit disc: convergence estimates and computational aspects
- A class of difference schemes with flexible local approximation
- The Exponentially Convergent Trapezoidal Rule
- A Survey of Trefftz Methods for the Helmholtz Equation
- A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems
- Flexible approximation schemes with numerical and semi‐analytical bases
- Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the p-Version
- Non-asymptotic theory of random matrices: extreme singular values
- A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers
- Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
- Plane wave discontinuous Galerkin methods: Analysis of theh-version
- Smallest singular value of a random rectangular matrix
- THE PARTITION OF UNITY METHOD
- Trefftz method: A general theory
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- A priorierror analysis of space–time Trefftz discontinuous Galerkin methods for wave problems
- Trigonometric Interpolation and Quadrature in Perturbed Points
- GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE
- Numerical inverting of matrices of high order
This page was built for publication: Trefftz approximations in complex media: accuracy and applications