{"paper":{"title":"A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","physics.class-ph","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Chanhao Yan, Wei Cai, Xuan Zeng","submitted_at":"2012-10-04T15:36:35Z","abstract_excerpt":"In this paper, we will present a new approach for solving Laplace equations in general 3-D domains. The approach is based on a local computation method for the DtN mapping of the Laplace equation by combining a deterministic (local) boundary integral equation method and the probabilistic Feynman-Kac formula of PDE solutions. This hybridization produces a parallel algorithm where the bulk of the computation has no need for data communications. Given the Dirichlet data of the solution on a domain boundary, a local boundary integral equation (BIE) will be established over the boundary of a local "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1491","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}