Metal boundary modelling for non-orthogonal FDTD

This contribution looks into a technique to reduce numerical errors when employing non-orthogonal mesh in modelling curved structures. A novel technique is analysed using microstrip line and a patch antenna and the results are presented

Fundamental solutions, transition densities and the integration of Lie symmetries

In this paper we present some new applications of Lie symmetry analysis to problems in stochastic calculus. The major focus is on using Lie symmetries of parabolic PDEs to obtain fundamental solutions and transition densities. The method we use relies upon the fact that Lie symmetries can be integrated with respect to the group parameter. We obtain new results which show that for PDEs with nontrivial Lie symmetry algebras, the Lie symmetries naturally yield Fourier and Laplace transforms of fundamental solutions, and we derive explicit formulas for such transforms in terms of the coefficients of the PDE. © 2008 Elsevier Inc. All rights reserved

Fourier type transforms on Lie symmetry groups

© 2015 AIP Publishing LLC. In this paper, we construct operators on a Lie symmetry group which may be regarded as Fourier transforms. Essentially, we integrate solutions generated by Lie symmetries against suitable test functions. We show that this idea leads to a powerful method for solving Cauchy problems for parabolic and hyperbolic equations in two and higher dimensions. We also discuss applications to the elliptic case

Multilayer and conformal antennas using synthetic dielectric substrates

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Microwave Radar-Based Breast Cancer Detection:Imaging in Inhomogeneous Breast Phantoms

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Lie group symmetries as integral transforms of fundamental solutions

We obtain fundamental solutions for PDEs of the form ut = σ xγ ux x + f (x) ux - μ xr u by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of finding a fundamental solution can be reduced to inverting a Laplace transform or some other classical transform. © 2006 Elsevier Inc. All rights reserved