Hadamard integrators for wave equations in time and frequency domain: Eulerian formulations via butterfly algorithms
DOI10.1007/s10915-024-02631-0zbMATH Open1547.65164MaRDI QIDQ6604511
Robert Burridge, Yuxiao Wei, Jianliang Qian, Shingyu Leung, Jin Cheng
Publication date: 12 September 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Helmholtz equationcausticsHadamard's ansatzhigh-frequency wavebutterfly algorithmtime-dependent wave equation
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for discrete and fast Fourier transforms (65T50) Complexity and performance of numerical algorithms (65Y20) Green's functions for elliptic equations (35J08) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Fast multiscale Gaussian beam methods for wave equations in bounded convex domains
- Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime
- Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
- The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
- Asymptotic solutions of oscillatory initial value problems
- Fast sweeping method for the factored eikonal equation
- Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
- Gaussian beam decomposition of high frequency wave fields
- On accuracy conditions for the numerical computation of waves
- Weighted essentially non-oscillatory schemes
- A perfectly matched layer for the absorption of electromagnetic waves
- An introduction to Eulerian geometrical optics (1992--2002)
- A slowness matching Eulerian method for multivalued solutions of eikonal equations
- Lectures on Cauchy's problem in linear partial differential equations.
- A fast Huygens sweeping method for capturing paraxial multi-color optical self-focusing in nematic liquid crystals
- Fast Huygens sweeping methods for Schrödinger equations in the semi-classical regime
- Fast Huygens sweeping methods for a class of nonlocal Schrödinger equations
- 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
- Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation
- Eulerian geometrical optics and fast Huygens sweeping methods for three-dimensional time-harmonic high-frequency Maxwell's equations in inhomogeneous media
- Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation
- Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
- The Stochastic Caustic
- Mountain Waves and Gaussian Beams
- A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
- High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations
- Computational high frequency wave propagation
- Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
- Weighted ENO Schemes for Hamilton--Jacobi Equations
- Extending Babich's Ansatz for Point-Source Maxwell's Equations Using Hadamard's Method
- A fast sweeping method for Eikonal equations
- Hadamard--Babich Ansatz for Point-Source Elastic Wave Equations in Variable Media at High Frequencies
- Fast Multiscale Gaussian Beam Method for Three-Dimensional Elastic Wave Equations in Bounded Domains
- Butterfly Factorization
- Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method
- Babich-Like Ansatz for Three-Dimensional Point-Source Maxwell's Equations in an Inhomogeneous Medium at High Frequencies
- 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
- Uniform asymptotic expansions at a caustic
- The short wave asymptotic form of the solution for the problem of a point source in an inhomogeneous medium
- Interpolative Butterfly Factorization
- Butterfly Factorization Via Randomized Matrix-Vector Multiplications
- 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
This page was built for publication: Hadamard integrators for wave equations in time and frequency domain: Eulerian formulations via butterfly algorithms
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6604511)