Fast elasto-plastic BEM with hierarchical matrices
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Beschreibung
Boundary element methods offer advantages for the simulation of problems in¬volving a large or infinite domain. Only the surface needs to be meshed and the radiation condition is fulfilled by the fundamental solutions. Unfortunately, the method leads to fully populated system matrices resulting in a quadratic numeri¬cal complexity in terms of storage and numerical effort. To overcome this draw¬back, fast summation methods have been developed, reducing the complexity to almost linear or even linear behavior. This is achieved mainly by splitting the domain into a near- and a far-field, where contributions of the latter are subject to numerical approximation. This thesis covers the application of the concept of Hierarchical Matrices to elastostatic and elasto-plastic problems with a collo¬cation-based boundary element method. The application of the adaptive cross approximation as well as kernel interpolation techniques are presented. The main objective is to efficiently solve inhomogeneous and non-linear problems. In this context, the focus is on the evaluation of internal results with body forces and the special treatment of discrete volume potentials. The successful implementation into a multi-purpose code and the application to various real-world problems with adequate accuracy of the results is demonstrated.
Autor*in
Jürgen Zechner
Themen in »Fast elasto-plastic BEM with hierarchical matrices«
Angewandte Mathematik Baustastik Elastostatik Randelemente-Methode Technische Mechanik Tunnelbau