An Aitken-like acceleration method applied to missing boundary data reconstruction for the Cauchy-Helmholtz problem

DOI10.1016/j.crma.2009.11.010zbMath1183.65133OpenAlexW1980660380MaRDI QIDQ847113

Amel Ben Abda, Riadh Ben Fatma, Damien Tromeur-Dervout

Publication date: 12 February 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.11.010

zbMATH Keywords

finite element methodCauchy problemnumerical examplesconvergence accelerationdomain decompositionHelmholtz equationAitken-Schwarz methodill-posed Cauchy-Helmholtz problem

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Ill-posed problems for PDEs (35R25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (2)

Data completion method for the Helmholtz equation via surface potentials for partial Cauchy data ⋮ A data completion algorithm using an integral representation of the Steklov-Poincaré operator

Cites Work

• An iterative method for solving the Cauchy problem for elliptic equations
• Missing boundary data recovering for the Helmholtz problem
• An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium
• Remarques sur l'observabilité pour l'équation de Laplace
• On some Aitken‐like acceleration of the Schwarz method
• Acceleration of the Schwarz Method for Elliptic Problems
• Approximate solution of a Cauchy problem for the Helmholtz equation
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