Parallel Iterative Linear Equation Solvers: An Investigation of Domain Decomposition Algorithms for Reservoir Simulation

1987 ◽  
Author(s):  
J.E. Killough ◽  
M.F. Wheeler
Keyword(s):  
Domain Decomposition ◽  
Linear Equation ◽  
Reservoir Simulation ◽  
Decomposition Algorithms ◽  
Parallel Iterative

scholarly journals Differential-difference iterative domain decomposition algorithms for unilateral multibody contact problems of elasticity

2017 ◽  
pp. 125-140 ◽  
Author(s):  
Ihor Prokopyshyn ◽  
Stepan Shakhno
Keyword(s):  
Finite Element ◽  
Convergence Rate ◽  
Domain Decomposition ◽  
Program Implementation ◽  
Iterative Algorithms ◽  
Contact Problems ◽  
Decomposition Algorithms ◽  
Finite Element Approximations ◽  
Parallel Iterative ◽  
Multibody Contact

Implicit two-point differential-difference parallel iterative domain decomposition algorithms are proposed to solve the multibody contact problems of elasticity. A program implementation of these algorithms based on the finite element approximations is made for the case of plane contact problems. The influence of the iterative parameters on the convergence rate of presented algorithms is investigated. The numerical efficiency of different two-point and one-point iterative algorithms is compared.

On the Design of Small Coarse Spaces for Domain Decomposition Algorithms

2017 ◽  
Vol 39 (4) ◽  
pp. A1466-A1488 ◽  
Author(s):  
Clark R. Dohrmann ◽  
Olof B. Widlund
Keyword(s):  
Domain Decomposition ◽  
Decomposition Algorithms

A Domain Decomposition Study for a Parallel Finite Element Code

1992 ◽  
Author(s):  
J. Rodriguez ◽  
J. Sun
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Performance Criteria ◽  
Communication Overhead ◽  
Decomposition Algorithms ◽  
System Matrix ◽  
Single Wave ◽  
Parallel Finite Element ◽  
Computational Structural Mechanics ◽  
Parallel Fem

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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