Hello World!

William Layton

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. I've worked in a number of scientific areas, authoring more than 100 refereed publications.

Scientific Interests:
Click for some papers by area.
Fluid Mechanics: Turbulence, Natural Convection, Large Eddy Simulation,
Numerial Analysis of Hyperbolic Systems and Elliptic-Hyperbolic Singular Perturbation Problems,
Long time behavior of reduced order models and numerical methods,
Modeling Aluminum Reduction Cells,
Parallel and Adaptive Algorithms, Multi-Level Newton Methods,
Applied Nonlinear Analysis: PDEs, ODEs, Functional Differential Equations, Almost Periodic Functions,

My Current Interests Include:
*Variational Methods ( FEM, Spectral...) -especially for flow problems
*Large Eddy Simulation - LES reports.
*Adaptive and parallel algorithms.
*Long Time Behavior of Numerical Methods. Click for LTB.

In all these areas, one common theme is:
Mathematical analysis as a guide to practical computation.

Books:
Mathematics of Large Eddy Simulation of Turbulent Flows
Springer Verlag: Series: Scientific Computation
L. C. Berselli, T. Iliescu, W. Layton
2005, Approx. 345 p., Hardcover
ISBN: 3-540-26316-0
Click Here for More Information.

My second book is out:
Introduction to Finite Element Methods for Incompressible, Viscous Flows,
W. Layton,
SIAM publications, 2008 / xx + 213 pages / Softcover / ISBN: 978-0-898716-57-3
Click Here for More Information.

Editorial Boards:
Journal Mathematical Analysis and Applications (JMAA),
Numerical Linear Algebra and Applications (NLAA) ,
SIAM Journal on Numerical Analysis (SINUM),
Advances in Numerical Analysis (ANA).



The Computational Mathematics Research Training Group:

Research Training Group in Computational Mathematics Read this if you are interested in grad school!!.

Computational Math RTG seminar annoucements
"How to give a 20 minute talk"



Large Eddy Simulation:
Here is a page with some LES reports to download.
There's also a wordy description of some of our work on turbulent flow
calculations here.


Teaching Resources, Class Home Pages and the Like:
Here's information about our NEW SCIENTIFIC COMPUTING major!
"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.

My Fantastic Students:

IN PROGRESS:



*A. Labovschii,
PhD 2008: Multiscale Computational Fluid Dynamics, Turbulence and Applications
ayl2@pitt.edu

Alex is currently a postdoc at the Universty of Misssouri
Alex's web page.
Report in preparation:
1. A. Labovschii,
A Defect Correction Method for the Time-Dependent Navier-Stokes Equations,
(to appear in Numerical Methods for Partial Differential Equations).pdf

2. A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz,
The Stabilized, Extrapolated Trapezoidal Finite Element Method for the Navier-Stokes Equations,
submitted to Theoretical and Computational Fluid Dynamics, 2007.pdf

3. N. Heitmann, A. Labovschii,
Numerical Analysis of a Method for High Peclet Number Transport in Porous Media,
to appear JMAA, 2007.

4. A. Labovschii,
A Defect Correction Method for the Evolutionary Convection Diffusion Problem with Increased Time Accuracy,
submitted to Computational Methods in Applied Mathematics, 2007.pdf

5. A. Labovschii, C. Trenchea,
Large Eddy Simulations for the MHD Flows,
submitted, 2007.

6. A. Labovschii, C. Trenchea,
A family of Approximate Deconvolution Models for MagnetoHydroDynamic Turbulence,
submitted, Technical report 2007.pdf
Conference Proceedings
7. A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz, I. Stanculescu, C. Trenchea,
Mathematical Architecture of Approximate Deconvolution Models of Turbulence,
invited presentation at Quality and Reliability of Large-Eddy Simulations 2007.
(to be published by Springer as part of the ERCOFTAC Series, with book title
"Quality and Reliability of Large-Eddy Simulations.")

Work in Preparation
8. A.Labovschii, C. Trenchea,
Identification of Averaging Radii for the LES in MHD Flows.

9. A.Labovschii, C. Trenchea,
LES models for compressible Navier-Stokes equations.

*Jeff Connor,
PhD Thesis Area: Multiscale Computational Fluid Dynamics, Turbulence and Application to uncoupling Ocean--Atmosphere models
Jeff is a third year PhD student who has written 3 papers so far.
Jeff passed his PhD prelims before even entering our program and without taking our prelim courses.
Jeff's web page.

1. J Connors,
"Convergence analysis and computational testing of the finite element discretization of the Navier-Stokes-alpha model",
submitted to NMPDEs, 2009.

2. J Connors, J Howell and W Layton
"Partitioned time stepping methods for a parabolic two-domain problem",
In Review: SIAM Journal on Numerical Analysis, 2008.

