Two-level substructuring and parallel mesh generation for domain decomposition methods

Abstract

This paper presents a new parallel mesh generation method leading to subdomains of shape well-suited to Schur based domain decomposition methods such as the FETI and BDD solvers. Starting from a coarse mesh, subdomains meshes are created in parallel through hierarchical mesh refinement and morphing techniques. The proposed methodology aims at limiting the occurrence of known pathological situations (jagged interfaces, misplaced heterogeneity with respect to the interfaces, . . . ) that penalize the convergence of the solver. Furthermore, it enables to distribute and parallelize the mesh generation step in the early phases of the whole analysis. Besides its good behavior towards convergence, the mesh generation is thus distributed. The method is assessed, on several academical and industrial test cases, for both its parallel efficiency when creating the mesh and its capability to generate decomposition resulting in less FETI iterations.

A New Hybrid Hierarchical Parallel Algorithm to Enhance the Performance of Large-Scale Structural Analysis Based on Heterogeneous Multicore Clusters

“…The hybrid method takes both advantage of direct and iterative schemes, which can improve parallel efficiency. And thus, it has been widely used in the finite elements structural field [2,[15][16][17][18][19]. Based on the CDDA, Miao et al [15] designed a hierarchical parallel calculation method in finite element analysis for static structures.…”

“…This method was later applied to a high-rise building to find its parallel solution to static structural characteristics. El Gharbi et al [16] utilized the CDDA to design a two-level parallel mesh algorithm. And they applied the algorithm to complete the mesh for a turbine blade.…”

“…The system equations of partitioned sub-domains at the moment of t + t can be expressed as the following equation equivalently with Schur formulation [15][16][17][18][19]: 2) and ( 3) with Newmark-HHT integral through the finitedifference method [28][29][30]:…”

“…2.2 Review of TPCA TPCA [16] was proposed to improve the parallel efficiency of large-scale structural dynamic analysis through two-level partitioning and two-level condensation based on CDDA, as shown in Fig. 2.…”

Efficient mesh deformation based on randomized RBF solvers

“…Figure (1 -b) represents the final mesh using an exact solver, Figure (1 -c) (respectively (1 -d)) represents the deformed mesh for the same number of steps but using a randomized direct solver with Gaussian (respectively Hadamard) random projectors, while keeping only 10% of the RBF matrix columns (which corresponds to l = 0.1n c ). The randomized mesh deformation approach had a similar behavior in terms of mesh quality distribution to the exact solver with an expected relative error up to 10 By decreasing the compression ratio, we were able to improve the accuracy of the randomized solver with an estimated error up to 10 −4 as shown in Table (2), but no significant improvement was noticed in terms of mesh quality distribution.…”