Dissertation > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > Computer applications > Information processing (information processing) > Pattern Recognition and devices > Image recognition device

A Parallel Algebraic Multigrid Solver for High-order Lagrange Finite Element Equations Based on HYPRE

Author CaoFang
Tutor ShuShi
School Xiangtan University
Course Computational Mathematics
Keywords HYPRE Parallel algebraic multi-layer grid method High-order Lagrange finite element Continuous subspace correction method X-AMG
CLC TP391.41
Type Master's thesis
Year 2008
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Usually can be divided into multi-layer grid method compared to the geometric multigrid method (GMG) and algebraic multigrid (AMG) method with GMG Law, the AMG law has more pervasive and robustness (robustness) It is solving many large-scale scientific and engineering computing problems is one of the most effective methods for partial differential equations discretized system. HYPRE is the internationally popular a massively parallel computer for solving large sparse linear equations, numerical package its purpose is to provide users with high-performance parallel solver and preconditioner, BoomerAMG one of the most commonly used parallel algebra multilayer grid solver. Based HYPRE platform stratified based high-order Lagrange finite element equation for the three-dimensional second-order elliptic boundary value problems, discuss its parallel AMG algorithm 1 our work. brief introduction HYPRE numerical package focuses on several classic AMG grid coarsening algorithm, RS algorithms, CLJP algorithms, as well as a commonly used parallel grid coarsening algorithm: Falgout algorithm, and finally introduced in recent years developed continuous subspace correction algorithm framework and its convergence theory. tetrahedral meshing, high-order finite element equation for a hierarchical-based three-dimensional second-order elliptic boundary value problems were designed to generate the total stiffness matrix and the total load vector serial algorithm and a parallel algorithm based on the sub-region by. For the latter, by introducing side partition edge and corner of the correlation matrix, and communication, to get the current process and other processes associated stiffness matrix and load vector. In addition, we stratified base using a reasonable sequence, not only for programming convenience, but also improve the the parallel AMG polishing efficiency numerical results show that our parallel algorithm design to expand the scale of the generation of the stiffness matrix, has better scalability. First, the design of the high-order finite element equation for the parallel generation and analysis based the auxiliary variational problems AMG (X-AMG) under the law in the contemplated consistent mesh continuous subspace correction theory to prove the the descent rate independent of the mesh size of the new AMG law, numerical results also verify the correctness of the theory, then design a parallel algorithm for the X-AMG, the first based on string line stiffness matrix structure of the algorithm, the number of iterations has better scalability but too often transformed into each other due to the parallel vector with serial vector, and the algorithm is too dependent on the selection of polished sub parallel efficiency thereby reducing therefore based on sub- zoning parallel matrix structure, we have given a more reasonable X-AMG parallel algorithms numerical results show that this parallel X-AMG algorithm for solving high-order finite element equation than BoomerAMG has a higher efficiency

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