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Applied and Computational Mathematics Division

Information Technology Laboratory

National Institute of Standards and Technology (NIST)

US Department of Commerce

Computer Scientist, Mathematical Software Group

National Institute of Standards and Technology

100 Bureau Dr., Stop 8910

Gaithersburg, MD 20899-8910 USA

Email : william.mitchell@nist.gov

Phone : (301) 975-3808

FAX : (301) 975-3553

Ph.D. 1988, University of Illinois at Urbana-Champaign, Computer Science

M.S. 1983, Purdue University, Computer Science

B.S. 1977, M.S. 1978, Clarkson University, Mathematics

vitae (pdf 115K)

PHAML (Parallel Hierarchical Adaptive MultiLevel) is a parallel implementation (SPMD message passing) of the techniques used by MGGHAT. This program is written in Fortran 90 and uses MPI for message passing. PHAML is an active research project, but the current version of the software is available.

The development of new algorithms and computer codes for the solution of partial differential equations (PDEs) usually involves the use of proof-of-concept test problems. Such test problems have a variety of uses such as demonstrating that a new algorithm is effective, verifying that a new code is correct in the sense of achieving the theoretical order of convergence, and comparing the performance of different algorithms and codes. The purpose of this web resource is to provide a standard set of problems suitable for benchmarking and testing adaptive mesh refinement algorithms and error estimators. The problems exhibit a variety of types of singularities (e.g. point and line singularities on the boundary and in the interior), near singularities (e.g. sharp peaks, boundary layers, and wave fronts), and other difficulties.

There are many scientific computing codes on the web, whose comparison and interoperability are extremely difficult due to different installation requirements, different input and output formats, and functionalities. The goal of FEMhub is to make scientific computing easier for everyone by creating an open source distribution of many scientific computing codes enhanced with a unified Python interface. FEMhub is developed by an open source community around the hp-FEM group at the University of Nevada, Reno. It is available for download as a desktop application, but all codes are also available online in the Networked Computing Laboratory ( NCLab)

The Zoltan Dynamic Load-Balancing Library provides critical capability to a number of parallel applications. Zoltan includes a suite of algorithms for dynamically computing partitions of problems over sets of processors; geometric, tree-based and graph-based algorithms are included. Zoltan's object-oriented interface is easy-to-use and enables Zoltan to be used by a number of different applications. Zoltan is designed to be flexible and extensible, so different algorithms can be used, compared and added easily.

f90gl is a fortran interface for Mesa, a freely distributable 3D graphics library with an API which is very similar to that of OpenGL, and GLUT, a window system independent API toolkit for writing OpenGL programs. It provides both fortran 77 and fortran 90 interfaces, and can also be used with native OpenGL implementations.

StopWatch is a Fortran 90 module for portable, easy-to-use measurement of execution time of program segments. It supports multiple watches simultaneously, each with four clocks (total cpu, user cpu, system cpu, and wall clock). StopWatch is used by inserting subroutine calls into your source code, where the subroutine calls correspond to the buttons of a stop watch.

MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a Fortran program for the solution of second order two dimensional elliptic partial differential equations, using adaptive refinement of second, third, or fourth order elements, and multigrid solution techniques.

If you do not have the software to read the available formats, an alternate format or a paper copy of these documents will be mailed to you if requested from William Mitchell.

** How High a Degree is High Enough for High Order Finite Elements?**,
* Procedia Computer Science*, 15, 2015, pp. 246-255.
(preprint, pdf, 583K)
(
link to journal)
DOI 10.1016/j.procs.2015.05.235

** A Comparison of hp-Adaptive Strategies for Elliptic
Partial Differential Equations**, with M. A. McClain,

** A Collection of 2D Elliptic Problems for Testing Adaptive Grid
Refinement Algorithms**, * Applied Mathematics and
Computation*, 220, 2013, pp. 350-364.
(preprint, pdf, 9.8M)
(
link to journal)
DOI 10.1016/j.amc.2013.05.068

** Resonant Control of Polar Molecules in an Optical Lattice**,
with T. M. Hanna, E. Tiesinga and P. S. Julienne,
*Physical Review A,* 85 (2), 2012.
arXiv:1111.0227v1, 2011.
(link to journal)
DOI 10.1103/PhysRevA.85.022703

** A Comparison of hp-Adaptive Strategies for Elliptic
Partial Differential Equations (long version)**, with M. A. McClain,

