Application to Solve Multiphysics Problems

This chapter uses the electromagnetic (EM) elastodynamic problem as an example to illustrate the solution of multiphysics problems by using the Nyström method. The chapter begins with an introduction to elastic wave equations and then the illustration of the Nyström solution for elastic wave scattering by regular or small elastic objects. It explains the incorporation of the Nyström method with the multilevel fast multipole algorithm (MLFMA) based on the elastic wave equations for solving large elastic wave problems. Since an acoustic wave is a special case of an elastic wave and they share many common characteristics, the chapter also investigates the acoustic wave equation and its Nyström solution with the MLFMA acceleration for solving acoustic wave scattering by very large objects. The chapter also uses the Nyström method with an iterative process to solve the coupled boundary integral equations and illustrates some numerical results for the interaction of EM wave with piezoelectric materials.