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Part of: Synthesis digital library of engineering and computer science.

Series from website.

Includes bibliographical references (p. 115-121).

1. Introduction -- 1.1 Background and motivation -- 1.2 Book overview --

2. Basics of the finite difference method and multiresolution analysis -- 2.1 Overview of the finite difference method -- 2.2 Overview of multiresolution analysis --

3. Formulation of the multiresolution frequency domain schemes -- 3.1 Derivation of the finite difference frequency domain scheme by the method of moments -- 3.2 Selection of the appropriate wavelet family -- 3.3 Derivation of the multiresolution frequency domain scheme --

4. Application of MRFD formulation to closed space structures -- 4.1 1D application: the Fabry-Perot resonator -- 4.2 2D application: propagation characteristics of general guided wave structures -- 4.3 3D application: the rectangular cavity resonator --

5. Application of MRFD formulation to open space structures -- 5.1 General scattered field formulation -- 5.2 Perfectly matched layer -- 5.3 Scattering from two-dimensional objects --

6. A multiresolution frequency domain formulation for inhomogeneous media -- 6.1 Derivation of the inhomogeneous multiresolution frequency domain scheme -- 6.2 1D application: dielectric slab loaded Fabry-Perot resonator --

7. Conclusion -- A. Resonance frequencies of a dielectric loaded Fabry-Perot resonator -- B. Propagation constant of rectangular waveguide structures -- C. Resonance frequencies of rectangular cavity resonators -- D. Near to far field transformation -- Bibliography -- Authors' biographies.

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In this book, a general frequency domain numerical method similar to the finite difference frequency domain (FDFD) technique is presented. The proposed method, called the multiresolution frequency domain (MRFD) technique, is based on orthogonal Battle-Lemarie and biorthogonal Cohen-Daubechies-Feauveau (CDF) wavelets. The objective of developing this new technique is to achieve a frequency domain scheme which exhibits improved computational efficiency figures compared to the traditional FDFD method: reduced memory and simulation time requirements while retaining numerical accuracy. The newly introduced MRFD scheme is successfully applied to the analysis of a number of electromagnetic problems, such as computation of resonance frequencies of one and three dimensional resonators, analysis of propagation characteristics of general guided wave structures, and electromagnetic scattering from two dimensional dielectric objects. The efficiency characteristics of MRFD techniques based on different wavelets are compared to each other and that of the FDFD method. Results indicate that the MRFD techniques provide substantial savings in terms of execution time and memory requirements, compared to the traditional FDFD method.

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