December, 2015

**STEPHEN F. McCORMICK**

Professor Emeritus

Department of Applied Mathematics

526 UCB

University of Colorado at Boulder

Boulder, CO 80309-0526

http://amath.colorado.edu/appm/faculty/stevem/

stevem@colorado.edu

**EDUCATION**

San Diego State College: B.A. with honors in Spring, l966. Phi Kappa Phi, Blue Key, Wilma Tyler Trott Scholarship, and Outstanding Senior Student Award.

University of Southern
California: Ph.D. in Spring, l971. Hughes Master Fellowship, NSF Traineeship,
and Teaching Assistantship. Thesis advisor: E. K. Blum. Thesis Title: *A General Approach to One-Step Iterative
Methods with Application to Eigenvalue Problems*

**SOCIETY MEMBERSHIPS**

ACM, AIAA, IEEE, SIAM, Sigma Xi, SIGNUM

**PROFESSIONAL EXPERIENCE**

9/66-1/69 Hughes Aircraft Company. Member of the technical staff for the Data Reduction Section, Surveyor Spacecraft Project.

1/69-6/70 University of Southern California. Teaching assistant.

8/70-9/73 Institute for Educational Computing, Claremont Colleges. Assistant to the Director.

9/70-6/72 Pomona College. Assistant Professor of Mathematics.

7/72-7/74 NSF Principal
Investigator. Project title: *A numerical
investigation of iterative methods for the solution of the linear eigenvalue
problem,* grant no. GJ 34737.

9/73-12/83 Colorado State University. Assistant (1973), Associate (1977), and Full (1981) Professor of Mathematics.

5/74-4/76 NSF Principal
Investigator. Project title: *A numerical
investigation of one-step iterative methods for the solution of nonlinear
equations*, grant no. GJ 42626.

9/74-6/80 Solar Environmental Engineering Company. Partner and Director of Computing.

3/75-2/77 NSF Associate
Investigator. Project title: *Information
processing for optimization of energy utilization in structures*, grant no.
DCR 75-03578.

6/76-6/78 NSF Principal
Investigator. Project title: *A numerical
investigation of iterative methods for solving linear and nonlinear equations*,
grant no. MSC 76-09215.

6/76-6/78 AFOSR Principal
Investigator. Project title: *An
investigation of numerical methods for the sparse generalized eigenvalue
problem*, grant no. AFOSR-76-3019.

9/76-9/78 NSF Research
Associate. Project title: *Efficient
software for elementary function evaluation on microprocessors*, grant no.
MCS 76-12457.

8/77-9/77 Organizer and
Program Chairman for the *1st Rocky
Mountain Symposium on Microcomputers: Systems, Software, Architecture*. Fort
Collins, Colorado. Funded by NSF, AFOSR, ARO and ONR.

2/78-3/78 Organizer and
Conference Co-chairman for the *2nd Rocky
Mountain Symposium on Microcomputers: Systems, Software, Architecture*. Fort
Collins, Colorado. Funded by AFOSR, ARO, and ONR.

9/77-9/78 Organizer and President of SIGNUM Rocky Mountain Chapter.

6/78-6/80 AFOSR Principal
Investigator. Project title: *A numerical
investigation of iterative techniques for solving eigenproblems and nonlinear
boundary value problems*, grant no. AFOSR-76-3019.

10/78-9/80 NSF Principal Investigator.
Project title: *A numerical investigation
of iterative techniques for solving eigenproblems and nonlinear boundary value
problems*, grant no. MCS 78-03847.

8/79-7/81 Lawrence Livermore Laboratory Consultant.

3/80-9/80 Battelle/ARO Consultant.

7/80-7/81 AFOSR Principal
Investigator. Project title: *An
investigation of numerical techniques for nonlinear boundary value and
eigenvalue problems*, grant no. AFOSR-80-0201.

10/80-9/82 NSF Principal Investigator.
Project title: *A numerical investigation
of surface mesh refinement techniques*, grant no. MCS 80-17056.

1/81-1/92 *Multigrid Newsletter* Founder and Editor.

3/81-2/82 National Center for Atmospheric Research. Consultant.

7/81-7/82 AFOSR Principal
Investigator. Project title: *Multigrid
methods for nonlinear problems*, grant no. AFOSR-F-81-090.

7/81-8/81 Lawrence Livermore Laboratory. Summer Hire.

8/10-1/81 *Multigrid Short Course* Organizer and Lecturer. Lockheed Palo Alto
Research Center, Palo Alto, CA.

1/82-6/84 Institute for Computational Studies. Research Scientist.

6/82-12/84 AFOSR Principal Investigator.
Project title: *Multigrid methods for
nonlinear problems*, contract no. AFOSR-F33615-82-3210.

7/82-8/85 National Bureau of Standards. Consultant.

4/83 Organizer
and Chairman of the *1st Copper Mountain
Multigrid Conference*, Copper Mountain, CO. Funded by AFOSR, NASA, and GMD.

6/83-8/83 Gesellschaft fŸr Mathematik und Datenverarbeitung. Visiting Scientist.

7/83 Editor,
Proceedings of the *1st Copper Mountain
Multigrid Conference*, AMC Special Issue.

8/83-9/91 Colorado Research and Development Corporation. Research Scientist, Treasurer, and Member of the Board.

11/83-2/92 Associate Editor, Applied Mathematics and Computation.

1/84-1/86 NASA Langley
Principal Investigator. Project title: *Algebraic
multigrid applied to finite elements with application to structural analysis
and elasticity problems*, grant no. NAS-1-453.

5/84-2/92 Los Alamos National Laboratory. Consultant.

6/84-12/84 Mobil Oil Research Corp.
Principal Investigator. Project title: *AMG
applied to oil reservoir simulation*.

8/84-8/93 University of Colorado at Denver. Professor of Mathematics.

10/84-4/87 DOE Principal Investigator.
Project title: *Fast adaptive composite
grid methods for high performance computer systems*, grant no.
DE-ACD3-84ER80155, Phases I and II.

1/85-1/87 Project with Veritas Research, Oslo. AMG in structures.

2/85-2/86 AFOSR Principal
Investigator. Project title: *Algebraic
multigrid and the fast adaptive composite grid method in large-scale
computation*, grant no. AFOSR-85-0118.

5/85 Organizer
and Chairman of the *2nd Copper Mountain
Multigrid Conference*, Copper Mountain, CO. Funded by AFOSR, NASA, and GMD.

9/85 Editor,
Proceedings of the *2nd Copper Mountain
Multigrid Conference*, AMC Special Issue.

Fall/85 Founded the Computational Mathematics Group at CU-Denver. Obtained support from the University Office of Space Science and Technology, the College of Liberal Arts and Sciences, the Computer Center, and CRDC, including funds for operation, peripheral computer equipment, work-stations, and an Intel PSC Hypercube multicomputer.

3/86 Editor, SIAM Frontier Series in Applied Mathematics, Vol. V. on Multigrid Methods, SIAM, Philadelphia, 1987, pp. 1-282.

5/86-9/95 AFOSR Principal
Investigator. Original title: *Algebraic
multigrid and the fast adaptive composite grid method in large-scale
computation*. Current title: *Multilevel
methods in large-scale computation*. Grant nos. AFOSR-86-0126 and
AFOSR-91-0156.

3/87 Organizer
and Chairman of the *3rd Copper Mountain
Multigrid Conference*, Copper Mountain, CO. Funded by AFOSR.

