Mikhail’s current research is devoted to application of low-rank approximations to the multidimensional integration and finite-difference schemes. It appears that for certain classes of functions this technique allows to decrease the dimensionality/complexity of the problem down to (almost) linear cost in flops and memory, giving a perspective to design new, fast and efficient algorithms in scientific computing.
Computational physics: ab initio calculations of atomic, molecular, and condensed matter structure.
Numerical mathematics, low-rank approximations, multidimensional integrals.
Ion-atomic and ion-molecular collisions, charge-changing processes.
Multiconfiguration Hartree-Fock method, Density functional theory.
Next Generation Fast Methods for Medical and Nanoscale Technology