Numerical validation of dispersion relations using a cylindrical wave for 2D FDTD methods

Abstract

AbstractThe numerical dispersion of a proposed new FDTD scheme is often evaluated and compared with that of well‐established FDTD methods. Because there may be a theoretical deficiency in the dispersion analysis, numerical experimentation is often used to validate the dispersion relation. This paper describes the “matching method” for validation using a cylindrical wave in the two‐dimensional (2D) case. The matching method is demonstrated by evaluating the numerical dispersion of Yee's FDTD and ADI‐FDTD. The result is compared with the analytical numerical dispersion relation, and excellent agreement is obtained. The difference between the theoretical value for the numerical dispersion and that from numerical experiments using the matching method is 10−5 for Yee's FDTD and 10−4–10−5 for ADI‐FDTD. The numerical velocity obtained from the matching method satisfies the theoretical dispersion relation with residual errors to the order of 10−6. Such accuracy is sufficient to conclude that a numerical dispersion relation is correct. Although the matching method uses a cylindrical wave to test the numerical dispersion relation, the cylindrical wave is not a solution of the difference equations, thus it cannot be used to derive a theoretical dispersion relation. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 138–142, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20400