Reduced Order Models for Spectral Domain Inversion: Galerkin Equivalence and Generation of Internal Data
Thursday, May 2, 2019 - 10:10am - 11:00am
We generate reduced order Galerkin models for inversion of problems in Schrodinger form given data in the spectral domain for one and two dimensional problems. We show that in one dimension, after tridiagonalization, the Galerkin system is precisely the same as the three point staggered finite di fference system on the corresponding spectrally matched grid. The orthogonalized basis functions depend only very weakly on the medium, and thus the spectral data yields highly accurate internal solutions, which suggests some natural inversion procedures. In higher dimensions the orthogonalized basis functions act as a generalization of the spectrally matched grid. This is joint work with Liliana Borcea, Vladimir Druskin, and Alex Mamonov.