Alexander Alekseenko, Assistant Professor,
Department of Mathematics
California State University Northridge
18111 Nordhoff St.,
Northridge, CA 91330-8313
Deterministic solution of the Boltzmann equation using Using a Discontinuous Galerkin
Velocity Discretization. 28 International Symposium on Rarefied Gas Dynamics, 2012
Applications of Discontinuous Galerkin Methods to the Solution of Kinetic Equations. Colloquium at the Georgia Southern University, 2012
Numerical Treatment of Differential Constraints in Evolution Systems. A talk at the Applied Mathematics Seminar at Purdue University. March 21, 2008.
with E. Josyula, Deterministic Solution of the Boltzmann Equation Using Discontinuous Galerkin Discretizations in Velocity Space. submitted to JCP. http://arxiv.org/abs/1301.1099
with E. Josyula, Deterministic solution of the Boltzmann equation using a discontinuous Galerkin velocity discretization. Proceedings of the 28th International Symposium on Rarefied Gas Dynamics, Spain 2012, AIP Conference Proceedings, 8 pp.
with S. Gimelshein and N. Gimelshein, The application of discontinuous Galerkin space and velocity discretization to model kinetic equations. to appear in International Journal of Computational Fluid Dynamics. (2011).
Numerical properties of constraint-preserving boundary conditions for a second orderwave equation. In preparatio nfor resubmission
Numerical properties of high order discrete velocity solutions to the BGK kinetic equation. Applied Numerical Mathematics (2009). Vol. 61 (2011), pp. 410–427. http://dx.doi.org/10.1016/j.apnum.2010.11.005
with A. Alexeenko and C. Galitzine, High order discontinuous Galerkin method for Boltzmann model equations, In: Proceedings of 40th AIAA Thermophysics Conference, Seattle, WA, June 23--26, 2008.
Constraint-preserving boundary conditions for the linearized BSSN formulation.Abstract and Applied Analysis, Vol. 2008, Article ID 742040 (2008), http://www.hindawi.com/getarticle.aspx?doi=10.1155/2008/742040
Well-posed initial-boundary value problem for a constrained evolution system and radiation-controlling constraint-preserving boundary conditions. Journal of Hyperbolic Differential Equations, Vol.4 (2007), No.4, pp.587--612. http://www.worldscinet.com/jhde/04/0404/S02198916070404.html http://arXiv.org/abs/gr-qc/0611011
with D. Arnold, New first-order formulation for the Einstein equations, Physical Review D, vol.68 (2003), 064013. http://arXiv.org/abs/gr-qc/0210071
with S. Kabanikhin, Numerical algorithms for identification problem in magnetoencephalography, Journal of Inverse and Ill-Posed Problems, vol.7 (1999), No.5, pp.387-408
with S. Kabanikhin,Uniqueness of the stationary point for the one-dimensional inverse problem in two-dimensional space, Journal of Inverse and Ill-Posed Problems, vol.6 (1998), No.2, pp.95-114
Two examples of constraint evolution: 3-1=2 and 6-3=5. research notes, California State University, Northridge (2006)