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dc.contributor.authorHuang, Tsung-Mingen_US
dc.contributor.authorLin, Wen-Weien_US
dc.contributor.authorTsai, Hsinhanen_US
dc.contributor.authorWang, Weichungen_US
dc.date.accessioned2019-12-13T01:12:23Z-
dc.date.available2019-12-13T01:12:23Z-
dc.date.issued2019-12-01en_US
dc.identifier.issn0010-4655en_US
dc.identifier.urihttp://dx.doi.org/10.1016/j.cpc.2019.07.007en_US
dc.identifier.urihttp://hdl.handle.net/11536/153243-
dc.description.abstractA null-space free method with the FFT-based matrix-vector multiplications was proposed to solve the Maxwell equations that model the three-dimensional photonic crystals. The most time-consuming parts of this method were the FFT-based matrix-vector multiplications. In this article, we propose new mathematical formulas to compute the FFT-based matrix-vector multiplications and derive highly efficient algorithms on top of the NVIDIA GPU architecture. The resulting algorithms are approximately two- to threefold faster than the previous algorithms. We have successfully used a single NVIDIA Tesla P100 GPU to solve a set of generalized eigenvalue problems of 5, 184, 000 dimensions in 17 to 22 seconds for each problem. Furthermore, we ported the codes to a GPU cluster and achieved near linear scalability. To our knowledge, these GPU implementations of the proposed algorithms are the fastest implementations. The schemes can be applied to simulate a three-dimensional photonic crystal with all 14 Bravais lattices. These highly efficient schemes and codes raise possibilities for large-scale and near real-time numerical simulations for novel physical discoveries and engineering applications of photonic crystals. (C) 2019 Elsevier B.V. All rights reserved.en_US
dc.language.isoen_USen_US
dc.subjectThree-dimensional photonic crystalsen_US
dc.subjectThe Maxwell equationsen_US
dc.subjectFast Fourier transformen_US
dc.subjectParallel GPU computingen_US
dc.subjectNull-space free methoden_US
dc.titleHighly efficient GPU eigensolver for three-dimensional photonic crystal band structures with any Bravais latticeen_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.cpc.2019.07.007en_US
dc.identifier.journalCOMPUTER PHYSICS COMMUNICATIONSen_US
dc.citation.volume245en_US
dc.citation.spage0en_US
dc.citation.epage0en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:000495477000001en_US
dc.citation.woscount0en_US
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