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The spectral order of accuracy: a new unified tool in the design methodology of excitation-adaptive wave equation FDTD schemes. (English) Zbl 1177.65122

Summary: We define a new concept, termed the spectral order of accuracy (SOoA), which is the spectral domain analogue of the familiar order of accuracy (OoA). The SOoA is pivotal in a refined version of a recently-introduced methodology for formulating excitation-adaptive wave equation FDTD (WE-FDTD) schemes. This concept is the basis for a unified classification for both existing and new schemes. Both one- and two-dimensional cases are presented for boundless, source free, homogeneous, isotropic and lossless media.
The 1-D and 2-D cases are developed in detail for the (\(3, 2M + 1\)) (temporal, spatial) and (3,3) 2-D stencils, respectively. Stability analysis is built into the methodology in terms of either analytical conditions or “stability maps” defined herein. The methodology is seen as a generalization of many existing schemes that also provides a unified tool for a systematical design of WE-FDTD schemes subject to specific requirements in terms of the spectral content of the excitation. The computational efficiency for all schemes remains the same for a given stencil, since the core of the FDTD code is unchanged between schemes, the difference being only in the values of scheme coefficients.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q61 Maxwell equations
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