9/87-9/93 NSF Principal Investigator.
Project title: *Multilevel algorithms for
advanced computers*, grant no. DMS-8704169.

12/87-5/88 NASA Principal Investigator.
Project title: *Asynchronous multilevel
adaptive methods for partial differential equations*, grant no. NASI-18606.

5/88 Editor,
Lecture Notes in Pure and Applied Mathematics/110, Marcel-Dekker (selected
papers of the *3rd Copper Mountain
Multigrid Conference*).

7/88-6/92 Associate Director of Applied Mathematics, Center for Applied Parallel Processing, University of Colorado.

10/88-9/90 Project with DRET (Paris) for *The use of algebraic multigrid (AMG) for the
numerical simulation of inviscid and viscous compressible flows using finite
element methods*.

3/89 Organizer
and Co-Chairman of the *4th Copper
Mountain Multigrid Conference*, Copper Mountain, CO. Funded by AFOSR.

6/89-12/89 NSF Co-Investigator. Project
Title: *SCREMS-Local Area Network
Equipment Grant*, grant no. DMS-8904404.

9/89-8/91 NASA Principle
Investigator. Project Title: *The NASA
Graduate Student Research Program*, grant no. NGT-50403.

11/89 Editor,
Proceedings of the *4th Copper Mountain Conference
on Multigrid* *Methods*, SIAM.

1/90-3/93 NASA
Co-Investigator. Project Title: *Parallel
multilevel adaptive methods for flows in transition*, Phases I and II, grant
no. SBIR 89-1-06-01-8633.

3/90 Program
Chairman of the *1st Copper Mountain
Conference on Iterative Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, and LANL.

5/90-11/90 AFOSR Co-Investigator. Project
Title: *Multilevel adaptive methods for
the Eagle code*, Phase I , grant no. SBIR
FO8635-90-C-0368.

7/90-6/95 Sandia project on *Fast numerical methods for flow models for
the WIPP project.*

10/90-now Front Range Scientific Computations, Inc. President.

12/90-9/93 Sandia Graduate Research WIPP Fellowship Advisor.

3/91 Organizer
and Co-Chairman of the *5th Copper
Mountain Conference on Multigrid Methods*, Copper Mountain, CO. Funded by
AFOSR, NSF, and IBM.

6/91 Principal
Lecturer, *NSF-CBMS Regional Research
Conference,* George Washington University, Washington, D.C.

7/91-9/96 Colorado Offices, Ecodynamics Research Associates, Inc. Vice-President.

4/92 Co-Chairman
of the *2nd Copper Mountain Conference on
Iterative Methods,* Copper Mountain, Colorado. Funded by DOE.

1/92-6/95 NASA
Co-Investigator. Project Title: *Multilevel
adaptive methods for combustion*, Phases I and II, grant no. SBIR
91-1-0101-4807.

12/92-1/96 ONR Co-Investigator. Project
Title: *Multilevel adaptive methods for
3-D Reynolds averaged Navier-Stokes solvers*, Phases I and II, grant no.
SBIR N00167-93-C-0009.

2/93-7/93 NASA
Co-Investigator. Project Title: *A C++
virtual shared grid based programming model for architecture-independent
development of structured grid codes*, Phase I, grant no. SBIR TBA.

4/93 Co-Chairman
of the *6th Copper Mountain Conference on
Multigrid Methods*, Copper Mountain, Colorado. Funded by DOE, NASA, and NSF.

8/93-now University of Colorado at Boulder, (Emeritus) Professor of Applied Mathematics.

8/93-12/99 Associate Editor, *SIAM Journal on Scientific Computing*.

4/94 Co-Chairman
of the *3rd Copper Mountain Conference on
Iterative Methods,* Breckenridge, Colorado. Funded by DOE and NSF.

4/94 Principal
Lecturer (with J. Bramble). *Australian
Workshop on Multigrid Methods*, Australian National University, Canberra.

5/94-11/97 NSF Principal Investigator. Cooperative research program with INRIA, grant no. INT-9310529.

6/94-6/95 Project with DRET
(Paris) for *Multilevel methods for the
Helmholtz equations.*

8/94-7/97 NSF Principal Investigator.
Project title: *Multilevel algorithms for
advanced computers*, grant no. DMS-9312752.

4/95 Co-Chairman
of the *7th Copper Mountain Conference on
Multigrid Methods*, Copper Mountain, Colorado. Funded by DOE, NASA, and NSF.

9/95 Editor,
English translation, *Optimization in
Solving Elliptic Problems*, Eugene G. D'Yakonov, CRC Press, 1995.

1/96-9/00 Associate Editor, *SIAM Journal on Numerical Analysis.*

4/96 Co-Chairman
of the *4th Copper Mountain Conference on
Iterative Methods,* Copper Mountain, Colorado. Funded by DOE and NSF.

4/97 Co-Chairman
of the *8th Copper Mountain Conference on
Multigrid Methods*, Copper Mountain, Colorado. Funded by DOE, IBM, the GMD,
and NSF.

4/97 Editor,
Special Issue of *E. T. N. A.* on
Multigrid Methods.

6/97-5/00 DOE Co-Investigator.
Project title: *Fast Algorithms for
Transport Models*, grant no. DE-FG03-95ER25217.

8/97-7/00 NSF Principal Investigator.
Project title: *Multilevel and Algebraic
Iterative Methods in Large-Scale Computing*, grant no. DMS-9706866.

12/97 Co-Principal Investigator. IBM Shared Research Grant of 12-Node SP supercomputer.

8/97-8/98 Council on Research and Creative Works Fellowship, University of Colorado at Boulder, half-year faculty research leave support.

4/98 Co-Chairman
of the *5th Copper Mountain Conference on
Iterative Methods,* Copper Mountain, Colorado. Funded by DOE, NSF, and IBM.

10/98-9/01 DOE ASCI Level II
Co-Investigator. Project Title: *Scalable
Algorithms for Massive Parallel Computation*.

10/98-9/01 NIH Co-Investigator. Project
Title: *Computational Biomechanics of
Coupled Systems via FOSLS*, grant no. 1-R01-EY12291-01.

4/99 Co-Chairman
of the *9th Copper Mountain Conference on
Multigrid Methods,* Copper Mountain, Colorado. Funded by DOE, NSF, and IBM.

4/00 Co-Chairman
of the *6th Copper Mountain Conference on
Iterative Methods,* Copper Mountain, Colorado. Funded by DOE, NSF, and IBM.

7/00-6/03 DOE
Co-Investigator. Project title: *First-Order
System Least Squares (FOSLS): Fundamentals and Applications*, grant no.
DE-FG03-99ER25217.

9/00 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

10/00-10/03 NSF Principal Investigator.
Project title: *First-Order System Least
Squares (FOSLS) for Partial Differential Equations*, grant no. DMS-0084438.

1/01-1004 Sandia National
Laboratories Co-Investigator. Project title: *Fast and Accurate Numerical Solution of Maxwell *Equations, grant
no. 1100.12.1512B.

1/01-12/05 Editor, *SIAM Journal on Multiscale Modeling and Simulation.*

4/01 Co-Chairman
of the *10th Copper Mountain Conference on
Multigrid Methods*, Copper Mountain, Colorado. Funded by DOE, NSF, and IBM.

7/01-7/06 DOE SciDAC Principal Investigator. Project title: *Terascale** Optimal PDE Simulations (TOPS)*, grant
number no. DE-FC02-01ER25479.

