A Parallel Algebraic Multigrid Solver for Highorder Lagrange Finite Element Equations Based on HYPRE 

Author  CaoFang 
Tutor  ShuShi 
School  Xiangtan University 
Course  Computational Mathematics 
Keywords  HYPRE Parallel algebraic multilayer grid method Highorder Lagrange finite element Continuous subspace correction method XAMG 
CLC  TP391.41 
Type  Master's thesis 
Year  2008 
Downloads  56 
Quotes  0 
Usually can be divided into multilayer 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 largescale 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 highperformance parallel solver and preconditioner, BoomerAMG one of the most commonly used parallel algebra multilayer grid solver. Based HYPRE platform stratified based highorder Lagrange finite element equation for the threedimensional secondorder 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, highorder finite element equation for a hierarchicalbased threedimensional secondorder 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 subregion 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 highorder finite element equation for the parallel generation and analysis based the auxiliary variational problems AMG (XAMG) 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 XAMG, 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 XAMG parallel algorithms numerical results show that this parallel XAMG algorithm for solving highorder finite element equation than BoomerAMG has a higher efficiency