On theory and application of the Helmholtz equation least squares method in inverse acoustics

DOI10.1088/0266-5611/18/4/313zbMath1022.35087OpenAlexW2030847326MaRDI QIDQ3146265

Victor Isakov, Sean F. Wu

Publication date: 9 October 2002

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/18/4/313

zbMATH Keywords

approximationspherical harmonicsHelmholtz equationexterior problemacoustic pressureradiating solutionLipschitz bounded domainreconstruction of acoustic fields in 3D-domains

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Hydro- and aero-acoustics (76Q05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

A meshless method for some inverse problems associated with the Helmholtz equation ⋮ Integral formulas for supersonic reconstruction of the acoustic field ⋮ Analyzing motorcycle low-frequency noise ⋮ Increased Stability in the Cauchy Problem for Some Elliptic Equations ⋮ The plane wave method for inverse problems associated with Helmholtz-type equations ⋮ Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation ⋮ A STOPPING RULE FOR THE CONJUGATE GRADIENT REGULARIZATION METHOD APPLIED TO INVERSE PROBLEMS IN ACOUSTICS ⋮ THEORY AND BOUNDARY ELEMENT METHODS FOR NEAR-FIELD ACOUSTIC HOLOGRAPHY ⋮ A new method based on polynomials equipped with a parameter to solve two parabolic inverse problems with a nonlocal boundary condition ⋮ Improved integral formulae for supersonic reconstruction of the acoustic field