9/01 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

3/02 Co-Chairman
of the *7th Copper Mountain Conference on
Iterative Methods*, Copper Mountain, Colorado. Funded by DOE, NSF, and IBM.

9/02 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

4/03 Conference
Committee of the *11th Copper Mountain
Conference on Multigrid Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, and IBM.

7/03-3/07 LLNL
Principal Investigator. Project Title: *FAC,
Adaptive AMG, and Compatible Relaxation for Solving Problems That Arise in LLNL
Applications*.

7/03-6/06 DOE Co-Investigator.
Project title: *First-Order System Least
Squares (FOSLS): Fundamentals and Applications (Fast Algorithms for Transport
Models)*.

9/03 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

10/04-10/07 NSF Co-Investigator.
Project title: *hp-adaptive FOSLS Methods
for Nonlinear PDE Problems with Singularities*, grant no. DMS-0410318.

3/04 Conference
Committee of the *8th Copper Mountain
Conference on Iterative Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, IBM, LANL, LLNL, and Sandia.

9/04 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

4/05 Conference
Committee of the *12th Copper Mountain
Conference on Multigrid Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, IBM, LANL, LLNL, and Sandia..

9/05 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

4/06 Conference
Committee of the *9th Copper Mountain
Conference on Iterative Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, IBM, LANL, LLNL, and Sandia.

9/06 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

9/06-8/11 NSF Co-Investigator.
Project Title: *CMG Research: Modeling
River Basin Dynamics: Parallel Computing and Advanced Numerical Methods.*

10/06-9/11 DOE Principal Investigator.
Project Title: *Towards Optimal Petascale Simulations (TOPS).*

10/06 Co-Editor,
*Multigrid Computing*, Special Issue of
Computing in Science and Engineering, Vol. 8, IEEE, pp. 1-104.

3/07 Conference
Committee of the *13th Copper Mountain
Conference on **Mutigrid** Methods. *Funded by
DOE, NSF, IBM, LANL, LLNL, and Sandia.

9/07 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

10/07-5/13 DOE
Co-Investigator. Project title: *First-order
system least squares (FOSLS) for nonlinear systems arising in DOE applications.*

11/07-9/09 LLNL Principal Investigator.
Project Title: *Geometric and Algebraic
Multigrid Methods for QCD, MHD, Elasticity, Transport, and Other DOE
Applications.*

12/07-12/11 NSF Principal
Investigator. Project Title: *Multigrid
QCD at the Petascale.*

4/08 Conference
Committee of the *10th Copper Mountain
Conference on Iterative Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, IBM, Boeing, LANL, LLNL, and Sandia.

9/08 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

10/08-9/11 NSF
Principal Investigator. Project Title: *Enhanced
Least-Squares Methods for PIV Analysis.*

3/09 Conference
Committee of the *14th Copper Mountain
Conference on **Mutigrid** Methods. *Funded by DOE, NSF, IBM, LANL,
LLNL, and Sandia.

9/09 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

3/10 Conference
Committee of the *11th Copper Mountain
Conference on Iterative Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, IBM, Boeing, LANL, LLNL, and Sandia.

10/10 Chair
of the *AMG Summit*, Boulder, Colorado.
Funded by FRSC and LLNL.

3/11 Conference
Committee of the *15th Copper Mountain
Conference on Mutigrid Methods. *Funded by DOE,
NSF, IBM, LANL, LLNL, and Sandia.

9/11 Chair
of the *AMG Summit*, Lake City,
Colorado. Funded by FRSC and LLNL.

3/12 Conference
Committee of the *12th Copper Mountain
Conference on Iterative Methods*, Copper Mountain, Colorado. Funded by DOE,
NSF, IBM, Boeing, LANL, LLNL, and Sandia.

10/12 Chair
of the *AMG Summit*, Boulder, Colorado.
Funded by FRSC and LLNL.

3/13-2/16 NSF
Co-Investigator. Project Title: *Collaborative
Research: Least-Squares Finite Element Methods for Data Assimilation in
Large-Scale Simulations.*

12/09-3/12 LLNL
Principal Investigator. Project Title: *Error
Estimators for Uncertainty Quantification, Adaptive Mesh Refinement, Multilevel
Solvers for Transport, Adaptive AMG/SA for Quantum Chromodynamics, and the AMG
Summit.*

9/12-10/15 AFOSR
Principal Investigator. Project Title: *Parallel
Multilevel Decomposition Methods for Plasma Fluid Models.*

3/12-3/15 LLNL
Principal Investigator. Project Title: *Error
Estimators for Uncertainty Quantification, Adaptive Mesh Refinement, Solvers
for Stochastic Partial Differential Equations, Parallel Adaptive AMG/SA, and
Parallel Solution of Systems of Partial Differential Equations.*

**PUBLICATIONS AND REPORTS **

1. *A general approach to one-step iterative methods with application to
eigenvalue problems*, J. Comput. Sys. Sci. 6 (l972), pp. 354-372.

2. *An iterative procedure for the solution of constrained nonlinear
equations with application to optimization problems*, Numer. Math. 23
(l975), pp. 371-385.

3. *A uniform approach to gradient methods for linear operator equations*,
J. Math. Anal. Appl. 49 (l975), pp. 275-285 (with G.H. Rodrigue).

4. *Some convergence results on the method of gradients for Ax =**lBx*,
J. Comput. Sys. Sci. 13 (l976), pp. 213-222.

5. *Simultaneous iteration for the matrix eigenvalue problem*, J. Lin.
Alg. Appl. 16 (l977), 43-56 (with A.D. Noe).

6. *Newton's method with mesh refinements for numerical solution of
nonlinear two-point boundary value problems*, Numer. Math. 29 (l978), pp.
237-260 (with E.L. Allgower).

7. *The methods of Kaczmarz and iterative row orthogonalization for
solution of linear equations in Hilbert space*, Indiana Univ. Math. J. 2
(l977), pp. 1137-1150.

8. *A general mesh independence principle for Newton's method applied to
second order boundary value problems*, Computing 23 (l979), pp. 223-246
(with E. Allgower and D. Pryor).

9. *A revised mesh refinement strategy for Newton's method applied to nonlinear two-point
boundary value problems*, Numerical treatment of differential equations in
applications (Proc. Meeting, Math. Res. Center, Oberwolfach,
1977), pp. 15-23, Lecture Notes in Math., 679, Springer, Berlin, 1978.

10. *Evaluation of square root functions on microprocessors*, Procs. of
ACM 76 (10/76) (with M. Andrews and G.D. Taylor).

11. *A microprocessor-based control system for solar heated/cooled
residential dwellings*, Procs. SIAM Joint Automatic Control Conf. (l977)
(with G. Johnson, D. Pryor, and B. Eisenberg).

12. *Evaluation of functions on microcomputers: square roots*, Comp.
Math. Appl. 4 (l979), pp. 359-367 (with M. Andrews and G.D. Taylor).

13. *Evaluation of functions on microcomputers: k-th roots*, Comp. Math.
Appl. 5 (l979), pp. 163-167 (with M. Andrews and G.D. Taylor).

14. *Evaluation of functions on microcomputers: exp(x)*, Comp. Math.
Appl. 7 (l981), pp. 503-508 (joint with M. Andrews, D. Jaeger, and G. Taylor).

15. *The microcomputer numerical software project at CSU*, Procs. 2nd
Rocky Mountain Symp. Microcomputers, IEEE, l978 (with M. Andrews, D. Jaeger, and
G. Taylor).

