79 citations · 263 across the 55 of their papers we have counts for
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Splitting Schemes for Non-Stationary Problems with a Rational Approximation for Fractional Powers of the Operator
Petr N. Vabishchevich
Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that th…
Splitting Schemes for Some Second-Order Evolution Equations
Petr N. Vabishchevich
We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is tha…
Temporal Splitting algorithms for non-stationary multiscale problems
Yalchin Efendiev, Sai-Mang Pun, Petr N. Vabishchevich
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multisca…
Numerical recovery of the piecewise constant leading coefficient of an elliptic equation
Aleksandr E. Kolesov, Petr N. Vabishchevich
We propose a numerical algorithm for the reconstruction of a piecewise constant leading coefficient of an elliptic problem. The inverse problem is reduced to a shape reconstruction…
Splitting methods for solution decomposition in nonstationary problems
Yalchin Efendiev, Petr N. Vabishchevich
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these a…
Modified Bee Colony optimization algorithm for computational parameter identification for pore scale transport in periodic porous media
Vasiliy V. Grigoriev, Oleg Iliev, Petr N. Vabishchevich
This paper discusses an optimization method called Modified Bee Colony algorithm (MBC) based on a particular intelligent behavior of honeybee swarms. The algorithm was checked in a…