Simulations are indispensable for engineering. They make it possible that one can perform faster and cheaper virtual experiments than physical ones on virtual environments based on numerical methods. One key factor to the performance of a simulation system is the speed of solving linear equations arising in the calculation at runtime. Based on a testing simulator, we have used Graphics Processing Units (GPUs) to accelerate the solution of the types of equations typically encountered in dynamic system simulators. Compared to commercial matrix solvers that run on a CPU, we realized speedups ranging from 5 (for system size =700) to 460 (for system size = 5, 800). While calculation time for the commercial matrix solver increased with matrix size = O(N)^2.3, our new GPU-based Preconditioned Generalized Minimal Residual (PGMRES) technique yielded scaling as O(N)^1.2. A significant component of this performance was achieved by development of new Basic Linear Algebra routines for the NVIDIA Tesla GPU that directly address characteristics typical of matrices that describe the time domain response of naturally-coupled dynamic systems. In addition, 20 to 100 speedup was achieved for other simulation procedures by successfully exploiting high performance algorithm engineering.
","abstract_html":"<p>Simulations are indispensable for engineering. They make it possible that one can perform faster and cheaper virtual experiments than physical ones on virtual environments based on numerical methods. One key factor to the performance of a simulation system is the speed of solving linear equations arising in the calculation at runtime. Based on a testing simulator, we have used Graphics Processing Units (GPUs) to accelerate the solution of the types of equations typically encountered in dynamic system simulators. Compared to commercial matrix solvers that run on a CPU, we realized speedups ranging from 5 (for system size =700) to 460 (for system size = 5, 800). While calculation time for the commercial matrix solver increased with matrix size = O(N)^2.3, our new GPU-based Preconditioned Generalized Minimal Residual (PGMRES) technique yielded scaling as O(N)^1.2. A significant component of this performance was achieved by development of new Basic Linear Algebra routines for the NVIDIA Tesla GPU that directly address characteristics typical of matrices that describe the time domain response of naturally-coupled dynamic systems. In addition, 20 to 100 speedup was achieved for other simulation procedures by successfully exploiting high performance algorithm engineering.</p>","abstract_has_math":false,"creators":["Shi, Jian"],"institution":null,"degree_name":"Ph.D.","degree_level":"Campus Access Dissertation","degree_discipline":"Computer Science and Engineering","degree_department":null,"school":null,"contributors":["Jijun Tang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T04:37:56Z","subjects":["Computer Sciences","Electrical and Computer Engineering","Engineering","Physical Sciences and Mathematics","GMRES","GPU","Linear equation","Simulation"],"languages":[],"rights":["© 2011, Jian Shi"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarcommons.sc.edu/etd/801","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jijun Tang"]},{"key":"dc:creator","label":"Author","values":["Shi, Jian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science and Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Sciences","Electrical and Computer Engineering","Engineering","Physical Sciences and Mathematics","GMRES","GPU","Linear equation","Simulation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© 2011, Jian Shi"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarcommons.sc.edu/etd/801"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Simulations are indispensable for engineering. They make it possible that one can perform faster and cheaper virtual experiments than physical ones on virtual environments based on numerical methods. One key factor to the performance of a simulation system is the speed of solving linear equations arising in the calculation at runtime. Based on a testing simulator, we have used Graphics Processing Units (GPUs) to accelerate the solution of the types of equations typically encountered in dynamic system simulators. Compared to commercial matrix solvers that run on a CPU, we realized speedups ranging from 5 (for system size =700) to 460 (for system size = 5, 800). While calculation time for the commercial matrix solver increased with matrix size = O(N)^2.3, our new GPU-based Preconditioned Generalized Minimal Residual (PGMRES) technique yielded scaling as O(N)^1.2. A significant component of this performance was achieved by development of new Basic Linear Algebra routines for the NVIDIA Tesla GPU that directly address characteristics typical of matrices that describe the time domain response of naturally-coupled dynamic systems. In addition, 20 to 100 speedup was achieved for other simulation procedures by successfully exploiting high performance algorithm engineering.
"]},{"key":"dc:title","label":"Title","values":["Improving Simulation Performance With Gpus"]}]}],"canonical_facts":{"dc:contributor":["Jijun Tang"],"dc:creator":["Shi, Jian"],"dc:description.abstract":["Simulations are indispensable for engineering. They make it possible that one can perform faster and cheaper virtual experiments than physical ones on virtual environments based on numerical methods. One key factor to the performance of a simulation system is the speed of solving linear equations arising in the calculation at runtime. Based on a testing simulator, we have used Graphics Processing Units (GPUs) to accelerate the solution of the types of equations typically encountered in dynamic system simulators. Compared to commercial matrix solvers that run on a CPU, we realized speedups ranging from 5 (for system size =700) to 460 (for system size = 5, 800). While calculation time for the commercial matrix solver increased with matrix size = O(N)^2.3, our new GPU-based Preconditioned Generalized Minimal Residual (PGMRES) technique yielded scaling as O(N)^1.2. A significant component of this performance was achieved by development of new Basic Linear Algebra routines for the NVIDIA Tesla GPU that directly address characteristics typical of matrices that describe the time domain response of naturally-coupled dynamic systems. In addition, 20 to 100 speedup was achieved for other simulation procedures by successfully exploiting high performance algorithm engineering.
"],"dc:identifier":["https://scholarcommons.sc.edu/etd/801"],"dc:rights":["© 2011, Jian Shi"],"dc:subject":["Computer Sciences","Electrical and Computer Engineering","Engineering","Physical Sciences and Mathematics","GMRES","GPU","Linear equation","Simulation"],"dc:title":["Improving Simulation Performance With Gpus"],"thesis:degree_discipline":["Computer Science and Engineering"],"thesis:degree_level":["Campus Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T04:37:56Z"}