{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/87997"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/87997","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Investigation of general-purpose computing on graphics processing units and its application to the finite element analysis of electromagnetic problems","abstract":"In this dissertation, the hardware and API architectures of GPUs are investigated, and the corresponding acceleration techniques are applied on the traditional frequency domain finite element method (FEM), the element-level time-domain methods, and the nonlinear discontinuous Galerkin method. First, the assembly and the solution phases of the FEM are parallelized and mapped onto the granular GPU processors. Efficient parallelization strategies for the finite element matrix assembly on a single GPU and on multiple GPUs are proposed. The parallelization strategies for the finite element matrix solution, in conjunction with parallelizable preconditioners are investigated to reduce the total solution time. Second, the element-level dual-field domain decomposition (DFDD-ELD) method is parallelized on GPU. The element-level algorithms treat each finite element as a subdomain, where the elements march the fields in time by exchanging fields and fluxes on the element boundary interfaces with the neighboring elements. The proposed parallelization framework is readily applicable to similar element-level algorithms, where the application to the discontinuous Galerkin time-domain (DGTD) methods show good acceleration results. Third, the element-level parallelization framework is further adapted to the acceleration of nonlinear DGTD algorithm, which has potential applications in the field of optics. The proposed nonlinear DGTD algorithm describes the third-order instantaneous nonlinear effect between the electromagnetic field and the medium permittivity. The Newton-Raphson method is incorporated to reduce the number of nonlinear iterations through its quadratic convergence. Various nonlinear examples are presented to show the different Kerr effects observed through the third-order nonlinearity. With the acceleration using MPI+GPU under large cluster environments, the solution times for the various linear and nonlinear examples are significantly reduced.","abstract_html":"In this dissertation, the hardware and API architectures of GPUs are investigated, and the corresponding acceleration techniques are applied on the traditional frequency domain finite element method (FEM), the element-level time-domain methods, and the nonlinear discontinuous Galerkin method. First, the assembly and the solution phases of the FEM are parallelized and mapped onto the granular GPU processors. Efficient parallelization strategies for the finite element matrix assembly on a single GPU and on multiple GPUs are proposed. The parallelization strategies for the finite element matrix solution, in conjunction with parallelizable preconditioners are investigated to reduce the total solution time. Second, the element-level dual-field domain decomposition (DFDD-ELD) method is parallelized on GPU. The element-level algorithms treat each finite element as a subdomain, where the elements march the fields in time by exchanging fields and fluxes on the element boundary interfaces with the neighboring elements. The proposed parallelization framework is readily applicable to similar element-level algorithms, where the application to the discontinuous Galerkin time-domain (DGTD) methods show good acceleration results. Third, the element-level parallelization framework is further adapted to the acceleration of nonlinear DGTD algorithm, which has potential applications in the field of optics. The proposed nonlinear DGTD algorithm describes the third-order instantaneous nonlinear effect between the electromagnetic field and the medium permittivity. The Newton-Raphson method is incorporated to reduce the number of nonlinear iterations through its quadratic convergence. Various nonlinear examples are presented to show the different Kerr effects observed through the third-order nonlinearity. With the acceleration using MPI+GPU under large cluster environments, the solution times for the various linear and nonlinear examples are significantly reduced.","abstract_has_math":false,"creators":["Meng, Huan-Ting"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engineering","degree_department":null,"school":null,"contributors":["Jin, Jianming","Schutt-Ainé, José E.","Chen, Deming","Kloeckner, Andreas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-29T20:38:01Z","date_published":"2015-09-29T20:38:01Z","updated_at":"2026-07-22T22:26:31Z","subjects":["Finite-Element Method (FEM)","Graphics Processing Unit (GPU)","General-purpose computing on graphics processing units (GPGPU)","Massive Parallelization","Compute Unified Device Architecture (CUDA)","Discontinuous Galerkin Time-Domain Method","discontinuous Galerkin time-domain (DGTD)","Element-Level Decomposition","Dual-Field Domain Decomposition","dual-field domain decomposition- element level decomposition (DFDD-ELD)","Kerr Nonlinearity","Third-Order Nonlinearity","Nonlinear Optics","Newton-Raphson Method"],"languages":["en"],"rights":["Copyright 2015 Huan-Ting Meng"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/87997","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jin, Jianming","Schutt-Ainé, José