CONCEPTS FOR HIGH PERFORMANCE GENERIC SCIENTIFIC COMPUTING
René Heinzl, P. Schwaha, Tibor Grasser · 2006
We present concepts for a generic environment for high performance scientific computing that impose no restrictions on geometry, topology, or discretization schemes. Therewith algorithms and discretization schemes can be formulated in a dimension and topology neutral way. 1. Motivation The scientific computing approach is used to gain an understanding of scientific and engineering problems by the analysis of mathematical models implemented in computer programs and solved by numerical techniques. Due to the diversity of the mathematical structures, combined with efficiency considerations, in particular in three dimensions, the development of high performance simulation software is quite challenging. In the field of TCAD, as in many others, the numerical simulation results are based on different discretization schemes such as finite differences, finite elements, and finite volumes. Each of these schemes has its merits and shortcomings and is therefore more or less suited for different classes of equations. All of these methods have in common that they require a proper tessellation and adaptation of the simulation domain (1, 2), so-called unstructured meshes or structured grids. Testing and validation are major problems in the development process of software for numerical applications. Errors are often not obvious to detect. It may already require a lot of experience to decide if a result from a simulation is erroneous or not. If the result is not correct, it may be due to a great number of reasons, e.g. to a programming bug, a logical error in the program flow, or a badly chosen parameter. Therefore the availability of already tested and proven modules can not be underestimated.