Scientific computing is a third methodological approach in addition to the two classical pillars of theory and experiment in natural and engineering sciences. Many questions and problems in these fields can only be solved by computer simulation, since the use of physical experiments would be impossible or uneconomical.
We analyze the applied mathematical and numerical models concerning their stability, discretize the equations, and solve the arising systems of equations efficiently and reliably. Special attention is paid to scalable algorithms in order to best utilize contemporary and future high-performance computers. Within these complex problems, we determine selected parameters through optimization.