On combining model reduction and Gauss-Newton algorithms for inverse partial differential equation problems. (English) Zbl 1127.65030
Summary: We 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 selfadjoint 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.
MSC:
65J22 | Numerical solution to inverse problems in abstract spaces |
35R30 | Inverse problems for PDEs |
65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
49M15 | Newton-type methods |