Accelerated unconditionally stable FDTD scheme with modified operators

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.

Citation

Zygiridis, T., Pyrialakos, G., Kantartzis, N. and Tsiboukis, T. (2015), "Accelerated unconditionally stable FDTD scheme with modified operators", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 34 No. 5, pp. 1564-1577. https://doi.org/10.1108/COMPEL-02-2015-0085