AMDiS- Adaptive multidimensional simulations: adaptive finite elements for complex domains

Abstract: Complicated meshes used in numerical simulations on complex geometries often limit the applica-bility of multilevel techniques for fast solvers. We propose a way how this limitation can be circumvented if domain adaptation is used. We represent the geometry implicitly by its signed distance function and solve the problem on a larger domain taking account of the complex shape by adaptive refinement and subelement assembling routines. The software concepts of AMDiS [1] allow to deal with this situation in a nearly standard way. An example is shown which allows a detailed convergence analysis by comparing the numerical solution with an analytical solution. Key-Words: mesh generation, distance function, composite finite elements.