Functional Analysis and Applications Seminar


(organized by the Functional Analysis and Applications Group)


Department of Mathematics, University of Aveiro



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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