Nowadays, transient analysis of electromagnetic systems is widely adopted as a virtual prototyping tool in the design electrical and electronic devices. Time domain (TD) methods for solutions Maxwell’s equations represent most obvious approach to tackling this type problem. Frequency (FD) techniques are also commonly used return TD response through inverse Fourier transform. This suffers from n...

My research is focused on differential equations, with emphasis on the study of singularities and asymptotic behavior of solutions, regularity, normal forms, the study of non-integrable systems and connection to chaos. I am applying new methods—analysis of equations in Borel space (after inverse Laplace transform) and a theory of generalized Borel summation of general formal solutions (transser...

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. Inversion formulas based on the Fourier-Laplace transform are used to establish the existence and uniqueness of solutions to this problem in planar, cylindrical, and spherical geometries.

We have seen before that Fourier analysis is very useful in the study of signals and linear and time invariant (LTI) systems. The main reason is that a lot of signals can be expressed as a linear combination of complex exponentials of the form e with s = jw. There are many properties that still apply when s is not restricted to be pure imaginary. That is why we introduce a generalization of the...

Laser-generated thermal wave diffraction theory is presented as a perturbative Born (or Rytav) approximation in a two-dimensional spatial domain for use with tomographic image reconstruction methodologies. The ranges of validity of the pertinent twodimensional spatial-frequencylthermal wavenumber domain complex plane contours are investigated in terms of the existence af inverse spatial Laplace...

Inverse problems of recovering surface fluxes on the boundary a domain from pointwise observations are considered. Sharp conditions data ensuring existence and uniqueness solutions in Sobolev classes exposed. They smoothness data, geometric location measurement points, domain. The proof relies asymptotics fundamental to corresponding elliptic Laplace transform. inverse problem is reduced linear...

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour ...