Wave propagation from lateral Cauchy data using a boundary element method

DOI10.1016/j.wavemoti.2019.102385OpenAlexW2964861442MaRDI QIDQ781619

Yuriy Muzychuk, Andriy Hlova, R. S. Chapko, B. Tomas Johansson

Publication date: 17 July 2020

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.wavemoti.2019.102385

zbMATH Keywords

Galerkin methodwave equationboundary element methodboundary integral equationsTikhonov regularizationsystem of elliptic equationsLaguerre transformhyperbolic lateral Cauchy inverse problemsingle-layer potentials

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Ill-posed problems for PDEs (35R25) Second-order hyperbolic equations (35L10) Second-order elliptic systems (35J47) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38)

Related Items (5)

A method of fundamental solutions with time-discretisation for wave motion from lateral Cauchy data ⋮ The Laguerre transform of a convolution product of vector-valued functions ⋮ A method of fundamental solutions for heat and wave propagation from lateral Cauchy data ⋮ Calculating heat and wave propagation from the lateral Cauchy data ⋮ Solution of the Cauchy problem for the wave equation using iterative regularization

Uses Software

• DGM

Cites Work

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• Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case
• Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs
• On variational formulations of inner boundary value problems for infinite systems of elliptic equations of special kind
• Boundary estimation of hyperbolic bio-heat conduction
• Reflectors in wave equation imaging
• Boundary integral equations
• A timelike Cauchy problem and an inverse problem for general hyperbolic equations
• Rothe's method for the heat equation and boundary integral equations
• Reconstruction of space-dependent potential and/or damping coefficients in the wave equation
• Regularization of an ill-posed Cauchy problem for the wave equation (numerical experiment)
• Inverse problems of 3D ultrasonic tomography with complete and incomplete range data
• An inverse obstacle problem for the wave equation in a finite time domain
• A boundary integral equation method for numerical solution of parabolic and hyperbolic Cauchy problems
• DGM: a deep learning algorithm for solving partial differential equations
• Integral equations for biharmonic data completion
• On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach
• Estimating the boundary condition in a 3D inverse hyperbolic heat conduction problem
• Integral equations for inverse problems in corrosion detection from partial Cauchy data
• Continuous dependence on data for solutions of partial differential equations with a prescribed bound
• The Quasi-Reversibility Method for Thermoacoustic Tomography in a Heterogeneous Medium
• Numerical solution of a time-like Cauchy problem for the wave equation
• Advanced Boundary Element Methods
• Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
• On the use of an integral equation approach for the numerical solution of a Cauchy problem for Laplace equation in a doubly connected planar domain
• Inverse problems for partial differential equations

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