On the nature of solutions produced by finite difference schemes in time domain

✍ Scribed by Dr. Malgorzata Celuch-Marcysiak; Wojciech K. Gwarek

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 364 KB
• Volume: 12
• Category: Article
• ISSN: 0894-3370
• DOI: 10.1002/(sici)1099-1204(199901/04)12:1/2<23::aid-jnm325>3.0.co;2-i

✦ Synopsis

This paper is a review discussing properties of "eld solutions produced by various "nite di!erence schemes in the time domain. Considered algorithms include standard FDTD as well as its modi"cations based on di!erent sets of electromagnetic equations and/or di!erent discretization in space. By developing their complete dispersion relations, conclusions are drawn regarding divergence, curl, and energy conservation by each of the emulated eigenmodes separately. This is in extension to previous works which were concerned with the total solution, and permits to formulate conditions for restricting the total solutions to physical uncoupled solenoidal and potential modes. Original classi"cation of spurious modes for the time domain "nite di!erence modelling is also proposed. It is shown that spurious compensating modes can propagate over the mesh in the case of penalty schemes with pO0, and that spurious degenerate modes at high-and low-frequencies appear in the case of condensed node discretization.