Vladimir Druskin and Mikhail Zaslavsky 2007 Inverse Problems 23 1599 doi:10.1088/0266-5611/23/4/013
Vladimir Druskin and Mikhail Zaslavsky
Show affiliationsWe suggest an approach to speed up the Gauss–Newton solution of inverse partial differential equation problems by minimizing the number of forward problem calls. The acceleration is based on effective incorporation of the information from the previous iterations via a reduced-order model (ROM). It is designed with the help of Galerkin and pseudo-Galerkin methods for self-adjoint and complex symmetric problems respectively. The constructed ROM generates effective multivariate rational interpolation matching the forward solutions and the Jacobians from the previous iterations. Numerical examples for the inverse conductivity problem for the 3D Maxwell system show significant accelerations.
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
Issue 4 (August 2007)
Received 20 November 2006, in final form 8 May 2007
Published 6 July 2007
Vladimir Druskin and Mikhail Zaslavsky 2007 Inverse Problems 23 1599
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