Transient finite/infinite element solutions for unbounded wave problems

Abstract

This thesis describes the results of a comprehensive numerical study into the performance of conjugated Astley-Leis infinite elements. Specifically the main goal of the research was to ascertain the effectiveness of combining the transient finite/infinite element (FE/IE) method, the Newmark time stepping scheme and Krylov subspace iterative methods in the solution of 'large' three-dimensional problems in exterior acoustics. The research has been restricted to the solution of the homogeneous wave equation with simple structural boundary conditions.

The results have shown that much lower solution times and computational memory overhead are required using this scheme when compared with traditional direct solutions methods. Only the non-zero terms of the system matrices need to be stored in the solution process and the solution times have been shown to scale approximately as N^1.1 where N is the number of degrees of freedom of the problem. Also when the transient scheme was used to emulate the time-harmonic solution by advancing the solution to steady state with a sinusoidal input, large savings in computational overheads were still achieved over direct methods.

Furthermore the research has shown that the iterative transient FE/IE scheme correctly models a range of benchmark problems, responds well to preconditioning, converges within a small number of iterations and is stable in time. Therefore further research is warranted to generalise the implementation of the method to include more detailed aspects of the physical model such as flow effects, acoustic lining and modal boundary conditions.

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