A fully globalized solver for discretized inverse elliptic coefficient problems with exact data
Year: 2026
Type: preprint
Abstract: We consider finite-dimensional nonlinear inverse problems arising from finite element discretizations of elliptic inverse coefficient problems such as the Calderón problem with finitely many measurements and unknowns. Such inverse coefficient problems are notorious for their nonlinearity and ill-posedness, and numerical solvers tend to depend strongly on good initial values. In this work, we develop a new locally convergent algorithm with an explicit residual criterion that ensures convergence to the inverse problem solution, and a globalized variant that is guaranteed to automatically switch to the faster locally convergent algorithm after finitely many global search steps.
Source: arXiv (Cornell University)
Author: Harrach, Bastian
Institution: Goethe University Frankfurt
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208716489