Department of Mathematics, University of Pittsburgh

Pittsburgh, PA 15260 , U.S.A.

My email address is: wjl@pitt.edu

phone: (412)624-8312/Math Office:(412)624-8375

I am a full professor in Pitt's math department. My research is mainly in numerical analysis.

Numerical analysis is one of the broadest areas of mathematics as it includes convergence

questions of analysis, including new convergence issues related to the rate of convergence,

problems of mechanics, nonlinear PDEs and applications across the spectrum of mathematics to graph theory.

I've worked in all these areas and a number of others too, authoring more than

160-odd refereed publications, 1 undergrad text, 1 grad text and 2 research monographs.

Through all this variety I have had an

abiding fascination with the deep mathematics of fluid motion,

which, paraphrasing, is an area of mathematics in which

" a gnat may bathe and an elephant may drown."

I've had 30 or so PhD students almost all of whom are active and accomplished researchers.

My PhD students now direct PhD students who are themselves doing very well.

I've directed a number of MS students who wrote excellent theses and I've advised undergrad researchers who did terrific work and moved forward to great things.

Outside of mathematics my other interests have been quite varied.

I was chess champion of Georgia in 1976 and played various sports over time. I am currently an avid mid-level

whitewater kayaker. I get many mathematical ideas from observations of turbulent flows in nature!

My current and

Nan Jiang

A Few of my most recent PhDs (& placements):

I also have had a number of PhD students visiting from other countries and other advisors:

(a partial list of recent ones)

These visits to our academic family here have been happy and productive!

some older papers.

*New Models and Algorithms for Complex Turbulence

This project involves developing models with a rigorous mathematical foundation

as well as numerical analysis of new methods for their solution.

Ensemble simulations are necessary for extending forecast skill,

dealing with errors from unknown data and parameterizations and

estimating sensitivities. However, they lead to the inevitable conflict

of high resolution single realizations and computing ensembles.

We have new methods breaking this deadlock. The new methods lead

to new models as well since ensemble data gives a simple

and calculable way to specify, WITHOUT MODELLING, the TKE.

We have also developed a NEW MIXING LENGTH which seems to

correct the inadequacies of standard mixing length theories.

* Partitioned time stepping methods for coupled, multi domain & physics:

Atmosphere-Ocean coupling in climate models,

multi-physics coupling, e.g., NSE & Maxwells eqns in MHD,

Fully evolutionary Stokes-Darcy-Biot coupling.

*Large Eddy Simulation

including VMS methods, Nonlinear filters, Approximate deconvolution models.

We are interested in improving current approaches, developing new ones and

and studying the interplay between numerical and modelling errors in turbulence.

This is a new collaboration including Alexandros Labrinidis, Peyman Givi,

Panos Chrysanthis and Patrick Pisciuneri.

*Algorithms for Flow in complex pebble bed geometries

I work on these to let undergrads get involved in research on

turbulent flows. There are a lot of interesting conjectures that can be

interrogated via shell and ET Models.

My personal preference is to work on problems

where mathematics can make a difference in extending

the boundary of what is predictable rather than perfecting

a theory where the main outlines are already known.

(There is nothing wrong in the latter. Math is hard enough that

progress will only be possible when we all work on whatever is

closest to our own hearts.)

In all these areas, one common theme is:

Mathematics of Large Eddy Simulation of Turbulent Flows

Springer Verlag: Series: Scientific Computation

L. C. Berselli, T. Iliescu, W. Layton

2005, ISBN: 3-540-26316-0

Click Here for More Information.

W. Layton, SIAM publications, 2008 / ISBN: 978-0-898716-57-3

Click Here for More Information.

W. Layton and L. Rebholz, Springer Lecture Notes in Math, V. 2042, 2012.

W Layton and M Sussman, Lulu press, ISBN 9781312329850, 2014.

( 20$ printed and free as a pdf file. This is what is within our power to address the cost of college

and the result of 30 years teaching and polishing.

ETNA,

Journal Mathematical Analysis and Applications (JMAA),

Numerical Linear Algebra and Applications (NLAA), inception to 2009,

SIAM Journal on Numerical Analysis (SINUM),

Advances in Numerical Analysis (ANA).

"How to give a 20 minute talk"

Resources for Math 1080-Numerical Linear Algebra.

Resources for Math 1070-Numerical Analysis.

Resources for Math 1360-Mathematical Modeling.

Resources for Math 2070-the Gateway course in Computational Mathematics.

Resources for Math 1470-the undergraduate PDE course.

aelabovs@mtu.edu

tenure track assistant professor position at Michigan Technological University.

Michigan Tech is a mid-sized math department with a strong PhD program in applied math.

Jeff completed his PhD in 4 years and wrote one of the most consequential PhD theses of our department.

Jeff was a postdoc at LLNL and is now a tenure track Asst. Prof at U Conn, Avery Point.

Prediction and modelling of the noise generated by turbulence

Alex completed a postdoc in France in computational mechanics and now works at Moscow State University.

High accuracy methods for ill-posed

problems and applications to an biomedical parameter identification problem with diagnostic implications.

Ross' web page. Ross is a leader in an industrial research group at Bettis since fall 2011.

