Applied and Computational Mathematics

Mathematics

For more information visit Personal Homepage
Email: plechac at math.utk.edu

My current research interests include

numerical analysis, computational methods for solving PDEs, multiresolution analysis and
numerical algorithms, numerical methods for high-dimensional problems.
multiscale computations and algorithms, applied stochastic analysis, Monte Carlo methods
and sampling algorithms, coarse-graining menthods, statistical mechanics.
computational methods in materials science, complex fluids and polymers.
analysis of large data sets, parallel computing.

Additional publications, including preprints in PDF and Postscript format, are available at
Preprints.

Numerical and statistical methods for the coarse-graining of many-particle stochastic systems.
to appear in J. Sci. Comp. (2008), (with M.A. Katsoulakis, and L. Rey-Bellet)
(preprint)
Mathematical strategies in the coarse-graining of extensive systems:
error quantification and adaptivity.
J. Non-Newtonian Fluid Mech., in press, available on-line 21 May, (2007)
(with M.A. Katsoulakis, L. Rey-Bellet and D. Tsagkarogiannos)
Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems.
ESAIM Math. Meth. Anal. Numer., 47, 627-660, (2007)
(with M.A. Katsoulakis, L. Rey-Bellet and D. Tsagkarogiannos)
(preprint)
Error analysis of coarse-graining for stochastic lattice dynamics.
SIAM J. Numer. Analysis, 2270-2296, (2006)
(with M.A. Katsoulakis and A. Sopasakis),
(SIAM reprint)
On self-similar singular solutions of the complex Ginzburg-Landau equation.
Comm. Pure and Appl. Math., 54, 1215-1242, (2001),
(with V. Sverak), (preprint)
On functional separately convex hulls.
Discrete Comput. Geom. , 19, No.1, 105-130 (1998),
(with J. Matousek)
Numerical solution of the scalar double-well problem allowing microstructure.
Math. Comput., 66, No.219, 997-1026 (1997), (with C. Carstensen)