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

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Includes bibliographical references.

1. Introduction -- 1.1. Time-domain modeling in computational electromagnetics -- 1.2. The FDTD method for waveguide and antenna analysis -- 1.3. The higher order FDTD formulation -- References -- 2. Conventional higher order FDTD differentiation -- 2.1. Introduction -- 2.2. Fundamentals -- 2.3. Development of the basic conventional algorithm -- 2.4. Higher order FDTD modeling of boundaries and material interfaces -- 2.5. Dispersion-optimized higher order FDTD techniques -- 2.6. Higher order FDTD schemes in curvilinear coordinates -- References -- 3. Higher order nonstandard FDTD methodology -- 3.1. Introduction -- 3.2. The nonstandard finite-difference algorithm -- 3.3. Development of the higher order nonstandard forms in Cartesian coordinates -- 3.4. Generalized higher order curvilinear FDTD method -- 3.5. Dispersion error and stability analysis -- 3.6. Issues of practical implementation -- References -- 4. Absorbing boundary conditions and widened spatial stencils -- 4.1. Introduction -- 4.2. Higher order FDTD formulation of analytical ABCs -- 4.3. Higher order PML absorbers -- 4.4. Widened spatial stencils and dissimilar media interfaces -- References -- 5. Structural extensions and temporal integration -- 5.1. Introduction -- 5.2. Modeling of lossy and dispersive media with higher order FDTD schemes -- 5.3. Improvement via the correction of material parameters -- 5.4. Enhanced spatial approximations -- 5.5. Generalizing temporal integration -- References -- 6. Hybrid and alternative higher order FDTD schemes -- 6.1. Introduction -- 6.2. Hybrid second-order and higher order FDTD techniques -- 6.3. Discrete singular convolution and symplectic operators -- 6.4. The higher order ADI-FDTD method -- 6.5. Higher order weighted essentially nonoscillatory schemes in the time domain -- References -- 7. Selected applications in waveguide systems -- 7.1. Introduction -- 7.2. Excitation schemes and open-end truncation -- 7.3. Multimodal higher order FDTD analysis -- 7.4. Applications : numerical results -- References -- 8. Selected applications in antenna structures -- 8.1. Introduction -- 8.2. Excitation issues and feeding models -- 8.3. Analysis of essential structures -- 8.4. Contemporary antenna configurations -- References.

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This publication provides a comprehensive and systematically organized coverage of higher order finite-difference time-domain or FDTD schemes, demonstrating their potential role as a powerful modeling tool in computational electromagnetics. Special emphasis is drawn on the analysis of contemporary waveguide and antenna structures. Acknowledged as a significant breakthrough in the evolution of the original Yee's algorithm, the higher order FDTD operators remain the subject of an ongoing scientific research. Among their indisputable merits, one can distinguish the enhanced levels of accuracy even for coarse grid resolutions, the fast convergence rates, and the adjustable stability. In fact, as the fabrication standards of modern systems get stricter, it is apparent that such properties become very appealing for the accomplishment of elaborate and credible designs.

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