16. *Toward optimal control of solar energy systems*, Procs. 1978 IEEE
Conf. Decision and Control (1/l9/79), San Diego.

17. *Microprocessor control in solar heating and cooling*, Int'l. Survey
in Applications of Microprocessors (l979), pp. 125-134, Infotech Int'l.,
Berkshire, England.

18. *Numerical software for fixed point microcomputer applications*,
report commissioned by ARO, Fall, l980 (with G.D. Taylor).

19. *Evaluation of functions on microcomputers: ln (x)*, Comp. Math.
Appl. 8 (l982), pp. 389-392 (with G.D. Taylor and D.V. Pryor).

20. *Simultaneous Rayleigh quotient minimization methods for Ax =**lBx*, Lin. Alg. Appl. 34 (l980), pp. 195-234 (with D.
Longsine).

21. *A mesh refinement method for Ax = **lBx*,
Math. Comp. 36 (l981), pp. 485-498.

22. *An adaptive differential-correction algorithm*, J. Approx. Theory 37
(1983), pp. 197-211 (with E. Kaufman and G.D. Taylor).

23. *The sparse matrix eigenproblem*, report, Colo. State Univ., l975.

24. *Multigrid methods: An alternate approach*, Lawrence Livermore Lab.
report, l979.

25. *An algebraic interpretation of multigrid methods*, SIAM J. Numer.
Anal. 19 (l982), pp. 548-560.

26. *Discrete correction methods for operator equations*, Procs. Conf.
Numerical Solution of Nonlinear Equations: Simplicial and Classical Methods,
Bremen, l980 (H.-O. Peitgen, ed.), Springer Lecture Notes in Mathematics, Vol.
878, l981 (with E. Allgower and K. Bšhmer).

27. *Multigrid methods for multiprocessor computers*, report, Lawrence
Livermore Lab. report, l979 (with G. Rodrigue).

28. *Mesh refinement methods for integral equations*, Numerical Treatment
of Integral Equations (J. Albrecht and L. Gilatz, eds.), 183-90, Birkhauser
Verlag, Berlin, l980.

29. *Multigrid methods for differential eigenproblems*, SIAM J. Sci.
Stat. Comp. 4 (l983), pp. 244-260 (with A. Brandt and J. Ruge).

30. *Discrete defect corrections: Basic ideas*, Zeit.
Ang. Math. Mech. 2 (l982), pp. 371-377 (with E. Allgower and K. Bšhmer).

31. *Numerical software for fixed point microprocessor applications and for
fast implementation of multigrid techniques*, Procs. US Army Num. Anal.
Comp. Conf., Feb., l981.

32. *Multigrid methods for variational problems*, SIAM J. Numer. Anal. 19
(l982), pp. 924-929 (with J. Ruge).

33. *Unigrid for multigrid simulation*, Math. Comp. 41 (l983), pp. 43-62
(with J. Ruge).

34. *Unigrid methods for boundary value problems on nonrectangular domains*,
J. Comp. Phys. 48 (l982), pp. 412-422 (with W. Holland and J. Ruge).

35. *Multigrid methods applied to water wave problems*, Procs. 3rd IntÕl.
Conf. Ship Hydrodynamics, Paris, June 1981.

36. *Multigrid methods for variational problems: the V-cycle*, Math. Comp. Sim. XXV (l983), pp. 63-65,
North Holland Pub. Co.

37. *Uniform rational approximation on large data sets*, Int'l. J. Numer.
Meth. Eng. (l982), pp. 1569-1575.

38. *Multigrid
methods for variational problems: further results*, SIAM J. Numer. Anal. 21
(l984), pp. 255-263.

39. *Algebraic multigrid (AMG) for automatic multigrid solution with application
to geodetic computations*, report, Inst. Comp. Studies, Colo. State Univ.,
l982 (with A. Brandt and J. Ruge).

40. *Multigrid image reconstruction*, Procs. Workshop Multi-Resolution
Image Processing and Anal., Leesburg, VA, July 1982 (A. Rosenfeld, ed.),
Springer, l983 (with G. Herman, H. Levkowitz, and H. Tuy).

41. *Successive overrelaxation, multigrid, and
preconditioned conjugate gradients algorithms for solving a diffusion problem
on a vector computer*, Appl. Math. Comp. Spec. Issue on Multigrid Methods
(S. McCormick and U. Trottenberg, eds.) 13 (l983), pp. 285-310 (with J. Gary
and R. Sweet).

42. *Multigrid methods for variational problems: general theory for the
V-cycle*, SIAM J. Numer. Anal. 22 (l985), pp. 634-643.

43. *A variational theory for multilevel adaptive techniques (MLAT)*,
Multigrid Methods for Integral and Differential Equations (D.J. Patton and H.
Holstein, Eds.), JMAA Conf. Ser., New Ser., New 3 (l985), pp. 225-230,
Clarendon Press.

44. *Multigrid methods and adaptive techniques for oil reservoir simulation*,
report, Inst. Comp. Studies, Colo. State Univ., 1983 (with J. Ruge, S.
Schaffer, and J. Thomas).

45. *Fast adaptive composite grid (FAC) methods: theory for the variational
case*, in Defect Correction Methods: Theory and Applications (K. Bšhmer and
H.J. Stetter, eds.), Computations Supplementation 5 (l984), pp. 115-122.

46. *Algebraic multigrid (AMG) for sparse matrix equations*, Sparsity and
Its Applications (D.J. Evans, ed.), Cambridge Univ. Press, l984 (with A. Brandt
and J. Ruge).

47. *The fast adaptive composite grid method for solving differential
boundary value problems*, Procs. 5th ASCE-EMD Specialty Conf., Aug., l984
(with R. Ewing and J. Thomas).

48. *The fast adaptive composite grid method (FAC) for elliptic equations*,
Math. Comp. 46 (1986), pp. 439-456 (with J. Thomas).

49. *An algebraic theory for multigrid methods for variational
problems*, SIAM J. Numer. Anal. 25 (1988), pp. 91-110 (with J. Mandel and J.
Ruge).

50. *A multilevel variational
method for **Au = **lBu on composite grids*, J. Comp. Phys. 80
(1989), pp. 442-450 (with J. Mandel).

51. *The fast adaptive composite grid method (FAC): algorithms for advanced
computers*, Appl. Math. Comp. Spec. Issue on Multigrid Methods, North
Holland, 1985 (with L. Hart, A. O'Gallagher, J. Thomas).

52. *The fast adaptive composite grid method in oil reservoir simulation*,
Procs. SEG-SIAM-SPE Conf. Math. Comput. Meths. Seismic Expl. and Res. Mod.,
Houston, Jan., l985 (with J. Thomas).

53. *Variational** multigrid theory*, Chapt. 5 in SIAM Frontiers in Applied Math.,
Vol. III on Multigrid Methods (S. McCormick, ed.), 1987 (with R. Bank and J.
Mandel).

54. *Fast adaptive methods and advanced architectures*, SUPRENUM Proj.
Rep. No. 51, GMD, St. Augustin, W. Germany, 1985.

55. *Introduction [to multigrid methods]*, Chapt. 1 in SIAM Frontiers in
Applied Math, Vol. III on Multigrid Methods (S. McCormick, ed.), 1987 (with W.
Briggs).

56. *Algebraic multigrid methods applied to problems in computational
structural mechanics*, A.M.D. State-of-the-Art Survey on Comp. Mech., Part
2, Chapt. 1, ASME, NY, 1989 (with J. Ruge).

