An inverse random source problem for the Helmholtz equation

DOI10.1090/S0025-5718-2013-02730-5zbMath1278.65005OpenAlexW2136080835MaRDI QIDQ2862526

Peijun Li, Gang Bao, Shui-Nee Chow, Hao-Min Zhou

Publication date: 15 November 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02730-5

zbMATH Keywords

stochastic differential equationnumerical examplesfast Fourier transformtwo-point boundary value probleminverse source problemstochastic Helmholtz equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Inverse problems involving ordinary differential equations (34A55) Linear boundary value problems for ordinary differential equations (34B05) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items (33)

The factorization method and Capon’s method for random source identification in experimental aeroacoustics ⋮ Inverse Random Source Scattering Problems in Several Dimensions ⋮ Identification of the material properties in nonuniform nanostructures ⋮ Inverse problems for stochastic parabolic equations with additive noise ⋮ Stability on the inverse random source scattering problem for the one-dimensional Helmholtz equation ⋮ Inverse Random Source Scattering for Elastic Waves ⋮ Reconstruction of Multiscale Elastic Sources from Multifrequency Sparse Far Field Patterns ⋮ Inverse Elastic Scattering for a Random Potential ⋮ Stability for the electromagnetic inverse source problem in inhomogeneous media ⋮ A Data-Assisted Two-Stage Method for the Inverse Random Source Problem ⋮ Stability of inverse random source scattering problems in a multi-layered medium ⋮ Mathematical analysis and numerical methods for inverse scattering problems ⋮ Inverse random source scattering for the Helmholtz equation in inhomogeneous media ⋮ Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves ⋮ Finite volume method for solving the stochastic Helmholtz equation ⋮ Stability for the Acoustic Inverse Source Problem in Inhomogeneous Media ⋮ On the Asymptotical Regularization for Linear Inverse Problems in Presence of White Noise ⋮ An inverse random source problem for the one-dimensional Helmholtz equation with attenuation ⋮ Radiating and non-radiating sources in elasticity ⋮ Correlation imaging in inverse scattering is tomography on probability distributions ⋮ Reconstruction of a compactly supported sound profile in the presence of a random background medium ⋮ Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation ⋮ Inverse acoustic scattering problem in half-space with anisotropic random impedance ⋮ Stability for the inverse source problems in elastic and electromagnetic waves ⋮ Cauchy problem of non-homogenous stochastic heat equation and application to inverse random source problem ⋮ Inverse random source problems for time-harmonic acoustic and elastic waves ⋮ Inverse Random Source Scattering for the Helmholtz Equation with Attenuation ⋮ A fourth-order Cartesian grid method for multiple acoustic scattering on closely packed obstacles ⋮ An inverse source problem for the stochastic wave equation ⋮ Inverse Elastic Scattering for a Random Source ⋮ An inverse random source problem in a stochastic fractional diffusion equation ⋮ An inverse random source problem for the time fractional diffusion equation driven by a fractional Brownian motion ⋮ A Recursive Algorithm for MultiFrequency Acoustic Inverse Source Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A multi-frequency inverse source problem
• An inverse source problem with multiple frequency data
• Linear stochastic differential equations with boundary conditions
• Boundary value problems for stochastic differential equations
• Inverse acoustic and electromagnetic scattering theory.
• Statistical and computational inverse problems.
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• An inverse random source scattering problem in inhomogeneous media
• Central Limits and Homogenization in Random Media
• On the determination of a differential equation from its spectral function
• Numerical solution of an inverse medium scattering problem with a stochastic source
• Physics-based models for measurement correlations: application to an inverse Sturm–Liouville problem
• Acoustic source identification using multiple frequency information
• Fine scale uncertainty in parameter estimation for elliptic equations
• On the inverse scattering problem for the Helmholtz equation in one dimension
• The inverse source problem of electromagnetics: linear inversion formulation and minimum energy solution
• Nonuniqueness in inverse source and scattering problems
• Inverse Source Problem in Nonhomogeneous Background Media
• Introduction to Bayesian Scientific Computing
• Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
• Wave Propagation in a One-Dimensional Random Medium

This page was built for publication: An inverse random source problem for the Helmholtz equation