The boundary element method (BEM) and the finite element method (FEM) may be computationally expensive if complex problems are to be solved; thus there is the need of implementing…
Abstract
The boundary element method (BEM) and the finite element method (FEM) may be computationally expensive if complex problems are to be solved; thus there is the need of implementing them on fast computer architectures, especially parallel computers. Because these methods are complementary to each other, the coupling of FEM and BEM is widely used. In this paper, the coupling of displacement‐based FEM and collocation BEM and its implementation on a distributed memory system (Parsytec MultiCluster2) is described. The parallelization is performed by data partitioning which leads to a very high efficiency. As model problems, we assume linear elasticity for the boundary element method and elastoplasticity for the finite element method. The efficiency of our implementation is shown by various test examples. By numerical examples we show that a multiplicative Schwarz method for coupling BEM with FEM is very well suited for parallel implementation.
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O. Klaas, M. Kreienmeyer and E. Stein
This paper presents the development of a parallel finiteelement algorithm for a MIMD parallel computer. Theelements are distributed, onto the processors, in such a waythat…
Abstract
This paper presents the development of a parallel finite element algorithm for a MIMD parallel computer. The elements are distributed, onto the processors, in such a way that neighbouring elements are placed onto neighbouring processors. This guarantees a good load‐balancing even in physically non‐linear computations. The distribution of the columns of the global system of equations is done by an election algorithm. For solving the global system of equations we use a parallel preconditioned conjugate gradient solver. Tests were done with an elastoplastic material model for proving the efficiency of assembling and solving the system of equations.
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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics…
Abstract
This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.