57. *Application of the fast adaptive composite grid method to computational
fluid dynamics*, Procs. 5th Int. Conf. Numer. Meths. in Laminar and
Turbulent Flow, Montreal, Canada, 1987 (with J. Thomas and A. Thomas).

58. *Multigrid load balancing for multiprocessors - an outline*, report,
CU-Denver, 1986 (with D. Quinlan).

59. *Applications of the fast adaptive composite grid method*, Lecture
Notes in Pure and Applied Mathematics/110, Marcel-Dekker, May, 1988 (with M.
Heroux, S. McKay, and J. Thomas).

60. *Multigrid methods on a hypercube*, Lecture Notes in Pure and Applied
Mathematics/110, Marcel-Dekker, May, 1988 (with W. Briggs, L. Hart, and D.
Quinlan).

61. *Multigrid, elliptic grid generation and the fast adaptive composite
grid method for solving transonic potential flow equations*, Lecture Notes
in Pure and Applied Mathematics/110, Marcel-Dekker, May, 1988 (with C. Liu).

62. *Asynchronous multilevel adaptive methods for
solving partial differential equations on multiprocessors: **basic ideas*, Parallel Computing 12
(1989), pp. 131-144 (with L. Hart).

63. *Computational complexity of the Schwarz alternating procedure*,
IntÕl. J. High Speed Computing 1 (1989), pp. 1-28 (with Z. Cai).

64. *The finite volume element method for planar cavity flow*, Procs.
11th Int'l. Conf. on Numer. Meths. in Fluid Dyns., Williamsburg, June 27 - July
1, 1988 (with C. Liu).

65. *Multigrid trends*, SIAM News, Vol. 21, No. 1, Jan., 1988.

66. *Iterative solution of elliptic equations with refinement: the two-level
case*, Procs. 2nd Conf. on Domain Decomposition, Los Ang., Jan., 1988 (with
J. Mandel).

67. *Iterative solution of elliptic equations with refinement: the model
multilevel case*, Procs. 2nd Conf. on Domain Decomposition, Los Ang., Jan.,
1988 (with J. Mandel).

68. *Multigrid, the rotated hybrid scheme, and the fast adaptive composite
grid method for planar cavity flow*, Procs. 12th IMACS Congress on
Scientific Computation, Paris, July, 1988 (with C. Liu).

69. *On the accuracy of the finite volume element method for diffusion
equations on composite grids*, SIAM J. Numer. Anal. 27 (1990), pp. 636-655
(with Z. Cai).

70. *Parallel asynchronous multilevel adaptive methods*, Procs. 11th
Int'l. Conf. on Numer. Meths. in Fluid Dyns., Williamsburg, June 27-July 1,
1988 (with B. Dowell, M. Govett, and D. Quinlan).

71. *The realization problem for a class of nonlinear systems*, SIAM J.
on Matrix Anal. Appl. 11 (1990), pp. 113-127 (with L. Tiejun).

72. *Computational complexity of the fast adaptive composite grid (FAC)
method*, Appl. Numer. Math. 6 (1990), Special Issue on Domain Decomposition
(W. Proskurowski, ed.) (with M. McKay and J. Thomas).

73. *The finite volume element technique and fast adaptive composite grid
method for time-dependent differential equations*, Procs. 7th IntÕl Conf. on
Finite Element Methods in Flow Problems, Univ. of Alabama, Huntsville, April
3-7, 1989.

74. *Dynamic grid refinement for partial differential equations in parallel
computers*, Procs. 7th IntÕl Conf. on Finite Element Methods in Flow
Problems, Univ. of Alabama, Huntsville, April 3-7, 1989 (with D. Quinlan).

75. *Multigrid methods for three-dimensional petroleum reservoir simulation*,
Procs. 10th SPE Sym. Reservoir Sim., Feb. 6-8, 1989 (with J. Dendy, J. Ruge, T.
Russell, and S. Schaffer).

76. *Asynchronous multilevel adaptive methods for solving partial
differential equations on multiprocessors: performance results*, Parallel
Computing 12 (1989), pp. 145-156 (with D. Quinlan).

77. *Computation: breaking the matrix speed limit*, Nature Magazine (News
and Views) 337 (1989), pp. 205.

78. *Multilevel adaptive schemes and domain decomposition methods*,
Procs. 5th IntÕl. Symp. Numer. Meth. Eng., Lausanne, Sept., 1989.

79. *Multilevel Adaptive Methods for Partial Differential Equations*,
SIAM, Philadelphia, 1989,162 pps.

80. *The finite volume element method for diffusion equations on general
triangulations*, SIAM J. Numer. Anal. 28 (1991), pp. 392-402 (with Z. Cai
and J. Mandel).

81. *Multigrid, the fast adaptive composite (FAC) grid method for solving
flow problems*, Procs. IntÕl Symp. on Comp. Fluid Dyn., Nagoya, Japan, Aug.
28-31, 1989 (with C. Liu).

82. *On local refinement higher order methods for elliptic partial
differential equations*, IntÕl. J. High Speed Comp. 2 (1990), pp. 331-334
(with U. RŸde).

83. *A finite volume convergence theory for the fast adaptive composite grid
method*, Appl. Numer. Math. 14 (1994), pp. 91-103 (with U. RŸde).

84. *MLAT vs. FAC*, report, CU-Denver, March, 1990.

85. *Multilevel adaptive methods for elliptic eigenproblems: two-level
convergence theory*, SIAM J. Numer. Anal. 31 (1994), pp. 1731-1745.

86. *Multigrid methods for flow transition in a planar channel*, Comp.
Phys. Comm. 65 (1991), pp. 188-200 (with C. Liu and Z. Liu).

87. *Multilevel adaptive methods for incompressible flow in grooved channels*,
J. Comp. Appl. Math. 38 (1991) (with C. Liu and Z. Liu).

88. *An efficient multigrid scheme for elliptic equations with discontinuous
coefficients*, Comms. Appl. Numer. Methods 8 (1992),
pp. 621-631 (with C. Liu and Z. Liu).

89. *Multilevel parameter estimation*, Procs. 5th Copper Mountain Conf.
on Multigrid Methods, April, 1991 (with G. Wade).

90. *Multilevel Riccati solvers*, Procs. 5th Copper Mountain Conf. on
Multigrid Methods, April, 1991 (with K. Ito and L. Tiejun).

91. *Multilevel Projection Methods for Partial Differential Equations*,
CBMS-NSF Series, SIAM, Philadelphia, 1992, 115 pps.

92. *Multilevel adaptive methods for the Eagle code*, Numer. Grid
Generation in C.F.D. and Related Fields (A.S. Arcilla, J. Hauser, P.R. Eiseman,
and J.F. Thompson, eds.), Elsevier, North Holland, 1991, pp. 687-701 (with C.
Liu and Z. Liu).

93. *Fast multigrid solver for neutron transport problems*, Procs. IMACS
1st Int'l. Conf. on Comp. Phys., Boulder, CO, June 11-15, 1990 (with T.
Manteuffel, J.E. Morel, and G. Yang).

94. *Multigrid solution of linearized, regularized least squares problems in
electrical impedance tomography*, Inverse Problems 9 (1993), pp. 697-713
(with G. Wade).

95. *High order finite volume and multigrid methods for flow transition in a
planar channel*, Procs. 4th IntÕl Symp. on C.F.D., UC Davis, CA, 1991 (with
C. Liu and Z. Liu).

