Load balancing for parallel multilevel substructuring and coarse mesh projection for nonlinear model reduction

Abstract

This dissertation proposes projection-based model reduction methods for efficient linear and nonlinear finite element analysis of structures. In linear dynamic analysis, the mode superposition method is widely used because the lowest modes dominate the response of a structure. However, in the mode superposition method for large-scale systems, solving the generalized eigenvalue problem incurs a huge computation time. In addition, in nonlinear model reduction, computing nonlinear terms still requires operations with the original dimension even though the reduced model is obtained. Since such computations are proportional to the original dimension, no significant speedup can be expected. These challenges are addressed by parallel multilevel substructuring and coarse mesh projection. A load balancing algorithm for the parallel automated multilevel substructuring (PAMLS) method is first presented to solve the generalized eigenvalue problem efficiently. To balance the workload among threads, the proposed algorithm consists of two types of granularity. Without repartitioning, the proposed algorithm significantly improves the efficiency of the PAMLS method. A coarse mesh projection method is also presented for efficient nonlinear model reduction. The proposed method computes the nonlinear terms on the coarse mesh representing the domain of the system, which considerably reduces the computational cost.