I am an applied mathematician primarily interested in real-life problems whose treatment requires analysis of a model / justification of the approximation or those that can be effectively tackled with analytical tools such as asymptotic methods or closed-form solution reducibility.
I enjoy learning new things while working on diverse subjects analyzing a problem, devising a constructive solution approach and verifying / implementing it numerically. The topics I have previously worked on include:
- wave propagation in porous media (fluid / solid inclusion scattering for Biot elastodynamics equations);
- nonlinear PDEs (analysis of one NLS model for laser beams in photopolymers; Darboux transformation);
- approximation theory (approximation of square-integrable functions by traces of analytic functions with certain properties such as pointwise constraints);
- integral equations and optimal bases construction (spectral theory for compact one-dimensional self-adjoint integral operators with convolution kernels);
- inverse magnetization problem (analytical estimation of net magnetization moment components from partial measurements of magnetic field);
- inverse obstacle problem (determining domain geometry for transient wave equation from partial Dirichlet+Neumann data).
At the present time, I am a postdoctoral researcher (project assistant) at Insitute of Analysis and Scientific Computing, TU Wien, Austria.
Together with Anton Arnold, we are working on development and investigation of hybrid asymptotic-numerical methods aimed at efficient treatment of high-frequency problems for wave equations, in particular, using long-time behaviour analysis for time-domain problems with variable coefficients.
You can contact me by email: firstname.lastname@example.org / email@example.com, or find me at:
Office DA 06 L14, Institute of Analysis & Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8, Vienna, Austria.