** A Collection of 2D Elliptic Problems for Testing Adaptive
Algorithms**, * NISTIR 7668*, 2010.
( pdf, 1.6M)

** A Survey of hp-Adaptive Strategies for Elliptic Partial
Differential Equations**, with M. A. McClain, in Recent Advances
in Computational and Applied Mathematics (T. E. Simos, ed.), Springer,
2011, pp. 227-258.
(preprint, pdf, 16M)

** The hp-Multigrid Method Applied to hp-Adaptive
Refinement of Triangular Grids**,

** Review of "Understanding and Implementing the Finite
Element Method" by Mark S. Gockenbach**, * SIAM Review, *
49 (3), 2007, pp. 532-533.
(preprint, pdf, 69K)

** A Refinement-tree Based Partitioning Method for Dynamic Load
Balancing with Adaptively Refined Grids**, * J. Par. Dist.
Comput., * 67 (4), 2007, pp. 417-429.
(preprint, pdf, 2.5M)
( link to journal )

** Effective-range Description of a Bose Gas Under Strong One- or
Two-dimensional Confinement**, with P. Naidon, E. Tiesinga and
P. Julienne, * New Journal of Physics * 9 (2007) 19.
(
link to journal )

** PHAML User's Guide**, * NISTIR 7374 *, 2006.
(original, pdf, 3.2M )
(latest revision, pdf)

** Adaptive Grid Refinement For a Model of Two Confined and Interacting
Atoms**, with E. Tiesinga, * Applied Numerical Mathematics *,
52, (2005), pp. 235-250.
( gzipped postscript, 233k)

** Hamiltonian Paths Through Two- and Three-Dimensional Grids**,
* NIST J. Res. *, 110, (2005), pp. 127-136.
( gzipped postscript, 79k)

** Parallel Adaptive Multilevel Methods with Full Domain Partitions**,
* App. Num. Anal. and Comp. Math.*, 1, (2004), pp. 36-48.
( gzipped postscript, 286k)

** The Design of a Parallel Adaptive Multi-Level Code in Fortran 90**,
*Proceedings of the 2002 International Conference on Computational
Science*, 2002.
( gzipped postscript, 50k)

** The Full Domain Partition Approach to Parallel Adaptive Refinement**,
* Grid Generation and Adaptive Algorithms*,
* IMA Volumes in Mathematics and its Applications*, 113,
Springer-Verlag, 1998, pp. 151-162.
( gzipped postscript, 138k)

** A Parallel Multigrid Method Using the Full Domain Partition**,
* Electronic Transactions on Numerical Analysis*, 6 (1998)
pp. 224-233, special issue for proceedings of the 8th Copper Mountain
Conference on Multigrid Methods.
( gzipped postscript, 95k)

**The Full Domain Partition Approach to Distributing
Adaptive Grids**, *Applied Numerical Mathematics*, 26 (1998)
pp. 265-275, special issue for proceedings of Grid Adaptation in
Computational PDEs: Theory and Applications.
(gzipped postscript, 102k)

** A Fortran 90 Interface for OpenGL: Revised January 1998**,
NISTIR 6134, 1998.
( gzipped postscript, 45k)

** StopWatch User's Guide Version 1.0**, NISTIR 5971, 1997.
(html)
(gzipped postscript, 78k)

**MGGHAT User's Guide Version 1.1**, NISTIR 5948, 1997.
(html)
(postscript)

**Optimal multilevel iterative methods for adaptive
grids**, *SIAM J. Sci. Statist. Comput.* 13 (1992),
pp. 146-167.

**Adaptive refinement for arbitrary finite element
spaces with hierarchical bases**, *J. Comp. Appl. Math.* 36
(1991), pp. 65-78.

**A comparison of adaptive refinement techniques
for elliptic problems**. *ACM Trans. Math. Soft.* 15 (1989),
pp. 326-347.

**Unified multilevel adaptive finite element
methods for elliptic problems**, Ph.D. thesis, Technical report
UIUCDCS-R-88-1436, Department of Computer Science, University
of Illinois, Urbana, IL, 1988.
(
gzipped postscript, 194k)
(pdf, 260K)

**Collocation software
for second-order elliptic partial differential equations**.
*ACM Trans. Math. Soft.* 11 (1985), pp. 379-412.
(with E.N. Houstis and J.R. Rice)

Look for me at the following conferences:

Last change to this page: September 30, 2015

Date this page created: 1994

Contact: William Mitchell