### 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

M. Bukac, I. Yotov, and P. Zunino,
* Dimensional model reduction for flow through fractures in poroelastic media*, submitted.
PDF file
O. Al-Hinai, M. F. Wheeler, and I. Yotov,
* A generalized mimetic finite difference method and two-point flux schemes over Voronoi diagrams
*, submitted.
PDF file
M. Bukac, I. Yotov, and P. Zunino,
* An operator-splitting approach for the interaction between a fluid and a
multilayered poroelastic structure*, Numerical Methods for
Partial Differential Equations, 31 (2015), pp. 1054–1100.
PDF file
M. Bukac, I. Yotov, R. Zakerzadeh, and P. Zunino,
* Partitioning strategies for the interaction of a fluid with a
poroelastic material based on a Nitsche's coupling approach*, to
Computer Methods in Applied Mechanics and Engineering, 292 (2015), pp. 138-170.
PDF file
B. Ganis, K. Kumar, G. Pencheva, M. F. Wheeler, and I. Yotov,
* A multiscale mortar method and two-stage preconditioner for multiphase
flow using a global Jacobian approach*, In proceedings of the SPE Large
Scale Computing and Big Data Challenges in Reservoir Simulation Conference,
September 2014, Istanbul, Turkey. SPE 172990-MS.
PDF file
B. Ganis, K. Kumar, G. Pencheva, M. F. Wheeler, and I. Yotov,
* A global Jacobian
method for mortar discretizations of a fully-implicit two-phase flow model*,
Multiscale Modeling and Simulation, 12:4 (2014), pp. 1401-1423.
PDF file
D. Vassilev, C. Wang, and I. Yotov, * Domain decomposition for coupled
Stokes and Darcy flows*, Computer Methods in Applied Mechanics and
Engineering, 268 (2014), pp. 264-283.
PDF file
V. Girault, D. Vassilev, and I. Yotov,
* Mortar multiscale finite element methods for Stokes-Darcy flows*,
Numerische Mathematik 127 (2014), pp 93-165.
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A. Arraras, L. Portero, and I. Yotov, Error analysis of multipoint flux
domain decomposition methods for evolutionary diffusion problems, Journal of
Computational Physics, 257 (2014), pp. 1321-1351.
PDF file
K. Lipnikov, D. Vassilev and I. Yotov,
*Discontinuous Galerkin and Mimetic Finite Difference Methods for Coupled Stokes-Darcy Flows on Polygonal and Polyhedral Grids*,
Numerische Mathematik, 126 (2014), pp. 321-360.
PDF file
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.
PDF file
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.
PDF file
M. F. Wheeler, G. Xue, and I. Yotov,
* Coupling multipoint flux mixed finite element methods with continuous
Galerkin methods for poroelasticity*, Computational Geosciences,
18 (2014) pp. 57-75.
PDF file
B. Ganis, M. Juntunen, G. Pencheva, M. F. Wheeler,
and I. Yotov, * A global Jacobian method for mortar discretizations
of nonlinear porous media flows*, SIAM J. Scientific Computing,
36, (2014) pp. A522-A542.
PDF file
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.
PDF file

B. Ganis, G. Pencheva, M. F. Wheeler, T. Wildey, and I. Yotov,
* A Frozen Jacobian Multiscale Mortar Preconditioner for Nonlinear Interface Operators*, Multiscale Modeling and Simulation, 10:3 (2012) pp. 853-873.
PDF file
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.
PDF file

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.
PDF file
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.
PDF file
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.
PDF file
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.
PDF file
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.
PDF file
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.
PDF file
D. Vassilev and I. Yotov,
* Coupling Stokes-Darcy flow with transport*, SIAM J. Sci. Comp.,
31:5 (2009) 3661-3684.
PDF file
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.
PDF file
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.
PDF file
K. Lipnikov, M. Shashkov, and I. Yotov,
*Local flux mimetic finite difference methods*, Numerische Mathematik,
112:1 (2009), 115-152.
PDF file
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.
PDF file
I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M. F. Wheeler and I. Yotov,
*Convergence of a symmetric MPFA method on quadrilateral grids*,
Computational Geosciences 11 (2007) 333-345.
PDF file
T. Arbogast, G. Pencheva, M. F. Wheeler, and I. Yotov,
*A multiscale mortar mixed finite element method*,
Multiscale Modeling and Simulation, 6:1 (2007) 319-346.
PDF file
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.
PDF file
M. F. Wheeler and I. Yotov,
*A multipoint flux mixed finite element method*, SIAM J. Numer. Anal.
44:5 (2006) 2082-2106.
PDF file
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.
PDF file
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.
PDF file
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.
PDF file
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.
PDF file

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
PDF file

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.
PDF file

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.
PostScript file

M. F. Wheeler and I. Yotov,*
Physical and computational domain decompositions for modeling subsurface flows
* Contemporary Mathematics 218, American Mathematical Society (1998) 217-228.
PDF file

I. Yotov,*
Mortar mixed finite element methods on irregular multiblock domains,
* IMACS Series in Comp. Appl. Math. vol. 4 (1998) 239-244.
PDF file

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.
PDF file

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.
PDF file
### Selected Presentations

Parallel multiblock reservoir simulation