Selection of numerical methods in specific simulation applications

Abstract

When designing a technical system, simulation is an important concept to study the behavior of the planned system. Often a cycle of parameter variation and simulation is necessary to analyze the system behavior in detail or to improve the design of the system. Thus, the efficiency by which simulation can be carried out plays a role with respect to time, quality, and cost of the design process.The paper in hand shows in which way the simulation of technical systems can be speeded up. Starting point is the observation that for the different mathematical problems, which must be solved when simulating a system, several numerical methods are at hand. For instance, a system of ordinary differential equations can be solved by means of an explicit or an implicit Runge Kutta procedure.Since the different numerical methods are designed with respect to different qualities of a mathematical problem, there exists among the set of competing methods usually one suited best to do the required job. I.e., the qualities of a concrete mathematical problem can be used to select the best method. A central contribution of this paper is to show how this selection process can be operationalized.