Chapter 10 - Models of Physical Systems

Abstract

This chapter focuses on the models of physical systems. Large problem size and fine granularity are the needs for high performance. The chapter presents some examples of scientific problems to be simulated and some of the mathematics used to describe the system. There are two methods for solving the equations that are very suited to high performance computing: the finite differences method, and the finite element method. The chapter discusses the complexity of mapping a physical model to a coordinate system. Two kinds of problem decomposition are—data decomposition and domain decomposition. A large collection of physical systems are described in the chapter using differential equations, and consequently, many applications are implemented using the finite differences or the finite elements methods. These applications are structural analysis, airplane design, automobile crash analysis, and weather.