96. *Fourth order finite difference and multigrid methods for modeling
instabilities in flat plate boundary layers*, report to NASA (with C. Liu
and Z. Liu).

97. *Finite volume element and multilevel adaptive methods*, Procs. Comp.
Mech. Water Resources Conf., Denver, June 9-12, 1992.

98. *Parallel multigrid methods for transport equations*, Procs. 2nd.
Copper Mountain Conf. on Iterative Methods, April, 1992 (with T. Manteuffel, J.
Morel, S. Oliviera, and G. Yang).

99. *Multilevel projection methods for partial differential equations*,
Procs. NATO Advanced Res. Workshop on Asymptotic-Induced Numer. Methods for
PDEs, Critical Parameters, and Domain Decomposition, Beaune, France, May, 1992,
NATO ASI Series, Kluwer, pp. 287-292.

100. *Multigrid
methods for nearly singular linear equations and eigenvalue problems*, SIAM
J. Num. Anal. 34 (1997), pp. 178-200 (with Z. Cai and J. Mandel).

101. *Idealized
analysis of asynchronous multilevel methods,* Procs. Symp. on Adaptive,
Multilevel, and Hierarchical Computational Strategies (A.K. Noor, ed.) ASME
Winter Annual Meeting, Anaheim, CA, AMD 157 (1992), pp. 1-8 (with D. Quinlan).

102. *Adaptive
grid refinement in a multilevel solver for semi-implicit solution of shallow
water equations on a sphere*, Monthly Weather Review 123 (1995), pp.
2197-2205 (with J. Ruge and S. Yee).

103. *Multigrid
methods for numerical simulation of laminar diffusion flames*, AIAA Tech.
Paper No. 93-0236, 1993 (with C. Liu and Z. Liu).

104. *A fast
multigrid algorithm for isotropic transport problems*, *Part I: pure scattering*, SIAM J. Sci. Comp.16 (1995), pp.
601-635 (with T. Manteuffel, J. Morel, S. Oliviera, and G. Yang).

105. *A
parallel version of a multigrid algorithm for isotropic transport equations*,
SIAM J. Sci. Comp. 15 (1994), pp. 474-493 (with T. Manteuffel, J.
Morel, S. Oliviera, and G. Yang).

106. *Accurate
discretization for singular perturbations: the one-dimensional case*, SIAM
J. Numer Anal. 32 (1995), pp. 83-109 (with X.C. Hu, T. Manteuffel, and T.
Russell).

107. *Multilevel
adaptive methods for laminar diffusion flames*, SIAM J. Sci. Comp. 8 (1993),
pp. 341-355 (with C. Liu and Z. Liu).

108. *A fast
multigrid algorithm for isotropic transport problems*,* Part II: with absorption*, SIAM J. Sci. Comp., 17 (1996), pp.
1449-1474 (with T. Manteuffel, J. Morel, and G. Yang).

109. *A
semi-Lagrangian approach to shallow water equations,* Procs. 6th Copper
Mountain Conf. on Multigrid Methods, NASA, 1993 (with J. R. Bates, J. Ruge, D.
Sholl, and I. Yavneh).

110. *Multilevel
methods for flow transition in a plane channel with roughness elements*,
Procs. 6th Copper Mountain Conf. on Multigrid Methods, NASA, 1993 (with C. Liu,
Z. Liu, and Z.X. Liu).

111. *Optimal
resolution in maximum entropy image reconstruction from projections with
multigrid acceleration*, Procs. 6th Copper Mountain Conf. on Multigrid
Methods, NASA, 1993 (with M. Limber, T. Manteuffel, and D. Sholl).

112. *Schwarz
alternating procedure for elliptic problems discretized by least squares mixed
finite elements*, report (with Z. Cai).

113. *First-order
system least squares for second-order partial differential equations: Part I*,
SIAM J. Numer. Anal. 31 (1994), pp. 1785-1802 (with Z. Cai, R. D. Lazarov, and
T. Manteuffel).

114. *First-order
system least squares for second-order partial differential equations: Part II*,
SIAM J. Numer. Anal. 34 (1997), pp. 425-454 (with Z. Cai and T. Manteuffel).

115. *Multilevel
projection methodology*, Procs. CTAC Conference, Austr. NatÕl Univ., May,
1993.

116. *Multilevel
projection methods for first-order system least squares, Procs. *ASME Fluids
Eng. Div. Summer Mtg., Lake Tahoe, CA, June 9-23, 1994 (with T. Manteuffel).

117. *Numerical
integration of the primitive equations based on the semi-Lagrangian advection
of potential vorticity*, Procs. Symp. Cyclones, Bergen, Norway, June 27-July
1, 1994 (with J.R. Bates, A. Brandt, Y. Li, and J. Ruge).

118.* A
nonlinear multigrid solver for a semi-Lagrangian potential vorticity based
shallow water model on a sphere,* SIAM J. Sci. Comp. 21 (2000), pp.
2381-2398 (with J.R. Bates, A. Brandt, Y. Li, and J. Ruge).

119. *First-order
system least squares for the Stokes equations, with application to linear
elasticity, *SIAM J. Numer. Anal. 34 (1997), pp. 1727-1741 (with Z. Cai and
T. Manteuffel).

120. *Multilevel
first-order system least-squares (FOSLS) for Helmholtz equations*, Procs.
2nd IntÕl Conf. on Approx. and Num. Meths. for the Solution of the Maxwell
Equations, Oct., 1993 (with B. Lee, T. Manteuffel, and J. Ruge).

121. *First-order
system least squares (FOSLS) for planar linear elasticity: pure traction
problem, *SIAM J. Numer. Anal. 35 (1998), pp. 320-335 (with Z. Cai, T.
Manteuffel, and S. Parter).

122. *Analysis
of velocity-flux least-squares principles for the Navier-Stokes equations: Part
I, *SIAM J. Numer. Anal. 35 (1998), pp. 990-1009 (with P. Bochev, Z. Cai,
and T. Manteuffel).

123. *First-order
system least squares for second-order elliptic problems with discontinuous
coefficients, *Procs. 7th Copper Mountain Conf. on Multigrid Methods, NASA
Pubs., Hampton, VA (1996), pp. 535-550 (with T. Manteuffel and G. Starke).

124. *First-order
system least squares for the velocity-pressure-vorticity form of the Stokes
equations, with application to linear elasticity, *E.T.N.A. 3 (1995), pp.
150-159 (with Z. Cai and T. Manteuffel).

125. *A
global shallow water numerical model based on the semi-Lagrangian advection of
potential vorticity*, Quart. J. Royal Met. Soc., Q. J. R. Meteorol. Soc. 121
(1995), pp. 1981-2005 (with J.R. Bates, A. Brandt, Y. Li, and J. Ruge).

126. *Multilevel
image reconstruction with natural pixels, *SIAM J. Sci. Comp. 17 (1996), pp.
193-216 (with V. Henson, M. Limber, and B. Robinson).

127. *First-order
system least squares (FOSLS) for convection-diffusion problems: numerical
results*, SIAM J. Sci. Comp., 19 (1998), pp. 1958-1979 (with J.-M. Fiard and
T. Manteuffel).

128. *Parallel
multigrid methods*, NASA/LaRC Interdisciplinary Series in Science and
Engineering, *Parallel Numerical
Algorithms* (D. Keyes, A. Sameh, V. Venkatakrishnan, eds.), Kluwer, 1997
(with J. Jones).

