PreprintCC BY 4.0arXiv
A fully globalized solver for discretized inverse elliptic coefficient problems with exact data
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.
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BibTeX
@misc{harrach2026fully,
title = {{A fully globalized solver for discretized inverse elliptic coefficient problems with exact data}},
author = {Bastian Harrach},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03631},
eprint = {2609.03631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03631},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A fully globalized solver for discretized inverse elliptic coefficient problems with exact data
AU - Bastian Harrach
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03631
UR - https://arxiv.org/abs/2609.03631
AB - 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.
ER -