3. J Connors and W Layton,,
"On the accuracy of the finite element method plus time relaxation",
in review after submitting revised draft from reviewer comments, Math. of Computation, 2008.

Conference Research Talks
"Partitioned time stepping algorithms for a parabolic problem on two subdomains" ,
SIAM CSE09, Miami, FL, Coming up March '09!

"Partitioned time stepping methods providing stable decoupling of heat equations on two subdomains" ,
RSV80 Conference in honor of Richard S. Varga's 80th birthday, Kent State Univ., Oct. 17, 2008.

"Convergence of NS-alpha model finite element discretizations",
SIMUMAT Summer School on Fluid Dynamics, Control and Optimization,
CIEM, Castro Urdiales, Cantabria, Spain, July 7, 2008. SIMUMAT '08

*Alex Lozovskiy, avl4@pitt.edu, Ty 604
PhD Thesis Area: Prediction and modelling of the noise generated by turbulence
Alex is beginning research on noise generation by turbulent flows
and prediction.

*Nate Mays,
PhD Thesis Area:
Nate is beginning research on some high accuracy methods for ill-posed problems and applications.
Nate's Papers (so far):
1. Ingram, R.N., Layton, W.J., Mays, N.
"Iterated Tikhonov Regularization for Ill-Posed Problems"
(Rev 0, submitted for publication, email to request update)


*Ross Ingram,
PhD Thesis Area:
Ross' interests are in numerical analysis , large scale computing and applications.

Ross' web page.
He is beginning research on 3 applications:
1. Flow of fluid in the eye and Glaucoma,
2. Models and simulatoion of pellet fusion reactors,
3. Optimization of wind turbiune placement.

Ross' Papers (so far):
1. Ingram, R.N., Layton, W.J., Mays, N.
"Iterated Tikhonov Regularization for Ill-Posed Problems"
(Rev 0, submitted for publication, email me to request update)

2. Ingram, R.N., Lewis, A.S., Tutwiler, R.L.,
"An automatic nonlinear correlation approach for processing of hyperspectral images,
"International Journal of Remote Sensing, Vol. 25, Number 22, 2004, 4981-4998(18).

Presentations
" Sensitivity Relation in an Iterated Tikhonov Regularization Scheme ,"
Varga Conference, Kent State University, Oct. 18, 2008.

Completed:

* A. Sunmonu, Ph.D. 1992, "Numerical Analysis of Nonlinear Models of Electrically and Thermally Conducting Materials"
Currently: Tenured Associate Professor, Department of Mathematics and Computer Science,
City University of New York- York
A.Sunmonu's web page.

* F.Fairag, Ph.D., 1998, "A two-level discretization method for the stream-function form of the Navier-Stokes equations"
Tenure Track Assistant Professor,
Department of Mathematics, King Fahd University of Petroulem and Minerals
F.Fairag's web page.

*D.C.O'Neal, Certificate in Scientific Computing, 1990,
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.

* A. Liakos,
Ph.D., 1999: " Weak Imposition of boundary conditions in the Navier Stokes equations"
Tenured Associate Professor, Department of Mathematics,
U.S. Naval Academy, Annapolis
Previously:
Second place in 1998 SIAM Student Research Paper Competition
 Postdoc: Center for Fibers and Films, Clemson University
E-mail: liakos@usna.edu
Tas Liakos' web page.

* Traian Iliescu,
Ph.D., 2000: "Numerical Analysis of Large Eddy Simulation"
currently:
Tenured Associate Professor, Mathematics Department,
Virginia Polytechnic University.
previously:
Culver Prize, Department of Mathematics, University of Pittsburgh
Mellon Predoctoral Fellow, University of Pittsburgh
First prize: 1999 SIAM Student Research Paper Competition
2000 Wilkinson Fellow, Argonne National Labs,
T. Iliescu's web page.
E-mail: iliescu@math.vt.edu

*Melanie Fitzgerald, M.S. 2000, thesis: Large Eddy Motion in Shallow Water and Estuaries,
M. Fitzgerald's web page.

* Huasin Al-Attas,
Ph.D. 2002: Reliability of Porous Media Flow and Parallel Sensitivity Computation,
Tenure Track Assistant Professor of Mathematics, King Fahd University of Petroleum and Minerals
E-mail:
huast1+@pitt.edu

* Atife Caglar,
Ph.D. 2002: "Reliable finite element simulation of boundary driven turbulence",
Honorable Mention: 2002 SIAM Student Research Paper Competition
 Mathematics of Information Technology and Complex Systems Postdoctoral Research Fellowship
Department of Mathematics, University of British Columbia
Currently: Tenure Track Assistant Professor,
Department of Mathematics, University of Wisconsin-Green Bay
E-mail:
caglara@uwgb.edu
A. Caglar's web page.