129. *Analysis
of first-order system least squares (FOSLS) for elliptic problems with
discontinuous coefficients: Part I*, SIAM J. Numer.
Anal. 43 (2005), pp. 386-408 (with M. Berndt, T. Manteuffel,
and G. Starke).

130. *Multilevel
first-order system least squares methodology*, Supercomputing in Nonlinear
and Disordered Systems, World Scientific, New Jersey (1996), pp. 25-36.

131. *Control-volume
mixed finite element methods*, Computational Geosciences 1 (1997), pp.
289-315 (with Z. Cai, J. Jones, and T. Russell).

132. *Local
error estimates and adaptive refinement for first-order system least squares
(FOSLS)*, E.T.N.A. 6 (1998), pp. 35-43 (with M. Berndt and T. Manteuffel).

133. *Analysis
of velocity-flux least-squares principles for the Navier-Stokes equations: Part
II, *SIAM J. Numer. Anal. 36 (1999), pp. 1125-1144 (with P. Bochev, Z. Cai,
and T. Manteuffel).

134. *First-order
system least-squares (FOSLS) for the Helmholtz equation, *SIAM J. Sci. Comp.
21 (2000), pp. 1927-1949 (with B. Lee, T. Manteuffel, and J. Ruge).

135. *First-order
system least squares for the Stokes and elasticity equations: further results, *SIAM
J. Sci. Comp. 21 (2000), pp. 1728-1739 (with Z. Cai, C.-O. Lee, and T.
Manteuffel).

136. *First-order
system least squares for planar linear elasticity: numerical results, *SIAM
J. Sci. Comp. 21 (2000), pp. 1706-1727 (with Z. Cai, C.-O. Lee, and T. Manteuffel).

137. *First-order
system least squares (FOSLS) for spatial linear elasticity: pure traction*,
SIAM J. Numer. Anal. 38 (2001), pp. 1454-1482 (with
S.-D. Kim and T. Manteuffel).

138. *Robustness
and scalability of algebraic multigrid, *SIAM J. Sci. Comp. 21 (2000), pp.
1886-1908 (with A. Cleary, R. Falgout, V. Henson, J. Jones, T. Manteuffel, G.
Miranda, and J. Ruge).

139. *Algebraic
multigrid based on element interpolation (AMGe)*, SIAM J. Sci. Comp. 22
(2001), pp. 1570-1592 (with M. Brezina, A. Cleary, R. Falgout, V. Henson, J.
Jones, T. Manteuffel, and J. Ruge).

140. *Improved
discretization error estimates for first-order system least squares (FOSLS)*,
J. Numer. Math., 11 (2003), pp.163-177 (with T. Manteuffel and C. Pflaum).

141. *A
Multigrid Tutorial, *second edition, SIAM, Philadelphia, June, 2000, 193 pps. (with W. Briggs and V. Henson).

142. *Analysis
of first-order system least squares (FOSLS) for elliptic problems with
discontinuous coefficients: Part II*, SIAM J. Numer.
Anal. 43 (2005), pp. 409-436 (with M. Berndt and T. Manteuffel).

143. *First-order system LL* (FOSLL*): scalar elliptic partial differential
equations*, SIAM J. Numer. Anal. 39 (2001), pp. 1418-1445 (with Z. Cai, T. Manteuffel, and J. Ruge).

144. *Spectral
AMGe*, SIAM J. Sci. Comp. 25 (2003), pp. 1-26
(with T. Chartier, R. Falgout,
V. E. Henson, J. Jones, T. Manteuffel, J. Ruge, and P. Vassilevski).

145.* Spectral
element agglomerate AMGe*, Lecture Notes Sci. Eng.
55 (2007) pp.513-521 (with T. Chartier, R. Falgout, V. E. Henson, J. Jones, T. Manteuffel,
J. Ruge, and P. Vassilevski).

146. *Multilevel
first-order system least squares for nonlinear elliptic partial differential
equations*, SIAM J. Numer. Anal.
41 (2003), pp. 2197-2209 (with A. Codd
and T. Manteuffel).

147. *Asynchronous
fast adaptive composite-grid methods for elliptic problems: theoretical
foundations*, SIAM J. Numer. Anal. 42 (2004), pp.
130-152 (with B. Lee, B. Philip, and D. Quinlan).

148. *Multilevel
first-order system least squares for elliptic grid generation*, SIAM
J. Numer. Anal. 41 (2003),
pp. 2210-2232 (with A. Codd, T. Manteuffel, and J. Ruge).

149. *Adaptive
smoothed aggregation (*a*SA)*, SIAM J. Sci. Comp. 25 (2004), pp.
1896-1920 (with M. Brezina, R. Falgout,
S. MacLachlan, T. Manteuffel,
and J. Ruge).

150. *First-order system least squares and electrical impedance
tomography*, SIAM J. Numer.
Anal. 42 (2004), pp. 461-483 (with H. MacMillan and T. Manteuffel).

151. *First-order system least squares and electrical impedance
tomography: part II*, report (2003) (with
H. MacMillan and T. Manteuffel).

152. *Asynchronous
fast adaptive composite-grid methods: numerical results*, SIAM J. Sci. Comp.
25 (2003), pp. 682-700 (with B. Lee, B. Philip, and D. Quinlan).

153. *Least-squares finite element methods and
algebraic multigrid solvers for linear hyperbolic PDEs*, SIAM J. Sci. Comp.
26 (2004), pp. 31-54 (with H. de Sterck, T. Manteuffel, and L. Olson).

154. *First-order
system least squares for **elastohydrodynamics** with application to flow in compliant blood
vessels*, Biomed. Sci. Instrum. 38 (2002), pp.
277-282 (with J. J. Heys, C. G. DeGroff,
T. Manteuffel, and W. W. Orlando).

155. *Adaptive
algebraic multigrid*, SIAM J. Sci. Comp. 27 (2006), pp. 1261-1286 (with
M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, and J.
Ruge).

156. *First-order system LL* (FOSLL*) for general scalar elliptic problems in
the plane*, SIAM J. Num. Anal. 43 (2006), 2098-2120 (with T. Manteuffel, J. Ruge, and J. G.
Schmidt).

157. *First-order
system least squares (FOSLS) for coupled fluid-elasticity problems*, J.
Comp. Physics 195 (2004), pp. 560-575
(with J. Heys, T. Manteuffel,
and J. Ruge).

158. *Numerical conservation properties of
H(div)-conforming least-squares finite element methods for the Burgers
equation,* SIAM J. Sci. Comp. 26
(2005), pp. 1573-1597 (with H. de Sterck, T. Manteuffel, and L.
Olson).

159. *A robust approach to minimizing H(div)
dominated functionals in an H ^{1}-conforming
finite element space*, J. Num. Lin. Alg. App. 11 (2004), pp. 115-140 (with
T. Austin and T. Manteuffel).

160. *First-order system least-squares for the Oseen equations*, J. Num. Lin. Alg. Appl. 13 (2006), pp.
461-486 (with S.-D. Kim, C.-O. Lee, T. Manteuffel,
and O. Ršhrle).

161. *Modeling
3-d compliant blood flow with FOSLS*, Biomed Sci Instrum. 40 (2004), pp. 193-199 (with J. J. Heys, C. G. DeGroff, T. Manteuffel, and H. Tufo).

162. *Projection multilevel methods for
quasilinear elliptic partial differential equations: numerical results, *SIAM
J. Numer. Anal. 44 (2006), pp. 120-138 (with T. Manteuffel, O. Ršhrle,
and J. Ruge).

