{"doi":"10.1090/mcom/3102","title":"Non-iterative parallel Schwarz algorithms based on overlapping domain decomposition for parabolic partial differential equations","abstract":"<p>\n                    Two non-iterative parallel Schwarz algorithms (NIPSA) are presented to solve initial-boundary value problems of parabolic partial differential equations of second order. Algorithms are based on an overlapping domain decomposition and are fully parallel. A new idea is to introduce a partition of unity to distribute reasonably residuals of systems into sub-domains in the first algorithm and to sum weighted local corrections of solutions on sub-domains in the second one. Theoretical analysis shows that the algorithms have very good approximate property. At each time step, no iteration is required to reach the optimal order accuracy in\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L</mml:mi>\n                            <mml:mn>2</mml:mn>\n                          </mml:msup>\n                          <mml:annotation encoding=\"application/x-tex\">L^2</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    -norm. As well small overlapping can be used under some conditions for domain decomposition. Numerical results are also reported, which verify the theoretical analysis.\n                  </p>","journal":"Mathematics of Computation","year":2017,"id":680329,"datarank":0.31191623125197543,"base_score":2.0794415416798357,"endowment":2.0794415416798357,"self_citation_contribution":0.31191623125197543,"citation_network_contribution":0.0,"self_endowment_contribution":0.31191623125197543,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":7,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1777536,"name":"Danping Yang","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Non-iterative parallel Schwarz algorithms based on overlapping domain decomposition for parabolic partial differential equations","abstract":"<p>\n                    Two non-iterative parallel Schwarz algorithms (NIPSA) are presented to solve initial-boundary value problems of parabolic partial differential equations of second order. Algorithms are based on an overlapping domain decomposition and are fully parallel. A new idea is to introduce a partition of unity to distribute reasonably residuals of systems into sub-domains in the first algorithm and to sum weighted local corrections of solutions on sub-domains in the second one. Theoretical analysis shows that the algorithms have very good approximate property. At each time step, no iteration is required to reach the optimal order accuracy in\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L</mml:mi>\n                            <mml:mn>2</mml:mn>\n                          </mml:msup>\n                          <mml:annotation encoding=\"application/x-tex\">L^2</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    -norm. As well small overlapping can be used under some conditions for domain decomposition. Numerical results are also reported, which verify the theoretical analysis.\n                  </p>","is_dataset_classified":null,"base_score":2.0794415416798357,"endowment":2.0794415416798357,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"26207759","pmcid":null,"openalex_id":"https://openalex.org/W2327425776","authors":[],"funders":[],"total_grants":0,"fwci":0.5972,"citation_percentile":0.6690149,"influential_citations":0,"citation_trend":[{"year":2018,"count":1},{"year":2019,"count":1},{"year":2020,"count":3},{"year":2021,"count":1},{"year":2024,"count":1}],"oa_status":"closed","license":"https://www.ams.org/publications/copyright-and-permissions","oa_locations":[{"url":"http://www.ams.org/mcom/2017-86-308/S0025-5718-2017-03102-1/S0025-5718-2017-03102-1.pdf","host_type":"publisher"},{"url":"https://www.ams.org/mcom/2017-86-308/S0025-5718-2017-03102-1/S0025-5718-2017-03102-1.pdf","host_type":"publisher"},{"url":"https://doi.org/10.1090/mcom/3102","host_type":"journal"}],"fields_of_study":["Advanced Numerical Methods in Computational Mathematics","Numerical methods in engineering","Electromagnetic Simulation and Numerical Methods","Mathematics","Computer Science"],"mesh_terms":[],"keywords":["Domain decomposition methods","Mathematics","Schwarz alternating method","Partial differential equation","Partition of unity","Partition (number theory)","Iterative method","Additive Schwarz method","Boundary value problem","Algorithm","Norm (philosophy)","Domain (mathematical analysis)","Applied mathematics","Mathematical analysis","Finite element method","Combinatorics"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-17T14:52:43.581519Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}