Fast searching algorithm for candidate satellite-node set in NLMG

The Node-based Local Mesh Generation (NLMG) algorithm, which is free of mesh inconsistency, is one of core algorithms in the Node-based Local Finite Element Method (NLFEM) to achieve the seamless link between mesh generation and stiffness matrix calculation, and the seamless link helps to improve the parallel efficiency of FEM. Furthermore, the key to ensure the efficiency and reliability of NLMG is to determine the candidate satellite-node set of a central node quickly and accurately. This paper develops a Fast Local Search Method based on Uniform Bucket (FLSMUB) and a Fast Local Search Method based on Multilayer Bucket (FLSMMB), and applies them successfully to the decisive problems, i.e. presenting the candidate satellite-node set of any central node in NLMG algorithm. Using FLSMUB or FLSMMB, the NLMG algorithm becomes a practical tool to reduce the parallel computation cost of FEM. Parallel numerical experiments validate that either FLSMUB or FLSMMB is fast, reliable and efficient for their suitable problems and that they are especially effective for computing the large-scale parallel problems.