{"paper":{"title":"Scalable parallel 3-D TEM inversion via rational approximation of the matrix exponential","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","physics.geo-ph"],"primary_cat":"math.NA","authors_text":"Ralph-Uwe B\\\"orner, Stefan G\\\"uttel, Thomas G\\\"unther","submitted_at":"2026-05-19T15:05:03Z","abstract_excerpt":"We present a novel parallel implementation for large-scale three-dimensional electromagnetic inversion based on a Gauss-Newton framework combined with a rational near-best approximation of the matrix exponential for transient simulations. The method employs parallel direct solvers for the shifted linear systems arising from the partial fraction representation of the rational approximation and demonstrates efficient parallel execution on a shared-memory architecture using MPI. A key property of the approach is that the time dependence is entirely contained in the residuals of the employed ratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19951","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19951/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}