{"paper":{"title":"Effect of Choices of Boundary Conditions on the Numerical Efficiency of Direct Solutions of Finite Difference frequency Domain Systems with Perfectly Matched Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nathan Zhao, Shanhui Fan","submitted_at":"2022-02-28T05:39:20Z","abstract_excerpt":"Direct solvers are a common method for solving finite difference frequency domain (FDFD) systems that arise in numerical solutions of Maxwell's equations. In a direct solver, one factorizes the system matrix. Since the system matrix is typically very sparse, the fill-in of these factors is the single most important computational consideration in terms of time complexity and memory requirements. As a result, it is of great interest to determine ways in which this fill-in can be systematically reduced. In this paper, we show that in the context of commonly used perfectly matched boundary layer m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.13552","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/2202.13552/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"}