An Introduction to Fast Fourier Transform Methods for Partial Differential Equations with Applications (Electronic and Electrical Engineering Resear)

Fast Fourier transform (FFT) methods are well established for solving certain types of partial differential equations (PDE). This book is written at an introductory level with the non-specialist user in mind. It first deals with basic ideas and algorithms which may be used to solve problems using simple geometries--the fast Fourier transform is employed and thorough details of the computations are given for a number of illustrative problems. The text proceeds to problems with irregular boundaries, using the capacity matrix approach, and also to more advanced PDE, for which fast solvers may be used as the basis for iterative methods. The use of a numerical Laplace transform technique for certain time-dependent problems is also covered. Throughout the book, the approach is designed to illustrate the essential ideas of the methods employed. References are given for further reading of more advanced or specialized topics.