28 citations · 39 across the 10 of their papers we have counts for
10 papers
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations
G. Makrakis, C. Makridakis, D. Mitsoudis +2
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been…
The Anisotropic Gaussian Semi-Classical Schrödinger Propagator
Panos D. Karageorge, George N. Makrakis
We present a construction of the Anisotropic Gaussian Semi-Classical Schrödinger Propagator, emblematic of a class of Fourier Integral Operators of quadratic phase kernels related…
Asymptotic Approximations for the Phase Space Schrodinger Equation
Panos D. Karageorge, George N. Makrakis
We consider semi-classical time evolution for the phase space Schrödinger equation and present two methods of constructing short time asymptotic solutions. The first method consist…
Asymptotics for the Phase Space Schrödinger Equation
P. D. Karageorge, G. N. Makrakis
We consider semi-classical time evolution for the phase space Schrödinger equation. We construct a semi-classical phase space propagator in terms of semi-classical wave packets by…
An approximate series solution of the semiclassical Wigner equation
Konstantina-Stavroula Giannopoulou, George N. Makrakis
We propose a new approximate series solution of the semiclassical Wigner equation by uniformization of WKB approximations of the Schrödinger eigenfunctions.
Asymptotic Solutions of the Phase Space Schrodinger Equation: Anisotropic Gaussian Approximation
P. D. Karageorge, G. N. Makrakis
We consider the singular semiclassical initial value problem for the phase space Schrodinger equation. We approximate semiclassical quantum evolution in phase space by analyzing i…
Perturbation solutions of the semiclassical Wigner equation
E. K. Kalligiannaki, G. N. Makrakis
We present a perturbation analysis of the semiclassical Wigner equation which is based on the interplay between configuration and phase spaces via Wigner transform. We employ the s…
Formal asymptotic expansion of the Faddeev-Green function in unbounded domains
G. N. Makrakis
We consider the Faddeev-Green function in the three-dimensional space and in a slab, and we construct formal asymptotic expansions for the large complex parameter appearing in this…
New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics
S. Yu. Dobrokhotov, G. Makrakis, V. E. Nazaikinskii +1
We suggest a new representation of Maslov's canonical operator in a neighborhood of the caustics using a special class of coordinate systems ("eikonal coordinates") on Lagrangian m…
Fourier integrals and a new representation of Maslov's canonical operator near caustics
S. Yu. Dobrokhotov, G. Makrakis, V. E. Nazaikinskii
We suggest a new representation of Maslov's canonical operator in a neighborhood of the caustics using a special class of coordinate systems ("eikonal coordinates") on Lagrangian m…