Recent numerical methods - A challenge for efficient visualization

Abstract Together with a rapid development of computer hardware, sophisticated, efficient numerical algorithms allow simulation computations of complex physical phenomena. Methods, such as finite volume, multigrid finite element schemes, sparse grid, wavelet approaches, and particle methods or gridless discretizations, all carry data structures, which are tailored to the respective method. These data structures reflect the decomposition of the function space as well as the decomposition in physical space. In this paper an efficient multiresolutional visualization approach is described, which tries to reuse as much of the hierarchical structure in the numerical data as possible. The duality between grid and function space, both carrying an intrinsic hierarchical structure, is explained as the key issue of the approach. Furthermore, a general method of local error measurement is discussed, which allows a reliable representation of the desired multiresolutional data. Finally, the method of spatial, hierarchical subdivision combined with the procedural recovery of the local function spaces is presented to address fairly general numerical data. This leads to a visualization beyond prescribed data formats. Examples from various numerical methods and different data bases underline the applicability of the proposed concept.