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.
abstract
PDF file
G. Pencheva and I. Yotov,
Interior superconvergence in mortar and non-mortar
mixed finite element methods on non-matching grids, submitted.
abstract
PDF file
K. Lipnikov, M. Shashkov, and I. Yotov,
Local flux mimetic finite difference methods,
submitted.
abstract
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.
abstract
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,
Comput. Geosci. 11 (2007) 333-345.
abstract
PDF file
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.
abstract
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.
abstract
PDF file
M. F. Wheeler and I. Yotov,
A multipoint flux mixed finite element method, SIAM J. Numer. Anal.
44:5 (2006) 2082-2106.
abstract
PDF file
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.
abstract
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.
abstract
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.
abstract
PDF file
B. Riviere and I. Yotov,
Locally Conservative Coupling of Stokes and Darcy Flows,
SIAM J. Numer. Anal. 42:5 (2005) 1959--1977.
abstract
PDF file
W. J. Layton, F. Schieweck, and I. Yotov,
Coupling fluid flow with porous media flow,
SIAM J. Numer. Anal. 40:6 (2003) 2195-2218.
abstract
PDF file
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.
abstract
PDF file
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.
abstract
PDF file
M. Peszynska, M. F. Wheeler, and I. Yotov,
Mortar upscaling for multiphase flow in porous media,
Computational Geosciences 6:1 (2002) 73-100.
abstract
PDF file
I. Yotov, A multilevel Newton-Krylov interface solver for
multiphysics couplings of flow in porous media,
Numer. Linear Algebra Appl. 8 (2001) 551--570.
abstract
PDF file
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.
abstract
PDF file
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.
abstract
PostScript 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
abstract
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.
abstract
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.
abstract
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.
abstract
PostScript file
I. Yotov,
Mortar mixed finite element methods on irregular multiblock domains,
IMACS Series in Comp. Appl. Math. vol. 4 (1998) 239--244.
abstract
PostScript 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.
abstract
PDF file
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.
abstract
PostScript file
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.
abstract
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.
abstract
PDF file
Selected Presentations
Parallel multiblock reservoir simulation