Numerical Methods for Problems in Infinite Domains

This volume reviews and discusses the main numerical methods used today for solving problems in infinite domains. It also presents in detail one very effective method in this class, namely the Dirichlet-to-Neumann (DtN) finite element method. The book is intended to provide the researcher or engineer with the state-of-the-art in numerical solution methods for infinite domain problems, such as the problems encountered in acoustics and structural acoustics, fluid dynamics, meteorology, and many other fields of application. The emphasis is on the fundamentals of the various methods, and on reporting recent progress and forecasting future directions. An appendix at the end of the book provides an introduction to the essentials of the finite element method, and suggests a short list of texts on the subject which are categorized by their level of mathematics.

1. Introduction and overview. 2. Boundary integral and boundary element methods. 3. Artificial boundary conditions and NRBCs. 4. Local non-reflecting boundary conditions. 5. Nonlocal non-reflecting boundary conditions. 6. Special numerical procedures for unbounded and large domains. Part II. 7. The DtN method. 8. Computational aspects of the DtN method. 9. Application of the DtN method to beam and shell problems. 10. The DtN method for time-harmonic waves. 11. The DtN method for time dependent problems. Appendix: The finite element method. References. Index.