A. Alekseenko

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An approach based on a discontinuous Galerkin discretiza-tion is proposed for the Bhatnagar-Gross-Krook model kinetic equation. This approach allows for a high order polynomial approximation of molecular velocity distribution function both in spatial and velocity variables. It is applied to model normal shock wave and heat transfer problems. Convergence of(More)
We derive a new first-order formulation for Einstein's equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3ϩ1 decomposition with arbitrary lapse and shift. In the reduction to first-order form only eight particular combinations of the 18 first derivatives of the spatial(More)
We propose an approach for high order discretization of the Boltzmann equation in the velocity space using discontinuous Galerkin methods. Our approach employs a reformulation of the collision integral in the form of a bilinear operator with a time-independent kernel. In the fully non-linear case the complexity of the method is O(n 8) operations per spatial(More)
A well-posed initial-boundary value problem is formulated for the model problem of vector wave equation subject to the divergence-free constraint. Existence, uniqueness, and stability of the solution is proved by reduction to a system evolving the constraint quantity trivially, namely, the second time derivative of the constraint quantity is zero. A new set(More)
High-order Runge-Kutta discontinuous Galerkin (DG) method is applied to the kinetic model equations describing rarefied gas flows. A conservative DG discretization of non-linear collision relaxation term is formulated for Bhatnagar-Gross-Krook and ellipsoidal statistical models. The numerical solutions using RKDG method of order up to four are obtained for(More)
We present a new deterministic approach for the solution of the Boltzmann kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in velocity space. In the new approach the collision operator has the form of a bilinear operator with pre-computed kernel; its evaluation requires O(n 5) operations at every point of the phase space where n(More)
My expertize is in numerical analysis for partial differential equations, inverse problems, and optimization. I am interested in applications of analysis in which mathematical formulations with given properties have to be constructed for a set of governing equations, with the general goal of designing a robust numerical method. My recent work is in the area(More)
Fine structure phenomena in critical collapse [10] New numerical studies of critical phenomena in black hole formation for the spherically symmetric SU(2)-sigma model (wave maps) coupled to gravity. An interesting feature of this model is that the nature of the critical behavior depends on the coupling constant α characterizing the strength of gravitational(More)
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