Accelerated unconditionally stable FDTD scheme with modified operators. Issue 5 (7th September 2015)

• Record Type: Journal Article
• Authors: Zygiridis, Theodoros; Pyrialakos, Georgios; Kantartzis, Nikolaos; Tsiboukis, Theodoros
• Editors: Oszkár Bíró, Professor David A. Lowther and Dr Piergiorgio Alotto, Professor
• Is Part Of: Compel. Volume 34:Issue 5(2015)
• Page Start: 1564
• Page End: 1577
• Publication Date: 2015-09-07
• Subjects: FDTD -- Locally one-dimensional (LOD) method -- Numerical dispersion -- Parallel cyclic reduction; Electrical engineering -- Data Processing -- Periodicals; Electrical engineering -- Mathematics -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Data Processing -- Periodicals; Electronics -- Mathematics -- Periodicals; 621.3
• DOI: 10.1108/COMPEL-02-2015-0085
• Languages: English
• ISSNs: 0332-1649

Abstract

Abstract : Purpose: – The locally one-dimensional (LOD) finite-difference time-domain (FDTD) method features unconditional stability, yet its low accuracy in time can potentially become detrimental. Regarding the improvement of the method's reliability, existing solutions introduce high-order spatial operators, which nevertheless cannot deal with the augmented temporal errors. The purpose of the paper is to describe a systematic procedure that enables the efficient implementation of extended spatial stencils in the context of the LOD-FDTD scheme, capable of reducing the combined space-time flaws without additional computational cost. Design/methodology/approach: – To accomplish the goal, the authors introduce spatial derivative approximations in parametric form, and then construct error formulae from the update equations, once they are represented as a one-stage process. The unknown operators are determined with the aid of two error-minimization procedures, which equally suppress errors both in space and time. Furthermore, accelerated implementation of the scheme is accomplished via parallelization on a graphics-processing-unit (GPU), which greatly shortens the duration of implicit updates. Findings: – It is shown that the performance of the LOD-FDTD method can be improved significantly, if it is properly modified according to accuracy-preserving principles. In addition, the numerical results verify that a GPU implementation of the implicit solver can result in up to 100× acceleration. Overall, the formulation developed herein describes a fast, unconditionally stable technique that remains reliable, even at coarse temporal resolutions. Originality/value: – Dispersion-relation-preserving optimization is applied to an unconditionally stable FDTD technique. In addition, parallel cyclic reduction is adapted to hepta-diagonal systems, and it is proven that GPU parallelization can offer non-trivial benefits to implicit FDTD approaches as well.