The seed method is used for solving multiple linear systems A (i)x (i) =b (i) for 1≤i≤s, where the coefficient matrix A (i) and the right-hand side b (i) are different in general. It is known that the CG meth...The seed method is used for solving multiple linear systems A (i)x (i) =b (i) for 1≤i≤s, where the coefficient matrix A (i) and the right-hand side b (i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A (i). In this paper, the FOM method is employed to solve multiple linear sy stems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the resi duals of other systems are projected onto the generated Krylov subspace to get t he approximate solutions for the unsolved ones. The whole process is repeated u ntil all the systems are solved.展开更多
The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and st...The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and stored in two parts separately. One part is associated with the volume integral and the other is associated with the subsurface boundary integral. The equivalent multiple linear systems with closer right-hand sides than the original systems were constructed. A recycling Krylov subspace technique was employed to solve the multiple linear systems. The solution of the seed system was used as an initial guess for the subsequent systems. The results of two numerical experiments show that the improved algorithm reduces the iterations and CPU time by almost 50%, compared with the classical preconditioned conjugate gradient method.展开更多
A parallel finite element scheme for 3D resistivity method forward modeling is introduced in this article.The domain decomposition algorithm,along with a message passing interface,is used to implement parallelism.The ...A parallel finite element scheme for 3D resistivity method forward modeling is introduced in this article.The domain decomposition algorithm,along with a message passing interface,is used to implement parallelism.The computational domain is divided into subdomains,and mesh partitioning is combined with load balancing.Unstructured meshes and local mesh refinement strategies are used to realize high precision for complex topography models.Furthermore,an improved linear solver for multi-electrode resistivity method modeling is adopted.Recycling preconditioned conjugate gradient,which is a linear solver,is based on the similarity of linear systems between point sources.The multiple right-hand-side linear systems corresponding to different point source positions are constructed,and the accelerated convergence is obtained through recycling subspace using the linear solver.The computational accuracy and efficiency of the forward scheme for complex topography models are verified using the numerical test results.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10271075)
文摘The seed method is used for solving multiple linear systems A (i)x (i) =b (i) for 1≤i≤s, where the coefficient matrix A (i) and the right-hand side b (i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A (i). In this paper, the FOM method is employed to solve multiple linear sy stems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the resi duals of other systems are projected onto the generated Krylov subspace to get t he approximate solutions for the unsolved ones. The whole process is repeated u ntil all the systems are solved.
基金Projects(40974077,41164004)supported by the National Natural Science Foundation of ChinaProject(2007AA06Z134)supported by the National High Technology Research and Development Program of China+2 种基金Projects(2011GXNSFA018003,0832263)supported by the Natural Science Foundation of Guangxi Province,ChinaProject supported by Program for Excellent Talents in Guangxi Higher Education Institution,ChinaProject supported by the Foundation of Guilin University of Technology,China
文摘The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and stored in two parts separately. One part is associated with the volume integral and the other is associated with the subsurface boundary integral. The equivalent multiple linear systems with closer right-hand sides than the original systems were constructed. A recycling Krylov subspace technique was employed to solve the multiple linear systems. The solution of the seed system was used as an initial guess for the subsequent systems. The results of two numerical experiments show that the improved algorithm reduces the iterations and CPU time by almost 50%, compared with the classical preconditioned conjugate gradient method.
基金supported by the National Natural Science Foundation of China(No:42274182)Guangxi Natural Science Foundation(No:2020 GXNSFAA297079)。
文摘A parallel finite element scheme for 3D resistivity method forward modeling is introduced in this article.The domain decomposition algorithm,along with a message passing interface,is used to implement parallelism.The computational domain is divided into subdomains,and mesh partitioning is combined with load balancing.Unstructured meshes and local mesh refinement strategies are used to realize high precision for complex topography models.Furthermore,an improved linear solver for multi-electrode resistivity method modeling is adopted.Recycling preconditioned conjugate gradient,which is a linear solver,is based on the similarity of linear systems between point sources.The multiple right-hand-side linear systems corresponding to different point source positions are constructed,and the accelerated convergence is obtained through recycling subspace using the linear solver.The computational accuracy and efficiency of the forward scheme for complex topography models are verified using the numerical test results.
