A bubble-inspired algorithm for finite element mesh partitioning

摘要

This paper presents a bubble-inspired algorithm for partitioning finite element mesh into subdomains. Differing from previous diffusion BUBBLE and Center-oriented Bubble methods, the newly proposed algorithm employs the physics of real bubbles, including nucleation, spherical growth, bubble-bubble collision, reaching critical state, and the final competing growth. The realization of foaming process of real bubbles in the algorithm enables us to create partitions with good shape without having to specify large number of artificial controls. The minimum edge cut is simply achieved by increasing the volume of each bubble in the most energy efficient way. Moreover, the order, in which an element is gathered into a bubble, delivers the minimum number of surface cells at every gathering step; thus, the optimal numbering of elements in each subdomain has naturally achieved. Because finite element solvers, such as multifrontal method, must loop over all elements in the local subdomain condensation phase and the global interface solution phase, these two features have a huge payback in terms of solver efficiency. Experiments have been conducted on various structured and unstructured meshes. The obtained results are consistently better than the classical kMetis library in terms of the edge cut, partition shape, and partition connectivity.