scholarly journals Natural Domain Decomposition Algorithms for the Solution of Time-Harmonic Elastic Waves

2020 ◽  
Vol 42 (5) ◽  
pp. A3313-A3339
Author(s):  
R. Brunet ◽  
V. Dolean ◽  
M. J. Gander
Keyword(s):  
Domain Decomposition ◽  
Elastic Waves ◽  
Decomposition Algorithms ◽  
Time Harmonic ◽  
Natural Domain

scholarly journals Improved sweeping preconditioners for domain decomposition algorithms applied to time-harmonic Helmholtz and Maxwell problems

2018 ◽  
Vol 61 ◽  
pp. 93-111 ◽  
Author(s):  
Alexandre Vion ◽  
Christophe Geuzaine
Keyword(s):  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Harmonic Wave ◽  
Three Dimensions ◽  
Parallel Computer ◽  
Decomposition Algorithms ◽  
Perfectly Matched Layers ◽  
Time Harmonic ◽  
Inherent Problem ◽  
Matrix Free

Sweeping-type algorithms have recently gained a lot of interest for the solution of highfrequency time-harmonic wave problems, in particular when used in combination with perfectly matched layers. However, an inherent problem with sweeping approaches is the sequential nature of the process, which makes them inadequate for efficient implementation on parallel computers. We propose several improvements to the double-sweep preconditioner originally presented in [18], which uses sweeping as a matrix-free preconditioner for a Schwarz domain decomposition method. Similarly, the improved preconditioners are based on approximations of the inverse of the Schwarz iteration operator: the general methodology is to apply well-known algebraic techniques to the operator seen as a matrix, which in turn is processed to obtain equivalent matrix-free routines that we use as preconditioners. A notable feature of the new variants is the introduction of partial sweeps that can be performed concurrently in order to make a better usage of the resources. As these modifications still leave some unexploited computational power, we also propose to combine them with right-hand side pipelining to further improve parallelism and achieve significant speed-ups. Examples are presented on high-frequency Helmholtz and Maxwell problems, in two and three dimensions, to demonstrate the properties of our improvements on parallel computer architectures.

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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