I
implement state-of-the-art mathematical methods to engineering problems.
Currently, I work on applications of the Difference
Potential Method (DPM) that is a numerical method possessing many unique
properties. In particular, it allows reducing the solution of a boundary-value
problem in an arbitrary domain to the solution of a boundary equation without
the knowledge of Green’s function. The main ingredient of the method, the
difference potential, plays the role similar to that of the Cauchy-type
integral in the theory of analytic functions.
I
also work on the theory of boundary equations and the extension of Ryaben’kii’s potentials to continuous spaces: