Computational high frequency wave propagation
From MaRDI portal
Publication:4465272
DOI10.1017/S0962492902000119zbMath1049.65098OpenAlexW2169501376MaRDI QIDQ4465272
Publication date: 27 May 2004
Published in: Acta Numerica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0962492902000119
wave equationnumerical examplesmethod of characteristicsdiffractionLiouville equationgeometrical opticsray tracingseismologyunderwater acousticsmoment methodsphase functionseiconal equationradar cross sectionsystems of hyperbolic equationswave front methodoptical and microwaves
Wave equation (35L05) Diffraction, scattering (78A45) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial value problems for first-order hyperbolic systems (35L45) Geometric optics (78A05) Method of moments applied to problems in optics and electromagnetic theory (78M05)
Related Items
Convergence of frozen Gaussian approximation for high-frequency wave propagation, Numerical solutions for point-source high frequency Helmholtz equation through efficient time propagators for Schrödinger equation, Preasymptotic error analysis of the HDG method for Helmholtz equation with large wave number, Numerical microlocal analysis of harmonic wavefields, An asymptotic Green's function method for the wave equation, Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation, A Coupled Finite Difference – Gaussian Beam Method for High Frequency Wave Propagation, Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography, Babich's expansion and the fast Huygens sweeping method for the Helmholtz wave equation at high frequencies, Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime, Fast Algorithms for High Frequency Wave Propagation, A first order system least squares method for the Helmholtz equation, A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations, Frozen Gaussian approximation-based artificial boundary conditions for one-dimensional nonlinear Schrödinger equation in the semiclassical regime, A semi-Lagrangian numerical method for geometric optics type problems, An improved semi-Lagrangian time splitting spectral method for the semi-classical Schrödinger equation with vector potentials using NUFFT, Learning rays via deep neural network in a ray-based IPDG method for high-frequency Helmholtz equations in inhomogeneous media, The phase flow method, A uniformly second order fast sweeping method for eikonal equations, An adaptive spectral/DG method for a reduced phase-space based level set approach to geometrical optics on curved elements, Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime, Numerical approximation of the Schrödinger equation with the electromagnetic field by the Hagedorn wave packets, A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation, Compressed Absorbing Boundary Conditions via Matrix Probing, A level set framework for capturing multi-valued solutions of nonlinear first-order equations, An adaptive finite-difference method for accurate simulation of first-arrival traveltimes in heterogeneous media, Improved approximation of phase-space densities on triangulated domains using discrete flow mapping with \(p\)-refinement, An asymptotic Green's function method for time-dependent Schrödinger equations with application to Kohn-Sham equations, Frozen Gaussian approximation-based two-level methods for multi-frequency Schrödinger equation, Numerical Eulerian method for linearized gas dynamics in the high frequency regime, An asymptotic method based on a Hopf-Cole transformation for a kinetic BGK equation in the hyperbolic limit, Superposition of multi-valued solutions in high frequency wave dynamics, A high order numerical method for computing physical observables in the semiclassical limit of the one-dimensional linear Schrödinger equation with discontinuous potentials, Numerical solutions of the time‐dependent Schrödinger equation with position‐dependent effective mass, Hadamard integrator for time-dependent wave equations: Lagrangian formulation via ray tracing, Exact equations for smoothed Wigner transforms and homogenization of wave propagation, A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media, Quantum simulation for partial differential equations with physical boundary or interface conditions, Numerical geometric acoustics: an eikonal-based approach for modeling sound propagation in 3D environments, A fixed-point iteration method for high frequency vector wave equations, High-Frequency Limit of the Inverse Scattering Problem: Asymptotic Convergence from Inverse Helmholtz to Inverse Liouville, Gaussian beam decomposition of high frequency wave fields using expectation-maximization, Tomographic inverse problems: mathematical challenges and novel applications. Abstracts from the workshop held April 30 -- May 5, 2023, Tailored finite point method for first order wave equation, Nonlinear geometric optics method-based multi-scale numerical schemes for a class of highly oscillatory transport equations, Source point discovery through high frequency asymptotic time reversal, Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension, Gaussian beam formulations and interface conditions for the one-dimensional linear Schrödinger equation, Transport of phase space densities through tetrahedral meshes using discrete flow mapping, Computing highly oscillatory physical optics integral on the polygonal domain by an efficient numerical steepest descent path method, Computation of transmissions and reflections in geometrical optics via the reduced Liouville equation, Fast Huygens Sweeping Methods for Time-Dependent Schrödinger Equation with Perfectly Matched Layers, High order numerical methods to a type of delta function integrals, Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction, A review of numerical methods for nonlinear partial differential equations, Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations, On discreteness of the Hopf equation, Stochastic regularity of a quadratic observable of high-frequency waves, Spatial-temporal nonlocal homogenization model for transient anti-plane shear wave propagation in periodic viscoelastic composites, A New Earthquake Location Method Based on the Waveform Inversion, Error estimates for Gaussian beam superpositions, The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials, A hierarchy of approximations of the master equation scaled by a size parameter, A wavefront-based Gaussian beam method for computing high frequency wave propagation problems, Pre-asymptotic error analysis of \(hp\)-interior penalty discontinuous Galerkin methods for the Helmholtz equation with large wave number, An accurate spectral/discontinuous finite-element formulation of a phase-space-based level set approach to geometrical optics, Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. II: Impurities, confinement and Bloch oscillations, Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds, Local solutions to high-frequency 2D scattering problems, Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation, A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion, Gaussian beam methods for the Schrödinger equation with discontinuous potentials, Multiscale Computations for Highly Oscillatory Problems, On the convergence of time splitting methods for quantum dynamics in the semiclassical regime, Ordered line integral methods for solving the eikonal equation, Eulerian Geometrical Optics and Fast Huygens Sweeping Methods for Three-Dimensional Time-Harmonic High-Frequency Maxwell's Equations in Inhomogeneous Media, A second-order fast Huygens sweeping method for time-dependent Schrödinger equations with perfectly matched layers, A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations, ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number, A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures, The quadratic Wasserstein metric for earthquake location, Asymptotic solutions for high frequency Helmholtz equations in anisotropic media with Hankel functions, Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations, Gaussian beam decomposition of high frequency wave fields, The auxiliary function method for waveform based earthquake location, Nonlinear geometric optics based multiscale stochastic Galerkin methods for highly oscillatory transport equations with random inputs, Uncertainty quantification for phase-space boundary integral models of ray propagation, Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems, A Direction Preserving Discretization for Computing Phase-Space Densities, A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations, Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. III: From ab initio models to WKB for Schrödinger-Poisson, Ray-based inversion accounting for scattering for biomedical ultrasound tomography, A fixed-point iteration method for high frequency Helmholtz equations, A Gaussian Beam Method for High Frequency Solution of Symmetric Hyperbolic Systems with Polarized Waves, Efficient frozen Gaussian sampling algorithms for nonadiabatic quantum dynamics at metal surfaces
