A Multi Level Direct Sub-Structuring Multi-Frontal Parallel Solver for the hp-Finite Element Method
A Multi Level Direct Sub-Structuring Multi-Frontal Parallel Solver for the hp-Finite Element Method
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发表时间：
2007
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通讯作者：
M. Paszyński;David Pardo;C. Torres‐Verdín;L. Demkowicz;V. Calo
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作者：
M. Paszyński;David Pardo;C. Torres‐Verdín;L. Demkowicz;V. Calo
本文为HP精制网格提供了一个新的并行直接求解器，该求解器由2D HP自适应有限元方法（FEM）用于求解3D Direct Curr Ent（DC）钻孔电阻率测量问题。自适应HP FEM在全自动模式下生成一系列HP网格，从而使误差的指数收敛性与自由度数（D.O.F.）以及CPU时间相关。新的平行求解器在三级消除树上起作用，分布在Proc Essors中：（1）从初始网格元素生长的细化树，（2）初始网格元素树，以及（3）由域分解。求解器计算在每个树节点上进行补充，通过执行部分正向消除，不受影响的部分组装（或未组装）D.O.F. Schur补充存储在树节点上，当求解随后的HP网格（由自适应策略生成）时，可以重新利用，当该e HP网格包含未得到完善的元素时，因为它典型地发生在真实的情况下，申请。比较求解器的执行时间和内存使用量Ag Ag ast ainst由平行多额线传递的那些，并以（1）从主机处理器提交的集中式条目（2）分布式分布式EN tries从子域中提交的集中式条目，并以（1）的集中式条目从子域中提交了（1）。 ，和（3）当t并行的带有分布式条目的Tarallel Mumps求解器时，基于腮腺炎的直接子结构方法用于解决接口问题。
The paper presents a new parallel direct solver for hp refined meshes, utilized by a 2D hp adaptive Finite Element Method (FEM) to solve 3D Direct Curr ent (DC) borehole resistivity measurement problems. The self-adaptive hp FEM generates in a fully automatic mode a sequence of hp meshes delivering exponential convergence of the error wit h respect to the number of degrees of freedom (d.o.f.) as well as the CPU time. Th new parallel solver works on the three-level elimination tree, distributed into proc essors: (1) the refinement tree growing from initial mesh elements, (2) the initial mesh element tree, and (3) the sub-domain tree resulting from the domain decomposition. The solver comput es Schur complements at every tree node, by performing partial forward elimination, leav ing untouched partially assembled (or unassembled) d.o.f. The Schur complements are stored at tree nodes, and can be re-utilized when solving subsequent hp meshes (produced by the self-adaptive strategy), when thes e hp meshes contain elements that have not been refined, as it typi call occurs in real applications. Execution time and memory usage of the solver are compared ag ainst those delivered by the parallel MUltifrontl Massively Parallel sparse direct Sol ver (MUMPS) with (1) centralized entries submitted from the host processor, (2) distributed en tries submitted from sub-domains, and (3) the MUMPS based direct sub-structuring method when t parallel MUMPS solver with distributed entries is utilized to solve the interface problem.