Application of operator splitting to the Maxwell equations including a source term

DOI10.1016/j.apnum.2008.03.031zbMath1159.78346OpenAlexW2172117522MaRDI QIDQ1007376

István Faragó, Robert Horváth, Mikhail A. Botchev

Publication date: 20 March 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.03.031

zbMATH Keywords

Maxwell equationssplitting methodsKrylov subspace methodsstrang splittingGautschi cosine schemestaggered finite differencesWhitney finite elementsYee method

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Cites Work

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• Calculation of functions of unsymmetric matrices using Arnoldi's method
• Unified framework for numerical methods to solve the time-dependent Maxwell equations
• Weighted sequential splittings and their analysis
• Consistency analysis of operator splitting methods for \(C_{0}\)-semigroups expression
• On the convergence and local splitting error of different splitting schemes
• An iterative solution method for solving \(f(A)x=b\), using Krylov subspace information obtained for the symmetric positive definite matrix A
• Mixed finite elements in \(\mathbb{R}^3\)
• On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations
• A Gautschi-type method for oscillatory second-order differential equations
• Fourier analysis of numerical algorithms for the Maxwell equations
• The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations
• Numerical integration of ordinary differential equations based on trigonometric polynomials
• Accurate partial difference methods. I: Linear Cauchy problems
• A Vector Finite Element Time-Domain Method for Solving Maxwell's Equations on Unstructured Hexahedral Grids
• Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• Exponential Integrators for Large Systems of Differential Equations
• Time-domain finite-element methods
• Investigation of numerical time-integrations of Maxwell's equations using the staggered grid spatial discretization
• Finite Element Methods for Maxwell's Equations
• Iterative Krylov Methods for Large Linear Systems
• Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
• High-accuracy Yee algorithm based on nonstandard finite differences: new developments and verifications
• High-Order Symplectic Integration Methods for Finite Element Solutions to Time Dependent Maxwell Equations
• Some application of splitting-up methods to the solution of mathematical physics problems
• On the Construction and Comparison of Difference Schemes
• Two polynomial methods of calculating functions of symmetric matrices
• Geometric multigrid with applications to computational fluid dynamics