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

R. Liu, M. F. Wheeler, and I. Yotov, On the Spatial Formulation of Discontinuous Galerkin Methods for Finite Elastoplasticity, Computer Methods in Applied Mechanics and Engineering, 253 (2013) pp. 219--236.
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    • J. Barber, M. Tronzo, C. Horvat, G. Clermont, J. Upperman, Y. Vodovotz, and I. Yotov, A three-dimensional mathematical and computational model of necrotizing enterocolitis, J. Theoretical Biology, 322 (2013) pp. 17--32.
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    • M. F. Wheeler, G. Xue, and I. Yotov, Coupling multipoint flux mixed finite element methods with continuous Galerkin methods for poroelasticity, submitted.
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    • B. Ganis, M. Juntunen, G. Pencheva, M. F. Wheeler, and I. Yotov, A global Jacobian method for mortar discretizations of nonlinear porous media flows, submitted.
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    • V. Girault, D. Vassilev, and I. Yotov, Mortar multiscale finite element methods for Stokes-Darcy flows, submitted.
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    • K. Lipnikov, D. Vassilev and I. Yotov, Discontinuous Galerkin and Mimetic Finite Difference Methods for Coupled Stokes-Darcy Flows on Polygonal and Polyhedral Grids, submitted.
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    • M. F. Wheeler, G. Xue, and I. Yotov, Accurate Cell-Centered Discretizations for Modeling Multiphase Flow in Porous Media on General Hexahedral and Simplicial Grids, SPE Journal, 17:3 (2012) pp. 779-793.
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    • B. Ganis, G. Pencheva, M. F. Wheeler, T. Wildey, and I. Yotov, A Frozen Jacobian Multiscale Mortar Preconditioner for Nonlinear Interface Operators, SIAM J. Multiscale Modeling and Simulation, 10:3 (2012) pp. 853-873.
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    • M. F. Wheeler, G. Xue, and I. Yotov, A Multipoint Flux Mixed Finite Element Method on Distorted Quadrilaterals and Hexahedra, Numerische Mathematik, 121 (2012) pp. 165-204.
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    • M. F. Wheeler, G. Xue, and I. Yotov, A Multiscale Mortar Multipoint Flux Mixed Finite Element Method, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 46:4 (2012) pp. 759-796.
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    • M. F. Wheeler, G. Xue, and I. Yotov, Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra , International Journal of Numerical Analysis and Modeling, 9:3 (2012) pp. 607-627.
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    • B. Ganis, I. Yotov, and M. Zhong, A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types, SIAM J. Sci. Comp. 33:3 (2011) 1439-1474.
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    • R. Ingram, M. F. Wheeler, and I. Yotov, A multipoint flux mixed finite element method on hexahedra, SIAM J. Numer. Anal., 48:4 (2010) 1281-1312.
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    • M. F. Wheeler, T. Wildey, and I. Yotov, A multiscale preconditioner for stochastic mortar mixed finite elements,Comp. Meth. in Appl. Mech. and Engng. 200 (2011) 1251-1262.
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    • B. Ganis and I. Yotov, Implementation of a Mortar Mixed Finite Element Method using a Multiscale Flux Basis, Comp. Meth. in Appl. Mech. and Engng., 198 (2009) 3989-3998.
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    • D. Vassilev and I. Yotov, Coupling Stokes-Darcy flow with transport, SIAM J. Sci. Comp., 31:5 (2009) 3661-3684.
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    • 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, Comp. Meth. in Appl. Mech. and Engng., 197 (2008) 3547-3559.
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    • G. Pencheva and I. Yotov, Interior superconvergence in mortar and non-mortar mixed finite element methods on non-matching grids, Comp. Meth. in Appl. Mech. and Engng., 197 (2008) 4307-4318.
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    • K. Lipnikov, M. Shashkov, and I. Yotov, Local flux mimetic finite difference methods, Numerische Mathematik, 112:1 (2009), 115-152.
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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, Numerische Mathematik 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