Applied Mathematics/ Numerical Analysis/ Numerical Methods for PDEs
- 2006 – present, Associate Professor of Mathematics, New Mexico Institute of Mining and Technology, Socorro, New Mexico, U.S.A.
- 2001 – 2006, Assistant Professor of Mathematics, New Mexico Institute of Mining and Technology, Socorro, New Mexico, U.S.A.
- 2000 – 2001, Senior Lecturer, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, U.S.A.
- 1999 – 2000, Visiting Assistant Professor of Mathematics, Colorado State University, Fort Collins, Colorado, U.S.A.
- 1998 – 1999, Professional Research Assistant, Department of Computer Science, University of Colorado at Boulder, Boulder, Colorado, U.S.A. Supervisor - Prof. Xiao-Chuan Cai
- 1998 – 1999, Adjunct Instructor, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, U.S.A.
- 1994 – 1997, Research Assistant, Center for Computational Sciences, University of Kentucky, Lexington, Kentucky, U.S.A. Supervisor - Graeme Fairweather
- 1992 – 1994, Teaching Assistant, Department of Mathematics, University of Kentucky, Lexington, Kentucky, U.S.A.
- 1988 – 1989, Assistant Lecturer, Chair of Applied Analysis, Faculty of Mechanics and Applied Mathematics, Kazakh State University, Almaty, Kazakhstan.
- Ph.D. in mathematics, 1998, University of Kentucky, Lexington, Kentucky, U.S.A.
- Dissertation – “Orthogonal spline collocation for nonlinear elliptic boundary value problems,” adviser – Prof. Bernard Bialecki , mentor - Prof. Graeme Fairweather (Colorado School of Mines); major concentration – numerical analysis; minor concentration – partial differential equations.
- Candidate of physico-mathematical sciences, 1992, Kazakh State University, Almaty, Kazakhstan
- Specialization – application of computers, mathematical modeling and mathematical methods in scientific research; dissertation – “Finite difference schemes for nonlinear differential equations modeling filtration and hydraulic processes,” adviser – Prof. Shaltay Smagulov
- Higher education diploma with honors in applied mathematics, 1988, Kazakh State University, Almaty, Kazakhstan
- Specialization – computational methods for solving problems in mathematics, economics and control; thesis – “Finite difference schemes for Saint-Venant’s equations,” adviser – Prof. Shaltay Smagulov
basic concepts of mathematics
calculus
discrete mathematics
linear algebra
numerical analysis
numerical linear algebra
ordinary differential equations
partial differential equations
vector analysis
computational fluid dynamics
finite element method
numerical methods for sparse linear systems
numerical methods for partial differential equations
numerical methods for wave propagation
numerical modeling and simulation with COMSOL Multiphysics
GRADUATE STUDENT ADVISING
- Rishi Jumani (MS, 2018) Computational fluid dynamics simulation of advection dominated flow using a hybrid discontinuous Galerkin method in FEniCS
- Stella Doughan (MS, 2017) Modeling of low-density lipoprotein transport in arterial wall using Comsol Multiphysics
- Michael Culp (MS, 2012) OSC method for 2D elliptic problems with general boundary conditions, the OSC solution of a singular BVP with Dirichlet-Neumann boundary condition, and computation of the stress intensity factor
- Tuguluke Abulitibu (MS, 2012) Discontinuous Galerkin method for solving model two-point boundary value problems with various regularity assumptions, interface problems, and problems with non-smooth or discontinuous coefficients.
