A. Alekseenko

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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)
An approach based on a discontinuous Galerkin discretization 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 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(n8) operations per spatial(More)
We derive two sets of explicit homogeneous algebraic constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura BSSN system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN(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)
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)
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