Aziz will start a postdoc Fall, 2014 at Texas A&M University.

Hoang is a postdoc at ORNL working on UQ for turbulent flows.

Asst Prof, Middlebury College

* Nick Hurl

MS 2010, Phenomenology and Computations of a Regularization of the Navier-Stokes equations related to a

Non-Newtonian fluid model, currently: Scientific Analyst, UPMC.

Currently: Full Professor, Department of Mathematics and Computer Science,

City University of New York- York

A.Sunmonu's web page.

Tenure Track Assistant Professor,

Department of Mathematics, King Fahd University of Petroulem and Minerals

F.Fairag's web page.

Certificate project: "Optimization of Finite Element Codes"

currently: Senior Scientific Specialist, Application Development and Technical Support

Pittsburgh Supercomputing Center

Dave O'Neal's web page.

Tenured Associate Professor, Department of Mathematics,

U.S. Naval Academy, Annapolis

Previously:

E-mail: liakos@usna.edu

Tas Liakos' web page.

currently:

Full Professor, Mathematics Department,

Virginia Polytechnic University.

previously:

Mellon Predoctoral Fellow, University of Pittsburgh

First prize: 1999 SIAM Student Research Paper Competition

E-mail: iliescu@math.vt.edu

M. Fitzgerald's web page.

Tenure Track Assistant Professor of Mathematics, King Fahd University of Petroleum and Minerals

E-mail: huast1+@pitt.edu

* Atife Caglar,

Department of Mathematics, University of British Columbia

Currently: Tenured Associate Professor,

Department of Mathematics, University of Wisconsin-Green Bay

E-mail: caglara@uwgb.edu

A. Caglar's web page.

Currently: Tenured Associate Professor, Millersville State University

E-mail: email Noel Heitmann's web page.

Mathematics Department, Mugla University,

nisa6971@hotmail.com,

Postdoctoral Researcher,

Montana State University, Department of Mathematical Sciences and currently:

tenure track assistant professor, PSU Albington

Postdoc, Department of Mathematics, University of Michigan, 2004-2006,

Currently: Math Dept, Univ. Bucharest

Currently: Tenured Associate Professor

Middle East Technical University

previously:

Winner of the

2003-2004 Andrew Mellon PreDoctoral Fellow

Songul's web page.

Federal University of Rio Grande do Sul,

Porto Alegre-RS- Brazil

previously:

Mellon predoctoral fellow, 2005-2006 and Culver Prize, 2006

E-mail: cac15@pitt.edu

MS in Mathematics August 2006

MS thesis: Calculating functionals of solutions of large sparse systems

Currently: Algebra specialist, Davis schools , California

Department of Mathematical Sciences, Clemson University.

previously:

Culver Prize, 2006

PhD 2007:

Some papers:

[1] M. Anitescu, and G. Hart. Solving nonconvex problems of multibody dynamics with contact and small

friction by sequential convex relaxation.

To appear in: Mechanics of Machines and Structures.2003.

[2] M. Anitescu and G.Hart, A constraint-stabilized time-stepping approach for rigid multibody

dynamics with joints, contact and friction.

Preprint ANL/MCS-1002-1002. Submitted to International Journal for

Numerical Methods in Engineering.

[3] M. Anitescu and G. Hart. A Fixed-Point Iteration Approach for Multibody Dynamics with Contact and Small Friction.

Preprint ANL/MCS-P985-0802. To appear in Mathematical Programming Series B.,2003.

[4] M. Anitescu, A. Miller and G. Hart. Constraint stabilization for time-stepping approaches for rigid multibody dynamics with joints, contact and friction.

Preprint ANL/MCS-P1023-0203. To appear in the Proceedings of the Annual

Conference of the American Society of Mechanical Engineers, 2003.

[5] G. Hart and Mihai Anitescu. A hard constraint time-stepping approach for multibody dynamics with contact and friction.

To appear in the Proceedings of the Tapia Conference for Diversity in Computing, 2003.

Associate Professor, University of Nevada Las Vegas

Monika Neda's 30 minute research talk:

won one of 6 awards (which included a cash prize) for:

at the Joint MAA & SIAM Southeast Atlantic Section Meeting, 2006.

. Monika's web page.

Iuliana is an assistant professor at Nova Southeastern University in Ft Lauderdale Fl.

Iuliana's web page.

Updated 12/08.

I've worked in several related areas and I still have research interests

in these areas. In no particular order, some of these other areas

in which I've written a few papers include:

-we have developed massively data parallel algorithms for solving linear and nonlinear systems

arising from convection dominated phenomena. We have in particular

developed an element wise data parallel solution method which is proven

to converge uniformly in the Peclet number.

Here is a page which lists a few reports on data parallel domain decomposition algorithms.

Here is a page which lists a few reports in natural convection problems.

Here is a page which lists a few reports in nonlinear analysis.

Singular Perturbation Problems

Here is a page which lists some reports on FEM's and FDM's for this topic.

I have done some work developing these ideas for fluid flow problems.

More pictures.

Pitt's Math Department

Quotes to see

"How to give a 20 minute talk"

Let me know if you found something of interest
here so I'll know to work more on these pages.

E-mail me: