The Associated Hermite FDTD method: Developments and applications

Huang, Zheng-Yu; Shi, Lihua

doi:10.1109/isemc.2018.8394083

Cited by 1 publication

(2 citation statements)

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“…To overcome the numerical stability constraints of conventional finitedifference time-domain (FDTD) method [1,2], many unconditionally stable methods to reduce or eliminate requirements of the stability condition have been proposed and developed, such as alternating-direction implicit method [2,3] and locally one-dimensional schemes [3], explicit and unconditionally stable FDTD method [4], and orthogonal expansions in time domain [5][6][7][8]. For the orthogonal expansions schemes, field-versus-time variations in the FDTD space lattice are expanded using an appropriate set of orthogonal temporal basis and testing functions, such as weighted Laguerre polynomials (WLP) and associated Hermite (AH) functions, which leads to two different solution schemes: marching-on-in-order and paralleling-in-order, respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Huang¹,

Sun²,

He³

2019

Polynomials - Theory and Application

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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 "dual" 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.

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Section: Introductionmentioning

confidence: 99%

“…8), the partial differential term in Maxwell's equations can readily be dealt with, and finally, a five-point banded matrix equation for Hz component can be obtained[9].…”

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confidence: 99%