Mesh Generation, Error Estimation, and Adaptation

The automation and coupling of mesh generation and mesh adaptation process driven by error estimation - considering the partial differential equation`s discretization technique used and the subsequent properties of the equation system - are investigated. A mesh with as small as possible a number of elements that captures all relevant features of the investigated geometry is desired in order to support methods for fast numerical analysis as well as an accurate description of the geometry. This in particular aids the discretization of partial differential equations used for the solution in areas on able amount of time, computer resources, and minimal manual interaction. The technical problems we have to solve in our project are mostly caused by finite numerics in the discrete scheme of computer aided design. As a consequence algorithms based on geometrical predicates have to be designed very carefully with respect to numerical issues. From a software point of view the coupling of different software modules for modeling, generation, adaptation, and error estimation merit special consideration. This requires new and more sophisticated methods of software design with special attention to robustness, orthogonality, modularity, and reusability. The application of our approach is mostly focused on semiconductor device structures, but is not restricted to this field. Final results obtained from our meshing methodology will be demonstrated by real-world examples which surpass the capabilities of currently used meshing techniques.

The automation and coupling of a mesh generation and adaptation process driven by error estimation - considering the partial differential equations discretization technique used and the subsequent properties of the equation system - has been investigated. A mesh with as small as possible a number of elements that captures all relevant features of the investigated geometry is desired in order to support methods for fast numerical analysis as well as an accurate description of the geometry. This in particular aids the discretization of partial differential equations used for the solution within areas on able amount of time, computer resources, and minimal manual interaction. The technical problems we have solved in our project are mostly caused by finite numerics in the discrete scheme of computer-aided design. As a consequence algorithms based on geometrical predicates have been designed very carefully with respect to numerical issues. From a software point of view the coupling of different software modules for modeling, generation, adaptation, and error estimation merit special consideration. This required new and more sophisticated methods of software design with special attention to robustness, orthogonality, modularity, and reusability. The application of our approach is mostly focused on semiconductor device structures, but is not restricted to this field. Final results obtained from our meshing methodology have demonstrated with real-world examples, that the capabilities of previously used meshing techniques are now considerably surpassed.