Domain decomposition parallelization

Brown, Clarke, Okuda, and Yamazaki also adopted a domain decomposition parallelization strategy on the Fujitsu API 000 machine. " They describe an algorithm that is a development of a spatial decomposition technique due to Liem and co-workers but incorporated decomposition of three-dimensional space in all three dimensions with linked-cell and neighbor table techniques for enhanced efficiency. Communications between processors were minimized without incurring the penalties associated with redundant force calculation. 

D. Brown, J. H. R. Clarke, M. Okuda, and T. Yamazaik, Comput. Phys. Commun., 74, 67 (1993). A Domain Decomposition Parallelization Strategy for Molecular Dynamics Simulations on Distributed Memory Machines. 

D. Brown, H. Minoux, and B. Maigret, A domain decomposition parallel processing algorithm for molecular dynamics simulations of systems of arbitrary connectivity, Comput. Phys. Commun., 103 (1997), 170-186. 

Afshar, Y., Schmid, R, Kshevar, A., Worley, S. Exploiting seeding of random number generators for efficient domain decomposition parallelization of dissipative particle dynamics. Comput. Phys. Commun. 184(4), 1119-1128 (2013). doi 10.1016/j.cpc.2012.12.003... 

The previous section has shown that turbulence combined with a different domain decomposition (i.e. a different number of processors for the following) is sufEcient to lead to totally different instantaneous flow realizations. It is expected that a perturbation in initial conditions will have the same effect as domain decomposition. This is verified in runs TC3 and TC4 which are run on one processor only, thereby eliminating issues linked to parallel implementation. The only difference between TC3 and TC4 is that in TC4, the initial solution is identical to TC3 except at one random point where a 10 perturbation is applied to the streamwise velocity component. Simulations with different locations of the perturbation were run to ensure that their position did not affect results. 

Domain Decomposition The breakdown of a problem into separate processes for parallel execution based on the regularity in the data structures of the application. 

The domain decomposition algorithm described in Section 4.4.1 can be parallelized in a number of different ways. The MD algorithm contains opportunities for independent operations on several different levels. In principle, the interaction on each particle can be calculated independently of all the others and the same goes for time-integration. For an in-depth discussion of these issues we refer to the review by Fincham [97,98]. This fine-grain parallelism is not really used in... 

In this paper, we shall touch the development of such numerical methods intended for the solution of the coupled evolution problems as e.g. thermoelasticity, which is described in Section 2. Here we also discuss the discretization of the evolution problems. As the computational demands are concentrated mainly in the solution of the arising linear systems, we shall focus on the application of suitable, efficient and parallelizable iterative solvers for these linear systems. Section 3 deals with some general techniques enhancing the efficiency of the iterative solution of discrete evolution problems. Section 4 is devoted to a short discussion of the numerical results. In Section 5, we shall describe solvers, which exploit the domain decomposition and parallel computations. Here we also mention another division techniques as displacement decomposition or composite grid methods. 

The well-known domain decomposition (DD) methods, see e.g. Chan Mathew (1994), use data partition induced by a decomposition of the computational domain. This decomposition can be used for two purposes Firstly for parallel implementation of vector updates, inner products and matrix-vector multiplication, i.e. for parallel implementation of the CG method. Secondly, for a construction of efficient preconditioners. 

To use the parallel features of a high performance computing facility, the software has to meet parallel demands, too. A numerical problem that has to be solved in parallel must be divided into subproblems that can be subsequently delegated to different processors. This partitioning procedure can be done either with so-called domain decomposition (Fig. 5) or functional decomposition (Fig. 6). 

The term domain decomposition describes the approach to partition the input data and to process the same calculation on each available processor. Most of the parallel-implemented algorithms are based on this approach dividing the genomic databases into pieces and calculating, for instance, the sequence... 

Spectral domain-decomposition methods are suggested as an efficient way of resolving the limitation of conventional spectral methods. The basic idea behind the methods is to partition the whole domain into several subdomains and then to simultaneously solve the differential equations in each subdomain and appropriate matching conditions on each interface. These methods have very attractive features, such as rapid convergence, geometric flexibility, and suitability to parallel implementation. Thus, they are appropriate when particular regions need to be resolved or when flows in complex geometries are to be simulated. 

Because ofthe material non-linearities, the mechanical contacts with friction, the large number of elements, many iteration steps, and the choice of 500 Monte Carlo simulations, four parallel computers (with 26 CPU) were used to handle the large computational requirements for this problem. The FETI Domain Decomposition Method (i.e. apphcation of parallel computers) was used, see Figure 11. 

Cell level models with varying dimensionality have been reported. To mention a few, 2D models are reported by Li et al. [88], Billigham et al. [89], and Keegan et al. [90], Burt et al. extended a ID model to simulate a cell stack using domain decomposition and parallel execution of the code [91]. Aguiar et al. have also reported ID model for direct internal reforming conditions [81,92]. 

This article reviews some of the progress made in using parallel processor systems to study macromolecules. After an initial introduction to the key concepts required to understand parallelisation, the main part of the article focuses on molecular dynamics. It is shown that simple replicated data methods can be used to carry out molecular dynamics effectively, without the need for major changes from the approach used in scalar codes. Domain decomposition methods are then introduced as a path toward reducing inter-processor communication costs further to produce truly scalable simulation algorithms. Finally, some of the methods available for carrying out parallel Monte Carlo simulations are discussed. 

Parallel molecular dynamics the domain decomposition approach... 

Figure 8. Results showing the parallel performance of a domain decomposition molecular dynamics program using the first force evaluation strategy on a Cray T3D. The results are for a system of 16384 Gay-Berne particles using standard PVM calls on a Cray T3D. Improved performance over these results is possible by using cache-cache data transfers for the global sums at the end of the force evaluation.

Parallel finite element computations have been developed for a number of years mostly for elastic solids and structures. The static domain decomposition (DD) methodology is currently used almost exclusively for decomposing such elastic finite element domains in subdomains. This subdivision has two main purposes, namely (a) to distribute element computations to CPUs in an even manner and (b) to distribute system of equations evenly to CPUs for maximum efficiency in solution process. 

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