Automatic Construction of Boundary Parametrizations for Geometric Multigrid Solvers

We present an algorithm that constructs parametrizations of bound-ary and interface surfaces automatically. Starting with high-resolution tri-angulated surfaces describing the computational domains, we iteratively simplify the surfaces yielding a coarse approximation of the boundaries with the same topological type. While simplifying we construct a func-tion that is dened on the coarse surface and whose image is the original surface. This function allows access to the correct shape and surface nor-mals of the original surface as well as to any kind of data dened on it. Such information can be used by geometric multigrid solvers doing adap-tive mesh renement. Our algorithm runs stable on all types of input surfaces, including those that describe domains consisting of several ma-terials. We have used our method with success in dierent elds and we discuss examples from structural mechanics and biomechanics. 2 Figure 1: Using parametrized boundaries increases the geometric accuracy of local mesh renements.