Co-published with Oxford University Press. This new edition takes account of the most recent analytical progress that has been made in the field of electromagnetic wave propagation and the impact of the wider availability of powerful computers. The aim of this book is to develop a suitable framework of theory and numerical analysis with applications to various aspects of the propagation of electromagnetic waves. The conjugate gradient method and CGFFT are given extensive treatment. The coverage of finite methods has been expanded and conforming finite elements particularly appropriate to electromagnetic applications are described. New topics have been added to this edition including Sobolev spaces, vector optimization, absorbing boundary conditions, and surface radiation conditions.