TY - JOUR
T1 - A physics-motivated Centroidal Voronoi Particle domain decomposition method
AU - Fu, Lin
AU - Hu, Xiangyu Y.
AU - Adams, Nikolaus A.
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/4/15
Y1 - 2017/4/15
N2 - 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.
AB - 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.
KW - Centroidal Voronoi Particle
KW - Centroidal Voronoi Tessellation
KW - High-performance parallel computing
KW - Partitioning
KW - Voronoi Particle
UR - http://www.scopus.com/inward/record.url?scp=85011832584&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2017.01.051
DO - 10.1016/j.jcp.2017.01.051
M3 - Article
AN - SCOPUS:85011832584
SN - 0021-9991
VL - 335
SP - 718
EP - 735
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -