The enriched subspace iteration method and wave propagation dynamics with overlapping finite elements

Abstract

In structural dynamic problems, the mode superposition method is the most widely used solution approach. The largest computational effort (about 90% of the total solution time) in the mode superposition method is spent on calculating the required eigenpairs and it is of critical importance to develop effective eigensolvers. We present in this thesis a novel solution scheme for the generalized eigenvalue problem. The scheme is an extension of the Bathe subspace iteration method and a significant reduction in computational time is achieved. For the solution of wave propagation problems, the finite element method with direct time integration has been extensively employed. However, using the traditional finite element solution approach, accurate solutions can only be obtained of rather simple one-dimensional wave propagation problems. In this thesis, we investigate the solution characteristics of a solution scheme using 'overlapping finite elements', disks and novel elements, enriched with harmonic functions and the Bathe implicit time integration method to solve transient wave propagation problems. The proposed solution scheme shows two important properties: monotonic convergence of calculated solutions with decreasing time step size and a solution accuracy almost independent of the direction of wave travel through uniform, or distorted, meshes. These properties make the scheme promising to solve general wave propagation problems in complex geometries involving multiple waves.