A Software Strategy Towards Putting Domain Decomposition at the Centre of a Mesh-Based Simulation Process (original) (raw)
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Mesh partitioning techniques and domain decomposition methods
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MDEC: MeTiS-based Domain Decomposition for Parallel 2D Mesh Generation
Procedia Computer Science, 2011
Domain decomposition methods are commonly employed within the context of parallel numerical algorithms. Most often, the domain decomposition is performed before the main computation begins. Within the context of mesh generation, parallel mesh generation is desired when the goal is to mesh a very large geometric domain or if very high accuracy is required. In this paper, we propose a novel technique, which we call the MeTiS-based Domain Decomposition (MDEC) technique, for the decomposition of geometric domains into subdomains for use in parallel 2D mesh generation. Our technique is based upon discrete domain decomposition [1]. The algorithm proceeds by first constructing a background mesh which satisfies a minimum angle constraint of 30 degrees and second partitioning this initial coarse mesh or background mesh into subdomains. Finally, adjustments are applied to the triangles with small boundary angles so that all subdomains in the final decomposition contain boundary angles no smaller than 60 degrees which is a guaranteed property of the domain decomposition algorithm. We prove this guarantee for the boundary angles of the MDEC domain decomposition. Our results show that, in comparison to the medial axis domain decomposition (MADD) algorithm [2], our method provides a better balance of subdomain areas, better boundary angles, and a faster decomposition time. In addition, when the MDEC and MADD subdomains are used in conjunction with a parallel constained Delaunay mesh generation technique (PCDM) [3], the meshes are generated in approximately the same time and have very similar element quality.
International Journal for Numerical Methods in Engineering, 1995
Optimal domain decomposition methods have emerged as powerful iterative algorithms for parallel implicit computations. Their key preprocessing step is mesh partitioning, where research has focused so far on the automatic generation of load-balanced subdomains with minimum interface nodes. In this paper, we emphasize the importance of the subdomain aspect ratio as a mesh partitioning factor, and highlight its impact on the convergence rate of an optimal domain decomposition based iterative method. We also present a fast optimization algorithm for improving the aspect ratio of existing mesh partitions, and illustrate it with several examples from fluid dynamics and structural mechanics applications. For a stiffened shell problem decomposed by the optimal Recursive Spectral Bisection scheme and solved by the FETI method, this optimization algorithm is shown to improve the solution time by a factor equal to 1.54 and to restore numerical scalability.
Toward interoperable mesh, geometry and field components for PDE simulation development
Engineering With Computers, 2005
Mesh-based PDE simulation codes are becoming increasingly sophisticated and rely on advanced meshing and discretization tools. Unfortunately, it is still difficult to interchange or interoperate tools developed by different communities to experiment with various technologies or to develop new capabilities. To address these difficulties, we have developed component interfaces designed to support the information flow of mesh-based PDE simulations. We describe this information flow and discuss typical roles and services provided by the geometry, mesh, and field components of the simulation. Based on this delineation for the roles of each component, we give a high-level description of the abstract data model and set of interfaces developed by the Department of Energy's Interoperable Tools for Advanced Petascale Simulation (ITAPS) center. These common interfaces are critical to our interoperability goal, and we give examples of several services based upon these interfaces including mesh adaptation and mesh improvement.
Lecture Notes in Computer Science, 2005
In this paper, we compare the performance of some mesh-based applications in a Grid environment using the domain decomposition technique and unbalanced workload strategies. We propose unbalanced distributions in order to overlap computation with remote communications. Results are presented for typical cases in car crashing simulation where finite element schemes are applied in fine mesh. The expected execution time is basically the same when two unbalanced techniques are used, but it is up 34% smaller that the one requires by the classical balanced strategy. We also analyze the influence of the communication pattern on execution times using the Dimemas simulator.
Scalable system for large unstructured mesh simulation
2012
Dealing with large simulation is a growing challenge. Ideally for the wellparallelized software prepared for high performance, the problem solving capability depends on the available hardware resources. But in practice there are several technical details which reduce the scalability of the system and prevent the effective use of such a software for large problems. In this work we describe solutions implemented in order to obtain a scalable system to solve and visualize large scale problems. The present work is based on Kratos MutliPhysics [1] framework in combination with GiD [2] pre and post processor. The applied techniques are verified by CFD simulation and visualization of a wind tunnel problem with more than 100 millions of elements in our in-hose cluster in CIMNE.
Domain decomposition methods in computational fluid dynamics
International Journal for Numerical Methods in Fluids, 1992
The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately_ and they can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.
Domain Decomposition With Non-Conforming Polyhedral Grids
IEEE Access, 2021
A novel mortar approach for the domain decomposition of field problems discretized in terms of nodal variables by the cell method is here proposed. This approach allows the use of both arbitrary polyhedral meshes and non–conforming discretizations, without limitations or complications due to the mesh type or the model geometry. Therefore, it provides a new domain decomposition method that can be practically used in engineering applications for coupling different parts of a model, which can be independently discretized and then reassembled together. More precisely: 1) Any part of the computational domain is first separately modeled in order to assess the mesh type and size that are best suited for ensuring an accurate local field reconstruction; 2) The different discretized parts can be combined together in order to obtain an accurate solution of a composite problem, while maintaining the local discretizations already determined. As a main advantage over existing mortar approaches, t...