Isogeometric Analysis for the Elastic Wave Equation

In everyday life of an engineer, CAD (Computer Aided Design) and FE (Finite Element) programs play an important role. The two different structures, CAD and FE programs, use different mathematical functions. In CAD programs, so called NURBS find their applications while the standard functions used in FE programs are Lagrange polynomials. This differences in the structure of the two programs result in a significant effort of translation. The concept of Isogeometric Analysis tries to extend the FE method by using NURBS as basis for the analysis. In this report we give first an introduction to NURBS. We will see that, compared to a standard FE analysis, we have a richer repertory for refining a given NURBS basis. Then we will use NURBS as basis for analysis to solve numerically two problems of linear elasticity; an equilibrium problem and a simulation of an earthquake.