Babich-Like Ansatz for Three-Dimensional Point-Source Maxwell's Equations in an Inhomogeneous Medium at High Frequencies

DOI10.1137/15M1052469zbMath1352.65527OpenAlexW2510345035MaRDI QIDQ5298153

Jianliang Qian, Wangtao Lu, Robert Burridge

Publication date: 13 December 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1052469

zbMATH Keywords

transport equationeikonal equationMaxwell's equationdyadic Green's functionfast sweepingBabich-like ansatz

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (7)

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources ⋮ Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing ⋮ Unnamed Item ⋮ Hadamard--Babich Ansatz for Point-Source Elastic Wave Equations in Variable Media at High Frequencies ⋮ Extending Babich's Ansatz for Point-Source Maxwell's Equations Using Hadamard's Method ⋮ A point source of electromagnetic waves in an inhomogeneous medium: a high frequency ansatz and the dual nonstationary singular solution ⋮ Asymptotic solutions for high frequency Helmholtz equations in anisotropic media with Hankel functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime
• Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes
• Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
• Fast sweeping method for the factored eikonal equation
• High order fast sweeping methods for static Hamilton-Jacobi equations
• Weighted essentially non-oscillatory schemes
• A slowness matching Eulerian method for multivalued solutions of eikonal equations
• Efficient implementation of weighted ENO schemes
• Fast sweeping methods for factored anisotropic eikonal equations: multiplicative and additive factors
• Babich's expansion and the fast Huygens sweeping method for the Helmholtz wave equation at high frequencies
• Babich's expansion and high-order Eulerian asymptotics for point-source Helmholtz equations
• Eulerian Geometrical Optics and Fast Huygens Sweeping Methods for Three-Dimensional Time-Harmonic High-Frequency Maxwell's Equations in Inhomogeneous Media
• A Stopping Criterion for Higher-order Sweeping Schemes for Static Hamilton-Jacobi Equations
• High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations
• Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations
• Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
• Weighted ENO Schemes for Hamilton--Jacobi Equations
• A fast sweeping method for Eikonal equations
• Principles of Optics
• The high‐frequency asymptotic field of a point source in an inhomogeneous medium
• High-Order Factorization Based High-Order Hybrid Fast Sweeping Methods for Point-Source Eikonal Equations
• The short wave asymptotic form of the solution for the problem of a point source in an inhomogeneous medium
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

This page was built for publication: Babich-Like Ansatz for Three-Dimensional Point-Source Maxwell's Equations in an Inhomogeneous Medium at High Frequencies