# Computational Solid Wave Propagation Numerical Techniques and Industrial Applications

[Doktorsavhandling]

For wave propagation and many other physical phenomena, the dynamic effects are vital. In industrial applications, such problems are very complex and generally have to be treated by means of numerical methods. Advanced models with high resolution and long simulation times encourage further development and refinement of numerical methods but also usage of faster and larger computers. The purpose of this thesis is to contribute to development in the field of computational wave propagation in solid materials by means of the finite element method. The thesis attempts to give both an overview and detailed knowledge of existing methods, propose improvements and extensions of the methods and apply them to industrial problems.

The thesis consists of a summary and five appended papers (A-E). An initial study concerns application of the discontinuous Galerkin method dG(1,1), implemented for adaptive two-dimensional analysis, to wave propagation induced by moving loads. Further, explicit time integration methods for parallel execution are considered. An almost perfect parallel speed-up could be achieved for both the explicit version of the dG(1,1)-method and the central difference method. The qualities of the dG(1,1)-method for analysis of shock wave propagation in terms of high accuracy and its capability to damp spurious modes, but also the drawback in terms of high computational cost are confirmed.

In order to compensate for the drawbacks of the FEM in terms of reflecting boundaries, a hybrid method consisting of FEM and the Scaled Boundary Finite Element Method (SBFEM) is constructed. Like the BEM, the SBFEM is very computer intensive but could be used to accurately represent unbounded domains. In complex models, non-conforming grids and different element types are commonly used. Thus, solution processes for DAE-systems arising from the Lagrange multiplier approach to handle constraint equations in combination with the Newmark time integration method are further implemented. Iterative, preconditioned solution methods are developed in order to efficiently solve large-scale problems in 3D. For multigrid methods, the computational effort to solve a linear system of equations grows linearly with the number of unknowns. A combined algorithm for both linear and nonlinear wave propagation problems employing adaptivity and multigrid solution algorithms and strategies for successive refinement or regeneration of the grid sequences is presented. Some degradation in performance of the multigrid procedures is noticed as the difference between consecutive adaptively generated grids becomes small.

The computer program used in Paper B to E and important aspects regarding implementation based on object-oriented methodology in order to achieve good performance are described in the summary where also the proposed methods are used to solve industrial wave propagation problems; in particular high-speed train induced vibrations.

**Nyckelord: **wave propagation, FEM, SBFEM, iterative, multigrid, adaptivity, parallel

Denna post skapades 2006-08-28. Senast ändrad 2013-09-25.

CPL Pubid: 436