E.","Chen, Deming","Kloeckner, Andreas"]},{"key":"dc:creator","label":"Author","values":["Meng, Huan-Ting"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-29T20:38:01Z","2015-08","2015-07-08","2015-8"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Finite-Element Method (FEM)","Graphics Processing Unit (GPU)","General-purpose computing on graphics processing units (GPGPU)","Massive Parallelization","Compute Unified Device Architecture (CUDA)","Discontinuous Galerkin Time-Domain Method","discontinuous Galerkin time-domain (DGTD)","Element-Level Decomposition","Dual-Field Domain Decomposition","dual-field domain decomposition- element level decomposition (DFDD-ELD)","Kerr Nonlinearity","Third-Order Nonlinearity","Nonlinear Optics","Newton-Raphson Method"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Huan-Ting Meng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/87997"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this dissertation, the hardware and API architectures of GPUs are investigated, and the corresponding acceleration techniques are applied on the traditional frequency domain finite element method (FEM), the element-level time-domain methods, and the nonlinear discontinuous Galerkin method. First, the assembly and the solution phases of the FEM are parallelized and mapped onto the granular GPU processors. Efficient parallelization strategies for the finite element matrix assembly on a single GPU and on multiple GPUs are proposed. The parallelization strategies for the finite element matrix solution, in conjunction with parallelizable preconditioners are investigated to reduce the total solution time. Second, the element-level dual-field domain decomposition (DFDD-ELD) method is parallelized on GPU. The element-level algorithms treat each finite element as a subdomain, where the elements march the fields in time by exchanging fields and fluxes on the element boundary interfaces with the neighboring elements. The proposed parallelization framework is readily applicable to similar element-level algorithms, where the application to the discontinuous Galerkin time-domain (DGTD) methods show good acceleration results. Third, the element-level parallelization framework is further adapted to the acceleration of nonlinear DGTD algorithm, which has potential applications in the field of optics. The proposed nonlinear DGTD algorithm describes the third-order instantaneous nonlinear effect between the electromagnetic field and the medium permittivity. The Newton-Raphson method is incorporated to reduce the number of nonlinear iterations through its quadratic convergence. Various nonlinear examples are presented to show the different Kerr effects observed through the third-order nonlinearity. With the acceleration using MPI+GPU under large cluster environments, the solution times for the various linear and nonlinear examples are significantly reduced.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms","The student, Huan-Ting Meng, accepted the attached license on 2015-07-05 at 13:07.","The student, Huan-Ting Meng, submitted this Dissertation for approval on 2015-07-05 at 13:17.","This Dissertation was approved for publication on 2015-07-08 at 13:27.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8344 on 2015-09-29 at 13:21:56","Made available in DSpace on 2015-09-29T20:38:01Z (GMT). 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First, the assembly and the solution phases of the FEM are parallelized and mapped onto the granular GPU processors. Efficient parallelization strategies for the finite element matrix assembly on a single GPU and on multiple GPUs are proposed. The parallelization strategies for the finite element matrix solution, in conjunction with parallelizable preconditioners are investigated to reduce the total solution time. Second, the element-level dual-field domain decomposition (DFDD-ELD) method is parallelized on GPU. The element-level algorithms treat each finite element as a subdomain, where the elements march the fields in time by exchanging fields and fluxes on the element boundary interfaces with the neighboring elements. The proposed parallelization framework is readily applicable to similar element-level algorithms, where the application to the discontinuous Galerkin time-domain (DGTD) methods show good acceleration results. Third, the element-level parallelization framework is further adapted to the acceleration of nonlinear DGTD algorithm, which has potential applications in the field of optics. The proposed nonlinear DGTD algorithm describes the third-order instantaneous nonlinear effect between the electromagnetic field and the medium permittivity. The Newton-Raphson method is incorporated to reduce the number of nonlinear iterations through its quadratic convergence. Various nonlinear examples are presented to show the different Kerr effects observed through the third-order nonlinearity. With the acceleration using MPI+GPU under large cluster environments, the solution times for the various linear and nonlinear examples are significantly reduced.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms","The student, Huan-Ting Meng, accepted the attached license on 2015-07-05 at 13:07.","The student, Huan-Ting Meng, submitted this Dissertation for approval on 2015-07-05 at 13:17.","This Dissertation was approved for publication on 2015-07-08 at 13:27.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8344 on 2015-09-29 at 13:21:56","Made available in DSpace on 2015-09-29T20:38:01Z (GMT). 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