Boundary Element Method for 3D Shape Optimization Problems

Abstract

The rapid development of the boundary element method (BEM) during the last decades has allowed it to be considered in the shape optimization context, where it is necessary to solve a given state problem many times. We present a BEM-based shape optimization concept, which can also be used for the solution of inverse problems including the presented Bernoulli free-surface problem. To separate the computational and optimization meshes we use the hierarchy of control meshes constructed by means of subdivision surfaces known from the computer graphics. In the thesis we also address the important topic of efficient implementation of BEM on modern hardware architectures and accelerators. The theory is supported by a series of numerical experiments validating the proposed approach.

The rapid development of the boundary element method (BEM) during the last decades has allowed it to be considered in the shape optimization context, where it is necessary to solve a given state problem many times. We present a BEM-based shape optimization concept, which can also be used for the solution of inverse problems including the presented Bernoulli free-surface problem. To separate the computational and optimization meshes we use the hierarchy of control meshes constructed by means of subdivision surfaces known from the computer graphics. In the thesis we also address the important topic of efficient implementation of BEM on modern hardware architectures and accelerators. The theory is supported by a series of numerical experiments validating the proposed approach.