Element-topology-independent preconditioners for parallel finite element computations

1992 ◽  
Author(s):  
K. PARK ◽  
SCOTT ALEXANDER
2014 ◽  
Vol 31 (1) ◽  
pp. 2-17 ◽  
Author(s):  
S.H. Ju

Purpose – This paper develops C++ and Fortran-90 solvers to establish parallel solution procedures in a finite element or meshless analysis program using shared memory computers. The paper aims to discuss these issues. Design/methodology/approach – The stiffness matrix can be symmetrical or unsymmetrical, and the solution schemes include sky-line Cholesky and parallel preconditioned conjugate gradient-like methods. Findings – By using the features of C++ or Fortran-90, the stiffness matrix and its auxiliary arrays can be encapsulated into a class or module as private arrays. This class or module will handle how to allocate, renumber, assemble, parallelize and solve these complicated arrays automatically. Practical implications – The source codes can be obtained online at http//myweb.ncku.edu.tw/∼juju. The major advantage of the scheme is that it is simple and systematic, so an efficient parallel finite element or meshless program can be established easily. Originality/value – With the minimum requirement of computer memory, an object-oriented C++ class and a Fortran-90 module were established to allocate, renumber, assemble, parallel, and solve the global stiffness matrix, so that the programmer does not need to handle them directly.


2004 ◽  
Vol 272-276 ◽  
pp. 693-694 ◽  
Author(s):  
W Scholz ◽  
D Suess ◽  
R Dittrich ◽  
T Schrefl ◽  
V Tsiantos ◽  
...  

2013 ◽  
Vol 49 (5) ◽  
pp. 2413-2416 ◽  
Author(s):  
Yasuhito Takahashi ◽  
Tadashi Tokumasu ◽  
Masafumi Fujita ◽  
Takeshi Iwashita ◽  
Hiroshi Nakashima ◽  
...  

Author(s):  
J. Rodriguez ◽  
J. Sun

Abstract The primary objective of this study was the implementation and comparison of domain decomposition algorithms for a parallel Finite Element Method (FEM) used in the area of Computational Structural Mechanics (CSM). A parallelized FEM code exploits the concurrency inherent in the method to improve its computational efficiency. In order to use a larger size granularity in the parallel computation, the parallel FEM needs to partition its domain into subdomains in a proper manner. It is therefore necessary to search for domain decomposition algorithms to satisfy the special requirements of a parallel FEM. The domain decomposition algorithms investigated in this study physically decompose a meshed domain into a desired number of subdomains. Addressing the requirements of the parallel FEM, these algorithms are able to handle any type of two- and three-dimensional domains, balance the workloads across the multiple processors, minimize the communication overhead among the processors, maintain the integrity of each subdomain, minimize the overall bandwidth of the resulting system matrix, and require only a small amount of CPU time for the decomposition. Modifications to existing decomposition algorithms, such as the single wave propagating method and the bisecting method using vertical/horizontal cuts, are investigated. A new algorithm, based on the proposed multiple wave propagating method and the bisecting method using middle cuts, is formulated. These algorithms are compared with each other using performance criteria based on the overall FEM code and the algorithms themselves. An optimal combination algorithm is proposed. This algorithm combination is flexible and intelligent in some sense since several judgements are suggested to guide and organize different decompositions based on the general geometry of the meshes. The combination algorithm possesses both the desirable features of wave propagating and bisecting methods. As an application, the present algorithm is included in an existing parallel FEM code and some improvements in this code are made. The overall efficiency of the FEM code was increased.


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