In this study, in order to further improve the construction efficiency of sparse approximate inverse (SPAI) preconditioners, we attempt to explore the construction method of SPAI preconditioners in mixed-precision mod...
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In this study, in order to further improve the construction efficiency of sparse approximate inverse (SPAI) preconditioners, we attempt to explore the construction method of SPAI preconditioners in mixed-precision mode from the perspective of single and double precision mixing, and thus propose two mixed-precision SPAI preconditioning algorithms on GPU, abbreviated as MP-SSPAI and MP-HeuriSPAI, respectively. In MP-SSPAI, with original static SPAI preconditioning algorithm as the research object, we mainly consider the following factors to construct its preconditioner in mixed-precision mode: 1) use single precision as much as possible to improve computational efficiency of the preconditioner while ensuring its validity;2) store certain components in single precision after they have been determined to require single-precision computation to improve read efficiency;and 3) maintain the high-precision output of the preconditioner to ensure that it is computed with high precision when applied to the iterative algorithm. In MP-HeuriSPAI, a mixed-precision heuristic dynamic SPAI preconditioning algorithm on GPU is presented based on the above factors, using HeuriSPAI as the object of study. The experimental results demonstrate the effectiveness and high performance of the proposed MP-SSPAI and MP-HeuriSPAI by comparing them with their respective double-precision versions, single-precision versions, and extended versions.
In this paper, a preconditioning algorithm for sparse, symmetric, diagonally dominant (SDD) linear systems is proposed by using combinatorial techniques. Firstly, we construct preconditioners by finding a subgraph bas...
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ISBN:
(纸本)9781509032051
In this paper, a preconditioning algorithm for sparse, symmetric, diagonally dominant (SDD) linear systems is proposed by using combinatorial techniques. Firstly, we construct preconditioners by finding a subgraph based on the relationship between SDD matrices and undirected graphs. The subgraph is built by augmenting a low-stretch spanning tree with some extra high stretch edges. Then we implement the algorithm for building a low stretch tree and give a parallel implementation of the subgraph preconditioning algorithm based on PETSc software. Finally, numerical experiments arising from both elliptic PDEs and Laplacian systems of network graphs are tested to evaluate the performance of our algorithm. Numerical experiments show that preconditioners constructed by our algorithm are more efficient than incomplete Choleskey factorization preconditioners and Vaidya's preconditioners. Besides, based on the tree structure, our preconditioners perform respectable parallel scalability.
A PLU-SGS method based on a time-derivative preconditioning algorithm and LU-SGS method is developed in order to calculate the Navier-Stokes equations at all speeds. The equations were discretized using A USMPW scheme...
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A PLU-SGS method based on a time-derivative preconditioning algorithm and LU-SGS method is developed in order to calculate the Navier-Stokes equations at all speeds. The equations were discretized using A USMPW scheme in conjunction with the third-order MUSCL scheme with Van Leer limiter. The present method was applied to solve the multidimensional compressible Navier-Stokes equations in curvilinear coordinates. Characteristic boundary conditions based on the eigensystem of the preconditioned equations were employed. In order to examine the performance of present method, driven-cavity flow at various Reynolds numbers and viscous flow through a convergent-divergent nozzle at supersonic were selected to rest this method. The computed results were compared with the experimental data or the other numerical results available in literature and good agreements between them are obtained. The results show that the present method is accurate, self-adaptive and stable for a wide range of flow conditions from low speed to supersonic flows.
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