{"id":238123,"date":"2013-11-01T00:00:00","date_gmt":"2013-11-01T07:00:00","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/msr-research-item\/a-parallel-directional-fast-multipole-method\/"},"modified":"2018-10-16T22:00:18","modified_gmt":"2018-10-17T05:00:18","slug":"a-parallel-directional-fast-multipole-method","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/a-parallel-directional-fast-multipole-method\/","title":{"rendered":"A Parallel Directional Fast Multipole Method"},"content":{"rendered":"<div class=\"asset-content\">\n<p>This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data dependencies. We propose a simple partition at a fixed level of the octree and show that, if the partitions are properly balanced between p processes, the overall runtime is essentially O(N log N\/p+ p). By the structure of the low-rank criterion, we are able to avoid communication at the top of the octree. We demonstrate the effectiveness of our parallelization on several challenging models.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a more restrictive low-rank criterion than that of the low-frequency regime, and thus effective parallelizations must adapt to the modified data [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"SIAM - Society for Industrial and Applied Mathematics","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"4","msr_journal":"SIAM Journal on Scientific Computing","msr_number":"","msr_organization":"","msr_pages_string":"C335-C352","msr_page_range_start":"C335","msr_page_range_end":"C352","msr_series":"","msr_volume":"36","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"BJORN ENGQUIST","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2014-08-07","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":2013,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561,13546],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-238123","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"SIAM - Society for Industrial and Applied Mathematics","msr_edition":"","msr_affiliation":"","msr_published_date":"2014-08-07","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"C335-C352","msr_chapter":"","msr_isbn":"","msr_journal":"SIAM Journal on Scientific Computing","msr_volume":"36","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"4","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"238422","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"1311.4257.pdf","viewUrl":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-content\/uploads\/2016\/06\/1311.4257-1.pdf","id":238422,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Austin R. 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