Optimization of fast algorithms for global Quadrature by Expansion using target-specific expansions
We develop an algorithm for the asymptotically fast evaluation of layer potentials close to and on the source geometry, combining Geometric Global Accelerated QBX ('GIGAQBX') and target-specific expansions. GIGAQBX is a fast high-order scheme for evaluation of layer potentials based on Qua...
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Veröffentlicht in: | Journal of computational physics 2020-02, Vol.403, Article 108976 |
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description | We develop an algorithm for the asymptotically fast evaluation of layer potentials close to and on the source geometry, combining Geometric Global Accelerated QBX ('GIGAQBX') and target-specific expansions. GIGAQBX is a fast high-order scheme for evaluation of layer potentials based on Quadrature by Expansion ('QBX') using local expansions formed via the Fast Multipole Method (FMM). Target-specific expansions serve to lower the cost of the formation and evaluation of QBX local expansions, reducing the associated computational effort from 0 ((p + 1)(2)) to 0 (p + 1) in three dimensions, without any accuracy loss compared with conventional expansions, but with the loss of source/target separation in the expansion coefficients. GIGAQBX is a 'global' QBX scheme, meaning that the potential is mediated entirely through expansions for points close to or on the boundary. In our scheme, this single global expansion is decomposed into two parts that are evaluated separately: one part incorporating near-field contributions using target-specific expansions, and one part using conventional spherical harmonic expansions of far-field contributions, noting that convergence guarantees only exist for the sum of the two sub-expansions. By contrast, target-specific expansions were originally introduced as an acceleration mechanism for 'local' QBX schemes, in which the far-field does not contribute to the QBX expansion. Compared with the unmodified GIGAQBX algorithm, we show through a reproducible, time-calibrated cost model that the combined scheme yields a considerable cost reduction for the near-field evaluation part of the computation. We support the effectiveness of our scheme through numerical results demonstrating performance improvements for Laplace and Helmholtz kernels. (C) 2019 Elsevier Inc. All rights reserved. |
doi_str_mv | 10.1016/j.jcp.2019108976 |
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GIGAQBX is a fast high-order scheme for evaluation of layer potentials based on Quadrature by Expansion ('QBX') using local expansions formed via the Fast Multipole Method (FMM). Target-specific expansions serve to lower the cost of the formation and evaluation of QBX local expansions, reducing the associated computational effort from 0 ((p + 1)(2)) to 0 (p + 1) in three dimensions, without any accuracy loss compared with conventional expansions, but with the loss of source/target separation in the expansion coefficients. GIGAQBX is a 'global' QBX scheme, meaning that the potential is mediated entirely through expansions for points close to or on the boundary. In our scheme, this single global expansion is decomposed into two parts that are evaluated separately: one part incorporating near-field contributions using target-specific expansions, and one part using conventional spherical harmonic expansions of far-field contributions, noting that convergence guarantees only exist for the sum of the two sub-expansions. By contrast, target-specific expansions were originally introduced as an acceleration mechanism for 'local' QBX schemes, in which the far-field does not contribute to the QBX expansion. Compared with the unmodified GIGAQBX algorithm, we show through a reproducible, time-calibrated cost model that the combined scheme yields a considerable cost reduction for the near-field evaluation part of the computation. We support the effectiveness of our scheme through numerical results demonstrating performance improvements for Laplace and Helmholtz kernels. (C) 2019 Elsevier Inc. All rights reserved.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2019108976</identifier><language>eng</language><publisher>SAN DIEGO: Elsevier</publisher><subject>Computer Science ; Computer Science, Interdisciplinary Applications ; Physical Sciences ; Physics ; Physics, Mathematical ; Science & Technology ; Technology</subject><ispartof>Journal of computational physics, 2020-02, Vol.403, Article 108976</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>11</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000503737000021</woscitedreferencesoriginalsourcerecordid><cites>FETCH-webofscience_primary_0005037370000213</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Wala, Matt</creatorcontrib><creatorcontrib>Klockner, Andreas</creatorcontrib><title>Optimization of fast algorithms for global Quadrature by Expansion using target-specific expansions</title><title>Journal of computational physics</title><addtitle>J COMPUT PHYS</addtitle><description>We develop an algorithm for the asymptotically fast evaluation of layer potentials close to and on the source geometry, combining Geometric Global Accelerated QBX ('GIGAQBX') and target-specific expansions. GIGAQBX is a fast high-order scheme for evaluation of layer potentials based on Quadrature by Expansion ('QBX') using local expansions formed via the Fast Multipole Method (FMM). Target-specific expansions serve to lower the cost of the formation and evaluation of QBX local expansions, reducing the