*Noel Heitmann,
 Ph.D. 2003: " Subgrid Stabilization of Evolutionary Diffusive Transport Problems" ,
Currently: Tenure Track Assistant Professor, Millersville State University
E-mail:
email Noel Heitmann's web page.

* Niyazi Sahin,
Ph.D. 2003: "Derivation, Analysis and Testing of New Near Wall Models for Large Eddy Simulation",
Honorable Mention: 2000 SIAM Student Reserarch Paper Competition,
 Tenure Track Assistant Professor,
Mathematics Department, Mugla University,
nisa6971@hotmail.com,

*Faranak Pahlevani,
(co-advisor: M. Anitescu) PhD 2004: "Sensitivity Analysis of Eddy Viscosity Models"
Postdoctoral Researcher,
Montana State University, Department of Mathematical Sciences and currently:
tenure track assistant professor,
CUNY

* Adrian Dunca,
PhD 2004: Space Averaged Navier Stokes Equations in the Presence of Walls
Postdoc, Department of Mathematics, University of Michigan, 2004-2006.

*Songul Kaya-Merdan, (co--advisor: B. Riviere) PhD 2004:
"Numerical Analysis of a Variational Multiscale Method for Turbulence",
Currently: Tenured Associate Professor
Middle East Technical University
previously:
Winner of the 2004 HALES DISTINGUISHED RESEARCH AWARD for the Best Doctoral Dissertation.
2003-2004 Andrew Mellon PreDoctoral Fellow
Songul's web page.
2004-2005: Visiting Assistant Professor, Illinois Institute of Technology.


*Carolina Cardoso Manica,
PhD August 2006: Numerical Methods in Turbulence
 Postdoc: Department of Mathematics, University of Pittsburgh,
and starting fall 2007:

Assistant Professor,
Federal University of Rio Grande do Sul,
Porto Alegre-RS- Brazil
previously:
First Place: 2005 SIAM Student Research Paper Competition
Mellon predoctoral fellow, 2005-2006
Culver Prize, 2006
Carolina's web page.
E-mail:
cac15@pitt.edu

*Patricia Butler,
MS in Mathematics August 2006
MS thesis: Calculating functionals of solutions of large sparse systems
Currently: Algebra specialist, Davis schools , California

*Leo Rebholz,
PhD December 2006: Helicity and physical fidelity in models and algorithms
2006-2008: Staff Scientist, Bettis Laboratory
and Fall 2008 - present: Tenure Track Assistant Professor,
Department of Mathematical Sciences,
Clemson University.
previously:
Culver Prize, 2006
 Leo's webpage.

*Sara Marashinia,
MS in Mathematics August 2007
MS thesis: Analysis of Bernoulli's equation in LES turbulence models


*Gary Hart,
(co--advisor, primary advisor: Mihai Anitescu)
PhD 2007: A Constrained-Stabilized Time-Stepping Approach for Piecewise Smooth Multibody Dynamics
Currently:
Assistant Professor,
University of Pittsburgh at Greensburg
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.


*Monika Neda,
PhD August 2007: Numerical analysis of homogeneous isotropic turbulence
generated by higher order models of turbulence
As of fall 2007:
Tenure track Assistant Professor,
University of Nevada Las Vegas
Another Research Award:
Monika Neda's 30 minute research talk: "Time relaxation for turbulent flow problems"
won one of 6 awards (which included a cash prize) for:
The Most Outstanding Research Presentation by a PhD student
at the Joint Meeting Southeastern Section MAA & SIAM Southeast Atlantic Section, March 31 - April 1, 2006.
Mellon predoctoral fellow, 2006-2007

. Monika's web page.

*I. Stanculescu,
PhD 2008: Iuliana derived, tested and performed a complete numerical analysis
of "optimal" Approximate De-Convolution Models of turbulence.

Iuliana is an assistant professor at Nova Southeastern University in Ft Lauderdale Fl.
Iuliana's web page.

* Kristen Harnett, M.S. 2008, thesis: On duality and the bi-conjugate gradient method,

Updated 12/08.


Other Scientific Intrests:
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:

*Parallel Algorithms for Highly Nonsymmetric Problems
-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.



*Finite Element Methods for Natural Convection Problems
Here is a page which lists a few reports in natural convection problems.

* Nonlinear Analysis Applied to Ordinary and Partial Differential Equations

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

* Finite Difference Methods and FEM's for Hyperbolic Systems and Elliptic-Hyperbolic
Singular Perturbation Problems
Here is a page which lists some reports on FEM's and FDM's for this topic.

* Multi-Level Newton Methods
I have done some work developing these ideas for fluid flow problems.

* Modelling and Simulation of Aluminum Reduction Cells

*Numerical Linear Algebra


More pictures.
I like turbulence!



Miscellaneous Math Stuff:

Here are some math related links.
Pitt's Math Department
Quotes to see some quotes about mathematics.
"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:

wjl@pitt.edu