A memory reduction technique is proposed for solving stationary kinetic model equations. As implied by an integral solution of the stationary kinetic equation, a velocity distribution function can be reconstructed fro...A memory reduction technique is proposed for solving stationary kinetic model equations. As implied by an integral solution of the stationary kinetic equation, a velocity distribution function can be reconstructed from given macroscopic variables. Based on this fact, we propose a technique to reconstruct distribution function at discrete level, and employ it to develop an implicit numerical method for kinetic equations. The new implicit method only stores the macroscopic quantities which appear in the collision term, and does not store the distribution functions. As a result, enormous memory requirement for solving kinetic equations is totally relieved. Several boundary conditions, such as, inlet, outlet and isothermal boundaries, are discussed. Some numerical tests demonstrate the validity and efficiency of the technique.The new implicit solver provides nearly identical solution as the explicit kinetic solver, while the memory requirement is on the same order as the Navier–Stokes solver.展开更多
In finite element analysis(FEA),optimizing the storage requirements of the global stiffness matrix and enhancing the computational efficiency of solving finite element equations are pivotal objectives.To address these...In finite element analysis(FEA),optimizing the storage requirements of the global stiffness matrix and enhancing the computational efficiency of solving finite element equations are pivotal objectives.To address these goals,we present a novel method for compressing the storage of the global stiffness matrix,aimed at minimizing memory consumption and enhancing FEA efficiency.This method leverages the block symmetry of the global stiffness matrix,hence named the blocked symmetric compressed sparse column(BSCSC)method.We also detail the implementation scheme of the BSCSC method and the corresponding finite element equation solution method.This approach optimizes only the global stiffness matrix index,thereby reducing memory requirements without compromising FEA computational accuracy.We then demonstrate the efficiency and memory savings of the BSCSC method in FEA using 2D and 3D cantilever beams as examples.In addition,we employ the BSCSC method to an engine connecting rod model to showcase its superiority in solving complex engineering models.Furthermore,we extend the BSCSC method to isogeometric analysis and validate its scalability through two examples,achieving up to 66.13%memory reduction and up to 72.06%decrease in total computation time compared to the traditional compressed sparse column method.展开更多
基金supported by the National Natural Science Foundation of China(11602091 and 91530319)the National Key Research and Development Plan(2016YFB0600805)
文摘A memory reduction technique is proposed for solving stationary kinetic model equations. As implied by an integral solution of the stationary kinetic equation, a velocity distribution function can be reconstructed from given macroscopic variables. Based on this fact, we propose a technique to reconstruct distribution function at discrete level, and employ it to develop an implicit numerical method for kinetic equations. The new implicit method only stores the macroscopic quantities which appear in the collision term, and does not store the distribution functions. As a result, enormous memory requirement for solving kinetic equations is totally relieved. Several boundary conditions, such as, inlet, outlet and isothermal boundaries, are discussed. Some numerical tests demonstrate the validity and efficiency of the technique.The new implicit solver provides nearly identical solution as the explicit kinetic solver, while the memory requirement is on the same order as the Navier–Stokes solver.
基金supported by the National Natural Science Foundation of China(Grant No.52075184)Guangdong Basic and Applied Basic Research Foundation,China(Grant No.2024A1515011786).
文摘In finite element analysis(FEA),optimizing the storage requirements of the global stiffness matrix and enhancing the computational efficiency of solving finite element equations are pivotal objectives.To address these goals,we present a novel method for compressing the storage of the global stiffness matrix,aimed at minimizing memory consumption and enhancing FEA efficiency.This method leverages the block symmetry of the global stiffness matrix,hence named the blocked symmetric compressed sparse column(BSCSC)method.We also detail the implementation scheme of the BSCSC method and the corresponding finite element equation solution method.This approach optimizes only the global stiffness matrix index,thereby reducing memory requirements without compromising FEA computational accuracy.We then demonstrate the efficiency and memory savings of the BSCSC method in FEA using 2D and 3D cantilever beams as examples.In addition,we employ the BSCSC method to an engine connecting rod model to showcase its superiority in solving complex engineering models.Furthermore,we extend the BSCSC method to isogeometric analysis and validate its scalability through two examples,achieving up to 66.13%memory reduction and up to 72.06%decrease in total computation time compared to the traditional compressed sparse column method.
