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Next talk of the Seminar (14:30, Zoom Meeting)
27/10/2021: “Diffraction
problems for two-dimensional lattice waves”
David Kapanadze (Andrea Razmadze
Mathematical Institute, Tbilisi, Georgia)
Motivated by applications of
recent interest related to propagation problems in the left-handed 2D
inductor-capacitor metamaterial and standard 2D inductor-capacitor lattice,
we investigate diffraction problems for two-dimensional lattice
waves. In particular, we study exterior Dirichlet problems for the
two-dimensional discrete Helmholtz equation with the real wavenumber  . The investigation is carried
out without passing to the complex wavenumber. Similar to the continuum
theory, we use the notion of radiating solution. Then, the unique
solvability result and Green's representation formula are obtained with the
help of difference potentials. Finally, we propose a method for numerical
calculation. The efficiency of our approach is demonstrated on examples
related to the propagation problems in the left-handed 2D
inductor-capacitor metamaterials.
This Seminar is supported in part by the
Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia),
through CIDMA - Center for Research and Development in Mathematics and
Applications, within project UIDB/04106/2020.
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