Research Interests

My research interests are in the numerical analysis and solution of partial differential equations and large scale scientific computing with applications to fluid flow and transport. My current research focus is on the design and analysis of accurate multiscale adaptive discretization techniques (mixed finite elements, finite volumes, finite differences) and efficient linear and nonlinear iterative solvers (domain decomposition, multigrid, Newton-Krylov methods) for massively parallel simulations of coupled multiphase porous media and surface flows. Other areas of research interest include estimation of uncertainty in stochastic systems and mathematical and computational modeling for biomedical applications.

Ph.D. Thesis

Mixed Finite Element Methods for Flow in Porous Media, Technical Report TR96-09, Dept. Comp. Appl. Math., Rice University and Technical Report TICAM 96-23, University of Texas at Austin.

Selected publications

B. Ganis, H. Klie, M. F. Wheeler, T. Wildey, I. Yotov, and D. Zhang, Stochastic collocation and mixed finite elements for flow in porous media, submitted.
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    G. Pencheva and I. Yotov, Interior superconvergence in mortar and non-mortar mixed finite element methods on non-matching grids, submitted.
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    K. Lipnikov, M. Shashkov, and I. Yotov, Local flux mimetic finite difference methods, submitted.
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    V. Girault, S. Sun, M. F. Wheeler, and I. Yotov, Coupling Discontinuous Galerkin and Mixed Finite Element Discretizations using Mortar Finite Elements, SIAM J. Numer. Anal. 46:2 (2008) 949-979.
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    I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M. F. Wheeler and I. Yotov, Convergence of a symmetric MPFA method on quadrilateral grids, Comput. Geosci. 11 (2007) 333-345.
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    T. Arbogast, G. Pencheva, M. F. Wheeler, and I. Yotov, A multiscale mortar mixed finite element method, SIAM J. Multiscale Modeling and Simulation, 6:1 (2007) 319-346.
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    T. F. Russell, M. F. Wheeler and I. Yotov, Superconvergence for control-volume mixed finite element methods on rectangular grids, SIAM J. Numer. Anal. 45:1 (2007) 223-235.
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    M. F. Wheeler and I. Yotov, A multipoint flux mixed finite element method, SIAM J. Numer. Anal. 44:5 (2006) 2082-2106.
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    M. Berndt, K. Lipnikov, M. Shashkov, M. F. Wheeler, and I. Yotov, A mortar mimetic finite difference method on non-matching grids, Numer. Math. 102:2 (2005) 203-230.
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    M. F. Wheeler and I. Yotov, A posteriori error estimates for the mortar mixed finite element method, SIAM J. Numer. Anal. 43:3 (2005) 1021-1042.
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    M. Berndt, K. Lipnikov, M. Shashkov, M. F. Wheeler, and I. Yotov, Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals, SIAM J. Numer. Anal. 43:4 (2005) 1728-1749.
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    B. Riviere and I. Yotov, Locally Conservative Coupling of Stokes and Darcy Flows, SIAM J. Numer. Anal. 42:5 (2005) 1959--1977.
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    W. J. Layton, F. Schieweck, and I. Yotov, Coupling fluid flow with porous media flow, SIAM J. Numer. Anal. 40:6 (2003) 2195-2218.
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    G. Pencheva and I. Yotov, Balancing domain decomposition for mortar mixed finite element methods on non-matching grids, Numer. Linear Algebra Appl. 10:1-2 (2003) 159-180.
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    • J. A. Wheeler, M. F. Wheeler, and I. Yotov, Enhanced velocity mixed finite element methods for flow in multiblock domains, Computational Geosciences 6:3-4 (2002) 315-332.
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    M. Peszynska, M. F. Wheeler, and I. Yotov, Mortar upscaling for multiphase flow in porous media, Computational Geosciences 6:1 (2002) 73-100.
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    I. Yotov, A multilevel Newton-Krylov interface solver for multiphysics couplings of flow in porous media, Numer. Linear Algebra Appl. 8 (2001) 551--570.
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    • T. Kearsley, L. C. Cowsar, R. Glowinski, M. F. Wheeler, and I. Yotov, New optimization approach to multiphase flow, J. Optim. Theory Appl. 111 (2001) 473-488.
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    • I. Yotov, Interface solvers and preconditioners of domain decomposition type for multiphase flow in multiblock porous media, Advances in Computation: Theory and Practice, vol. 7 (2001) 157-167.
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    • T. Arbogast, L. C. Cowsar, M. F. Wheeler, and I. Yotov, Mixed finite element methods on non-matching multiblock grids , SIAM J. Numer. Anal. 37:4 (2000) 1295-1315
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    • M. F. Wheeler and I. Yotov, Multigrid on the interface for mortar mixed finite element methods for elliptic problems, Comp. Meth. in Appl. Mech. and Engng. 184 (2000) 287-302.
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    • M. F. Wheeler, T. Arbogast, S. Bryant, J. Eaton, Q. Lu, M. Peszynska and I. Yotov, A parallel multiblock/multidomain approach to reservoir simulation, Fifteenth SPE Symposium on Reservoir Simulation (1999) 51-62.
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    • M. F. Wheeler and I. Yotov, Physical and computational domain decompositions for modeling subsurface flows Contemporary Mathematics 218, American Mathematical Society (1998) 217--228.
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    • I. Yotov, Mortar mixed finite element methods on irregular multiblock domains, IMACS Series in Comp. Appl. Math. vol. 4 (1998) 239--244.
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    • T. Arbogast, C. N. Dawson, P. T. Keenan, M. F. Wheeler, and I. Yotov, Enhanced cell-centered finite differences for elliptic equations on general geometry, SIAM J. Sci. Comp. 19:2 (1998) 404--425.
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    • I. Yotov, A mixed finite element discretization on non-matching multiblock grids for a degenerate parabolic equation arising in porous media flow, East-West J. Numer. Math. 5 (1997) 211--230.
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    • T. Arbogast, M. F. Wheeler, and I. Yotov, Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences, SIAM J. Numer. Anal. 34:2 (1997) 828-852.
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    • T. Arbogast and I. Yotov, A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids, Comp. Meth. in Appl. Mech. and Engng. 149 (1997) 255-265.
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    • Selected Presentations

    Parallel multiblock reservoir simulation