Picture of DNA strand

Pioneering chemical biology & medicinal chemistry through Open Access research...

Strathprints makes available scholarly Open Access content by researchers in the Department of Pure & Applied Chemistry, based within the Faculty of Science.

Research here spans a wide range of topics from analytical chemistry to materials science, and from biological chemistry to theoretical chemistry. The specific work in chemical biology and medicinal chemistry, as an example, encompasses pioneering techniques in synthesis, bioinformatics, nucleic acid chemistry, amino acid chemistry, heterocyclic chemistry, biophysical chemistry and NMR spectroscopy.

Explore the Open Access research of the Department of Pure & Applied Chemistry. Or explore all of Strathclyde's Open Access research...

Dispersive properties of high order nedelec/edge element approximation of the time-harmonic Maxwell equations

Ainsworth, Mark (2004) Dispersive properties of high order nedelec/edge element approximation of the time-harmonic Maxwell equations. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 362 (1816). pp. 471-493. ISSN 1471-2962

[img]
Preview
Text (strathprints000064)
strathprints000064.pdf
Accepted Author Manuscript

Download (556kB)| Preview

    Abstract

    The dispersive behaviour of high-order Næ#169;dæ#169;lec element approximation of the time harmonic Maxwell equations at a prescribed temporal frequency ω on tensor-product meshes of size h is analysed. A simple argument is presented, showing that the discrete dispersion relation may be expressed in terms of that for the approximation of the scalar Helmholtz equation in one dimension. An explicit form for the one-dimensional dispersion relation is given, valid for arbitrary order of approximation. Explicit expressions for the leading term in the error in the regimes where ωh is small, showing that the dispersion relation is accurate to order 2p for a pth-order method; and in the high-wavenumber limit where 1«ωh, showing that in this case the error reduces at a super-exponential rate once the order of approximation exceeds a certain threshold, which is given explicitly.