{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/92863"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/92863","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A new hybrid numerical scheme for simulating fault ruptures with near fault bulk inhomogeneities","abstract":"\"The Finite Difference (FD) and the Boundary Integral (BI) Method have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. While FD has a large computational cost as it requires the discretization of the whole volume of interest, it can handle a greater variety of problems in comparison with BI, including bulk nonlinearities and heterogeneities. On the other hand, the BI method eliminates the necessity of simulating the wave propagation in the whole elastic medium by leveraging space-time convolutions with the source on the fault surface. The spectral implementation of the BI in particular is faster and much more computationally efficient than other bulk methods such as FD. However, the spectral boundary integral (SBI) formulation is restricted to linear elastic bulk and planar faults. This study proposes a new method, referred to herein as the \"\"Hybrid Method\"\", in which the two methods are combined. Benefiting from the flexibility of FD and the efficiency of BI, this method is capable of solving a wide range of problems in a computationally efficient way. In the Hybrid Method, nonlinearities or heterogeneities may be confined to a virtual narrow strip that includes the fault or the wave source. This strip, then, is discretized using a FD scheme in space and time while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We illustrate the accuracy and efficiency of the method using several examples. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art.\"","abstract_html":""The Finite Difference (FD) and the Boundary Integral (BI) Method have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. While FD has a large computational cost as it requires the discretization of the whole volume of interest, it can handle a greater variety of problems in comparison with BI, including bulk nonlinearities and heterogeneities. On the other hand, the BI method eliminates the necessity of simulating the wave propagation in the whole elastic medium by leveraging space-time convolutions with the source on the fault surface. The spectral implementation of the BI in particular is faster and much more computationally efficient than other bulk methods such as FD. However, the spectral boundary integral (SBI) formulation is restricted to linear elastic bulk and planar faults. This study proposes a new method, referred to herein as the ""Hybrid Method"", in which the two methods are combined. Benefiting from the flexibility of FD and the efficiency of BI, this method is capable of solving a wide range of problems in a computationally efficient way. In the Hybrid Method, nonlinearities or heterogeneities may be confined to a virtual narrow strip that includes the fault or the wave source. This strip, then, is discretized using a FD scheme in space and time while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We illustrate the accuracy and efficiency of the method using several examples. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art."","abstract_has_math":false,"creators":["Hajarolasvadi, Setare"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Elbanna, Ahmed Ettaf"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-11-10T17:55:17Z","date_published":"2016-11-10T17:55:17Z","updated_at":"2026-07-22T22:26:35Z","subjects":["finite difference","boundary integral method","spectral method","fracture","earthquake cycle"],"languages":["en"],"rights":["Copyright 2016 Setare Hajarolasvadi"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/92863","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Elbanna, Ahmed Ettaf"]},{"key":"dc:creator","label":"Author","values":["Hajarolasvadi, Setare"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-11-10T17:55:17Z","2016-07-18","2016-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Civil Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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 difference","boundary integral method","spectral method","fracture","earthquake cycle"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Setare Hajarolasvadi"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/92863"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"The Finite Difference (FD) and the Boundary Integral (BI) Method have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. While FD has a large computational cost as it requires the discretization of the whole volume of interest, it can handle a greater variety of problems in comparison with BI, including bulk nonlinearities and heterogeneities. On the other hand, the BI method eliminates the necessity of simulating the wave propagation in the whole elastic medium by leveraging space-time convolutions with the source on the fault surface. The spectral implementation of the BI in particular is faster and much more computationally efficient than other bulk methods such as FD. However, the spectral boundary integral (SBI) formulation is restricted to linear elastic bulk and planar faults. This study proposes a new method, referred to herein as the \"\"Hybrid Method\"\", in which the two methods are combined. Benefiting from the flexibility of FD and the efficiency of BI, this method is capable of solving a wide range of problems in a computationally efficient way. In the Hybrid Method, nonlinearities or heterogeneities may be confined to a virtual narrow strip that includes the fault or the wave source. This strip, then, is discretized using a FD scheme in space and time while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We illustrate the accuracy and efficiency of the method using several examples. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-11-09 without embargo terms","The student, Setare Hajarolasvadi, accepted the attached license on 2016-07-18 at 10:17.","The student, Setare Hajarolasvadi, submitted this Thesis for approval on 2016-07-18 at 10:32.","This Thesis was approved for publication on 2016-07-18 at 11:35.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9981 on 2016-11-09 at 10:25:22","Made available in DSpace on 2016-11-10T17:55:17Z (GMT). No. of bitstreams: 2 HAJAROLASVADI-THESIS-2016.pdf: 4073424 bytes, checksum: 3c95003aba3ce9ab1964c727f00ee7ff (MD5) LICENSE.txt: 4217 bytes, checksum: ae8f9d269211cc90d47f03ca7078399d (MD5) Previous issue date: 2016-07-18"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A new hybrid numerical scheme for simulating fault ruptures with near fault bulk inhomogeneities"]}]}],"canonical_facts":{"dc:contributor":["Elbanna, Ahmed Ettaf"],"dc:creator":["Hajarolasvadi, Setare"],"dc:date":["2016-11-10T17:55:17Z","2016-07-18","2016-08"],"dc:description":["\"The Finite Difference (FD) and the Boundary Integral (BI) Method have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. While FD has a large computational cost as it requires the discretization of the whole volume of interest, it can handle a greater variety of problems in comparison with BI, including bulk nonlinearities and heterogeneities. On the other hand, the BI method eliminates the necessity of simulating the wave propagation in the whole elastic medium by leveraging space-time convolutions with the source on the fault surface. The spectral implementation of the BI in particular is faster and much more computationally efficient than other bulk methods such as FD. However, the spectral boundary integral (SBI) formulation is restricted to linear elastic bulk and planar faults. This study proposes a new method, referred to herein as the \"\"Hybrid Method\"\", in which the two methods are combined. Benefiting from the flexibility of FD and the efficiency of BI, this method is capable of solving a wide range of problems in a computationally efficient way. In the Hybrid Method, nonlinearities or heterogeneities may be confined to a virtual narrow strip that includes the fault or the wave source. This strip, then, is discretized using a FD scheme in space and time while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We illustrate the accuracy and efficiency of the method using several examples. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-11-09 without embargo terms","The student, Setare Hajarolasvadi, accepted the attached license on 2016-07-18 at 10:17.","The student, Setare Hajarolasvadi, submitted this Thesis for approval on 2016-07-18 at 10:32.","This Thesis was approved for publication on 2016-07-18 at 11:35.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9981 on 2016-11-09 at 10:25:22","Made available in DSpace on 2016-11-10T17:55:17Z (GMT). No. of bitstreams: 2 HAJAROLASVADI-THESIS-2016.pdf: 4073424 bytes, checksum: 3c95003aba3ce9ab1964c727f00ee7ff (MD5) LICENSE.txt: 4217 bytes, checksum: ae8f9d269211cc90d47f03ca7078399d (MD5) Previous issue date: 2016-07-18"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/92863"],"dc:language":["en"],"dc:rights":["Copyright 2016 Setare Hajarolasvadi"],"dc:subject":["finite difference","boundary integral method","spectral method","fracture","earthquake cycle"],"dc:title":["A new hybrid numerical scheme for simulating fault ruptures with near fault bulk inhomogeneities"],"dc:type":["text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:35Z"}