associated computational effort from 0 ((p + 1)(2)) to 0 (p + 1) in three dimensions, without any accuracy loss compared with conventional expansions, but with the loss of source/target separation in the expansion coefficients. GIGAQBX is a 'global' QBX scheme, meaning that the potential is mediated entirely through expansions for points close to or on the boundary. In our scheme, this single global expansion is decomposed into two parts that are evaluated separately: one part incorporating near-field contributions using target-specific expansions, and one part using conventional spherical harmonic expansions of far-field contributions, noting that convergence guarantees only exist for the sum of the two sub-expansions. By contrast, target-specific expansions were originally introduced as an acceleration mechanism for 'local' QBX schemes, in which the far-field does not contribute to the QBX expansion. Compared with the unmodified GIGAQBX algorithm, we show through a reproducible, time-calibrated cost model that the combined scheme yields a considerable cost reduction for the near-field evaluation part of the computation. We support the effectiveness of our scheme through numerical results demonstrating performance improvements for Laplace and Helmholtz kernels. (C) 2019 Elsevier Inc. All rights reserved.</description><subject>Computer Science</subject><subject>Computer Science, Interdisciplinary Applications</subject><subject>Physical Sciences</subject><subject>Physics</subject><subject>Physics, Mathematical</subject><subject>Science & Technology</subject><subject>Technology</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>AOWDO</sourceid><recordid>eNqVT8FKxDAUDOKCdde7x9yl9aV12-ZcVryJ4H15jUl9pU1CkqLr11tF73qagZlhZhi7FlAIEPXtWIzKFyUIKaCVTX3GMgES8rIR9TnLAEqRSynFBbuMcQSAdn_XZkw9-kQzfWAiZ7kz3GBMHKfBBUqvc-TGBT5MrseJPy34EjAtQfP-xA_vHm38Si2R7MAThkGnPHqtyJDi-lePO7YxOEV99YNbdnN_eO4e8jfdOxMVaav00QeaMZyO67Q9VE3VrGQdXW1Z-3d3R-n7SecWm6r_FX0CNjhk3A</recordid><startdate>20200215</startdate><enddate>20200215</enddate><creator>Wala, Matt</creator><creator>Klockner, Andreas</creator><general>Elsevier</general><scope>AOWDO</scope><scope>BLEPL</scope><scope>DTL</scope></search><sort><creationdate>20200215</creationdate><title>Optimization of fast algorithms for global Quadrature by Expansion using target-specific expansions</title><author>Wala, Matt ; Klockner, Andreas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-webofscience_primary_0005037370000213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer Science</topic><topic>Computer Science, Interdisciplinary Applications</topic><topic>Physical Sciences</topic><topic>Physics</topic><topic>Physics, Mathematical</topic><topic>Science & Technology</topic><topic>Technology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wala, Matt</creatorcontrib><creatorcontrib>Klockner, Andreas</creatorcontrib><collection>Web of Science - Science Citation Index Expanded - 2020</collection><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wala, Matt</au><au>Klockner, Andreas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimization of fast algorithms for global Quadrature by Expansion using target-specific expansions</atitle><jtitle>Journal of computational physics</jtitle><stitle>J COMPUT PHYS</stitle><date>2020-02-15</date><risdate>2020</risdate><volume>403</volume><artnum>108976</artnum><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>We develop an algorithm for the asymptotically fast evaluation of layer potentials close to and on the source geometry, combining Geometric Global Accelerated QBX ('GIGAQBX') and target-specific expansions. GIGAQBX is a fast high-order scheme for evaluation of layer potentials based on Quadrature by Expansion ('QBX') using local expansions formed via the Fast Multipole Method (FMM). Target-specific expansions serve to lower the cost of the formation and evaluation of QBX local expansions, reducing the associated computational effort from 0 ((p + 1)(2)) to 0 (p + 1) in three dimensions, without any accuracy loss compared with conventional expansions, but with the loss of source/target separation in the expansion coefficients. GIGAQBX is a 'global' QBX scheme, meaning that the potential is mediated entirely through expansions for points close to or on the boundary. In our scheme, this single global expansion is decomposed into two parts that are evaluated separately: one part incorporating near-field contributions using target-specific expansions, and one part using conventional spherical harmonic expansions of far-field contributions, noting that convergence guarantees only exist for the sum of the two sub-expansions. By contrast, target-specific expansions were originally introduced as an acceleration mechanism for 'local' QBX schemes, in which the far-field does not contribute to the QBX expansion. Compared with the unmodified GIGAQBX algorithm, we show through a reproducible, time-calibrated cost model that the combined scheme yields a considerable cost reduction for the near-field evaluation part of the computation. We support the effectiveness of our scheme through numerical results demonstrating performance improvements for Laplace and Helmholtz kernels. (C) 2019 Elsevier Inc. All rights reserved.</abstract><cop>SAN DIEGO</cop><pub>Elsevier</pub><doi>10.1016/j.jcp.2019108976</doi><tpages>23</tpages></addata></record> |
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title | Optimization of fast algorithms for global Quadrature by Expansion using target-specific expansions |
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