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The Orthogonal Expansion in Time-Domain Method for Solving Maxwell Equations Using Paralleling-in-Order Scheme

2020 Electronic books
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Release : 2020
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Book Synopsis The Orthogonal Expansion in Time-Domain Method for Solving Maxwell Equations Using Paralleling-in-Order Scheme by : Zheng-Yu Huang

Download or read book The Orthogonal Expansion in Time-Domain Method for Solving Maxwell Equations Using Paralleling-in-Order Scheme written by Zheng-Yu Huang. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt: The orthogonal expansion in time-domain method is a new kind of unconditionally stable finite-difference time-domain (FDTD) method for solving the Maxwell equation efficiently. Generally, it can be implemented by two schemes: marching-on-in-order and paralleling-in-order, which, respectively, use weighted Laguerre polynomials and associated Hermite functions as temporal expansions and testing functions. This chapter summarized paralleling-in-order-based FDTD method using associated Hermite functions and Legendre polynomials. And a comparison from theoretical analysis to numerical examples is shown. The LD integral transfer matrix can be considered as a ,Äúdual,Äù transformation for AH differential matrix, which gives a possible way to find more potential orthogonal basis function to implement a paralleling-in-order scheme. In addition, the differences with these two orthogonal functions are also analyzed. From the numerical results, we can see their agreements in some general cases while differing in some cases such as shielding analysis with the long-time response requirement.

Polynomials

2019-05-02 Mathematics
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Release : 2019-05-02
Genre : Mathematics
Kind : eBook
Book Rating : 69X/5 ( reviews)

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Book Synopsis Polynomials by : Cheon Seoung Ryoo

Download or read book Polynomials written by Cheon Seoung Ryoo. This book was released on 2019-05-02. Available in PDF, EPUB and Kindle. Book excerpt: Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.

Development and Evaluation of Novel Finite-difference Time-domain Methods for Solving Maxwell's Equations

2004
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Release : 2004
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Book Synopsis Development and Evaluation of Novel Finite-difference Time-domain Methods for Solving Maxwell's Equations by : Guilin Sun

Download or read book Development and Evaluation of Novel Finite-difference Time-domain Methods for Solving Maxwell's Equations written by Guilin Sun. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt:

Time Domain Finite Difference Computation for Maxwell's Equations

1989
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Release : 1989
Genre :
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Book Synopsis Time Domain Finite Difference Computation for Maxwell's Equations by : Jiayuan Fang

Download or read book Time Domain Finite Difference Computation for Maxwell's Equations written by Jiayuan Fang. This book was released on 1989. Available in PDF, EPUB and Kindle. Book excerpt:

High-order Discontinuous Galerkin Methods for the Maxwell Equations

2018-02-28
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Release : 2018-02-28
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Book Rating : 206/5 ( reviews)

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Book Synopsis High-order Discontinuous Galerkin Methods for the Maxwell Equations by : Hassan Fahs

Download or read book High-order Discontinuous Galerkin Methods for the Maxwell Equations written by Hassan Fahs. This book was released on 2018-02-28. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with the development of a high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. First, we present a DGTD method based on high-order nodal basis functions for the approximation of the electromagnetic field within a simplex, a centered scheme for the calculation of the numerical flux at an interface between neighbouring elements, and a second-order leap-frog time integration scheme. Next, to reduce the computational costs of the method, we propose a hp-like DGTD method which combines local h-refinement and p-enrichment. Then, we report on a detailed numerical evaluation of the DGTD methods using several propagation problems. Finally, in order to improve the accuracy and rate of convergence of the DGTD methods previously studied, we study a family of high-order explicit leap-frog time schemes. These time schemes ensure the stability under some CFL-like condition. We also establish rigorously the convergence of the semi-discrete approximation to Maxwell's equations and we provide bounds on the global divergence error.

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