- Luis Zeron (PhD, in progress) Developement of a high-order method for elliptic interface problems
Orthogonal spline collocation (OSC) method
OSC method for PDEs with singular solutions: mixed boundary conditions, discontinuous coefficients, irregular domains
OSC method for a nonlinear elliptic boundary value problem: error analysis and solution methods
Multilevel preconditioners for nonselfadjoint or indefinite OSC problems
Preconditioned conjugate gradient method for nonselfadjoint or indefinite OSC problems
Matrix decomposition algorithms for OSC problems
Quadrature finite element Galerkin schemes
Domain decomposition methods
Preconditioning techniques
- “Exploring acoustic nonlinearity for monitoring complex aerospace structures, AFRL project, P.I. – Andrei Zagrai, Department of Mechanical Engineering, New Mexico Tech. Developed COMSOL multiphysics models of magneto-elastic active sensors that coupled electromagnetics and acoustics equations.
- Enhanced oil recovery techniques, DOE project, P.I. – Sayavur Bakhtiyarov, Department of Mechanical Engineering, New Mexico Tech. COMSOL multiphysics simulations of various effects in multiphase fluid flows.
- “Direct energy – tactical operations system simulation,” AFRL project, P.I. –Scott Tear, Dept. of Electrical Engineering, New Mexico Tech. Developed mathematical and numerical models of thermal blooming effects in laser operations.
- 16th International Conference on Domain Decomposition Methods, New York University, New York City, January 12–15, 2005. Contributed presentation “Convergence Analysis and Multilevel Preconditioners for a Quadrature Galerkin Approximation of a Biharmonic Problem”
- The Eight Copper Mountain Conference on Iterative methods, Copper Mountain, Colorado, March 28 – April 2, 2004. Contributed presentation “Multilevel preconditioners for nonselfadjoint or indefinite orthogonal spline collocation problems”.
- Directed Energy Modeling and Simulation Conference, Albuquerque, New Mexico, 25–27 March 2003. Platform independent interface for using supercomputers in modeling and simulation of directed energy weapons, S. Tear, D. Driscoll, M. Nunez, R. Aitbayev, V. Romero, S. Doerr, H. Schreiber, T. Lawson, G. Gusciora, C. Holmberg, L. Rigdon (presented by S. Tear).
- Regional meeting of the Southwestern Section of the Mathematical Association of America, April 2003. Section chair.
- Parallel Computational Fluid Dynamics 1999 Conference, Williamsburg, Virginia, May, 1999. Contributed presentation Parallel two-level methods for three-dimensional transonic compressible flow simulations on unstructured meshes”with X.-C. Cai and M. Paraschivoiu.
• Academic Assessment Workshop, Lisle, Illinois, February 7–9, 2007.
• Workshop, Introduction to COMSOL Multiphysics, organized by Brian Adolf, COMSOL
Inc, November 8, 2005, Albuquerque, at Imaging Concepts of New Mexico.
• Introduction to Domain Decomposition Methods, organized by Olof Widlund and
David Keyes, January 12, 2005, New York University.
• Introduction to PETSc, organized by the PETSc Project Group, Argonne National
Laboratory, January 11, 2005, Columbia University.
• Trilinos Project, organized by Michael Heroux (Sandia National Laboratories), Copper
Mountain, Colorado, March 28 – April 2, 2004.
• PDE Constrained Optimization, March 31, 7:30-10:00 pm, organized by Eldad Haber
(Emory University), Copper Mountain, Colorado, March 28 – April 2, 2004.
Computing on Campus Committee
Academic Tenure and Freedom Committee
Academic Standards and Admission Committee
General Degree Requirement Assessment Committee, chair
Budget, Funding and Support Committee
Dept of Mathematics Faculty Search Committees
Ph.D. advising committees
M.S. advising committees
B.S. advisor
Society for Industrial and Applied Mathematics (since 2002-2018)
- Introduction to Numerical Analysis, by Brian Bradie, Prentice Hall, 2005
- Proposal feedback on the third edition of David Watkins’ Fundamentals of Matrix Computations, Wiley, 2010.
- Numerical Methods for Partial Differential Equations, Wiley
- Applied Numerical Mathematics, Elsevier
- Numerical Algorithms, Springer
- Advances in Difference Equations, Hindawi Publishing
- Journal of King Saud University (Science)