{"paper":{"title":"Convergence of parallel overlapping domain decomposition methods with impedance boundary conditions for time-harmonic Maxwell equations in heterogeneous media","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Euan A. Spence, Luyu Cen, Shihua Gong, Yue Yu","submitted_at":"2026-06-03T15:04:22Z","abstract_excerpt":"This paper analyzes the convergence of parallel overlapping domain-decomposition methods with impedance boundary conditions for the time-harmonic Maxwell equations in heterogeneous media. We prove that the parallel iterative method is well-posed in an appropriate function space, and characterize the error propagation operator through impedance-to-impedance maps that describe interactions between neighboring subdomains. For strip domain decompositions, we derive explicit convergence estimates in terms of the norms of the impedance-to-impedance maps. At the discrete level, we develop the finite-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04982","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/2606.04982/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"}