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A physics-motivated centroidal Voronoi particle domain decomposition method. (English) Zbl 1380.65263
Summary: In this paper, we propose a novel domain decomposition method for large-scale simulations in continuum mechanics by merging the concepts of centroidal Voronoi tessellation (CVT) and Voronoi particle dynamics (VP). The CVT is introduced to achieve a high-level compactness of the partitioning subdomains by the Lloyd algorithm which monotonically decreases the CVT energy. The number of computational elements between neighboring partitioning subdomains, which scales the communication effort for parallel simulations, is optimized implicitly as the generated partitioning subdomains are convex and simply connected with small aspect-ratios. Moreover, Voronoi particle dynamics employing physical analogy with a tailored equation of state is developed, which relaxes the particle system towards the target partition with good load balance. Since the equilibrium is computed by an iterative approach, the partitioning subdomains exhibit locality and the incremental property. Numerical experiments reveal that the proposed centroidal Voronoi particle (CVP) based algorithm produces high-quality partitioning with high efficiency, independently of computational-element types. Thus, it can be used for a wide range of applications in computational science and engineering.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M28 Particle methods and lattice-gas methods
Software:
adsimp; Scotch
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