163. *Projection multilevel methods for
quasilinear elliptic partial differential equations: theoretical results, *SIAM
J. Numer. Anal. 44 (2006), pp. 139-152 (with
T. Manteuffel and O. Ršhrle).

164. *Projection multilevel methods for
quasilinear elliptic partial differential equations: V-cycle theory, *SIAM
J. Mult. Modeling Sim. 4 (2006), pp. 1339-1348.

165. *First-order system least squares (FOSLS) for
geometrically nonlinear elasticity*, SIAM J. Numer.
Anal 44 (2006), pp. 2057-2081 (with T. Manteuffel, J. Schmidt, and C. Westphal).* *

166. *Algebraic
multigrid (AMG) for higher-order finite elements*, J. Comp. Phys. 204 (2005), pp. 520-532
(with J. Heys, T. Manteuffel,
and L. Olson).

167. *Adaptive
smoothed aggregation (*a*SA) multigrid*, SIAM Review SIGEST 47
(2005), pp. 317-346 (with M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, and J. Ruge).

168. *Adaptive
smoothed aggregation in lattice QCD*, Lecture Notes Comp. Sci. Eng. 55
(2007), pp. 505-512 (J. Brannick, M. Brezina, D. Keyes, O. Livne, I. Livshits, S. MacLachlan, T. Manteuffel, J. Ruge, and L. Zikatanov).

169. *First-order
system least squares (FOSLS) for modeling blood flow*, Med. Eng. Phys. 28 (2006), pp. 495-503 (with J. J. Heys, C. G. DeGroff, and T. Manteuffel).

170. *An
energy-based AMG coarsening strategy*, J. Num. Lin. Alg. Appl. 13 (2006), pp. 133-148 (with J. Brannick, M. Brezina, S. MacLachlan, T. Manteuffel, and J. Ruge).

171. *New multigrid solver advances in TOPS*,
Proceedings of SciDAC 2005, Journal of Physics:
Conference Series, Institute of Physics, San Francisco, CA, June 26-30, 2005
(with R. Falgout, J. Brannick,
M. Brezina, and T. Manteuffel).

172. *On mass-conserving least-squares methods*,
SIAM J. Sci. Comp. 28 (2006), pp. 1675-1693 (with J. Heys,
E. Lee, and T. Manteuffel).

173. *Adaptive reduction-based AMG (*a*AMGr**)*, J. Num. Lin. Alg. Appl. 13 (2006), pp. 599-620 (with S. MacLachlan
and T. Manteuffel).

174. *An alternative least-squares formulation of
the Navier-Stokes equations with improved mass
conservation*, J. Comp. Phys. 226 (2008), pp. 994-1006 (with J. Heys, E. Lee, and T. Manteuffel).

,2

1435 +6+7 3 .0 ,9 8; :/<
> 3 G =0G/ > =0 .9) > 1 EL. G* ? M >
N;:*.0 O7,5 P7</QS + @5R;
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175. *Spatial
multigrid for isotropic neutron transport*, SIAM J. Sci. Comp. 29 (2007),
pp. 1900-1917 (with B. Chang, T. Manteuffel, J. Ruge, and B. Sheehan).

176. *Extending
the applicability of multigrid methods*, J. Phys.: Conf. Ser. 46 (2006), pp. 443-452 (with J. Brannick,
M. Brezina, R. Falgout, T.
Manteuffel,
J. Ruge, B. Sheehan, J. Xu, and L. Zikatanov).

177. *Multilevel adaptive aggregation for Markov chains, with application to
web ranking*, SIAM J. Sci. Comp. 30 (2008), pp. 2235-2262 (with H. de Sterck, T. Manteuffel, Q. Nguyen,
and J. Ruge).

178. *Efficiency-based h- and hp-refinement strategies for finite element
methods*, J. Num. Lin. Alg. Appl. 15 (2008), pp. 89-114 (with H. de Sterck, T. Manteuffel,
J. Nolting, J. Ruge, and L.
Tang).

179. *A
generalized eigensolver based on smoothed aggregation
(GES-SA) for initializing smoothed aggregation multigrid (SA)*, J. Num. Lin.
Alg. Appl. 15 (2008), pp. 249-270 (M.
Brezina, T. Manteuffel, J. Ruge, G. Sanders, and P. Vassilevski).

180. *Smoothed aggregation multigrid for Markov chains*, SIAM J. Sci.
Comp. 32 (2010), pp. 40-61 (with H. de Sterck, T. Manteuffel, J. Pearson, J. Ruge,
and G. Sanders).

181. *First-order system least squares for resistive magnetohydrodynamics*,
SIAM J. Sci. Comp. 32 (2010), pp. 229-248 (with J. Adler, T. Manteuffel, and J. Ruge).

182. *Towards adaptive smooth aggregation (*a*SA) for nonsymmetric problems*, SIAM J. Sci. Comp. 32 (2010),
pp. 14-39 (with M. Brezina, T. Manteuffel,
J. Ruge, and G. Sanders).

183. *Least-squares finite element methods for quantum electrodynamics,* SIAM
J. Sci. Comp. 32 (2010), pp. 398-417 (with J. Brannick,
C. Ketelsen, and T. Manteuffel).

184. *Enhanced
mass conservation in least-squares methods*, SIAM J. Sci. Comp. 31 (2009),
pp. 2303-2321 (with J. Heys, E. Lee, T. Manteuffel, and J. Ruge).

185. *The removal of critical slowing down,* Procs. XXVI IntÕl Symp. On Lattice Field Thoery,
July 14-19, 2008 (with J. Brannick, M. A. Clark, R.
C. Brower, T. Manteuffel, J. C. Osborn, and C. Rebbi).

186. *Weighted least-squares
finite elements for particle imaging velocimetry analysis*, JCP 229 (2010), pp. 107-118 (with M. Belohlavek, J. Heys,
T. Manteuffel, M. Milano, and E. McMahon).

187. *Algebraic multigrid for Markov chains*, SIAM
J. Sci. Comp. 32 (2010), pp. 544-562 (with H. de Sterck,
T. Manteuffel, K. Miller, J. Ruge,
and G. Sanders).

188. *Further results on error estimators for
local refinement with first-order system least squares (FOSLS)*, J. Num.
Lin. Alg. Appl. 17 (2010), pp. 387-413 (with T. Manteuffel,
J. Nolting, J. Ruge, and G.
Sanders).

189. *Operator-based interpolation for bootstrap
algebraic multigrid*, J. Num. Lin. Alg. Appl. 17 (2010), pp. 519-537 (with
T. Manteuffel, M. Park, and J. Ruge).

190. *Finite element methods for quantum electrodynamics
using a Helmholtz decomposition of the gauge field*, J. Num. Lin.
Alg. Appl. 17 (2010), pp. 539-556 (with C. Ketelsen,
T. Manteuffel, and J. Ruge).

191. *Nested
iteration and first-order system least squares for incompressible, resistive magnetohydrodynamics*, SIAM J. Sci. Comp. 32
(2010), pp. 1506-1526 (with J. Adler,
T. Manteuffel, J. Ruge, and
G. Sanders).

192. *An
efficiency-based adaptive refinement scheme applied to incompressible,
resistive magnetohydrodynamics*, Lecture
Notes in Computer Science 5910 (2010), pp. 1-13 (with J. Adler, T. Manteuffel,
J. Nolting, J. Ruge, and L.
Tang).

193. *Efficiency-based
adaptive local refinement for first-order system least-squares formulations*,
SIAM
J. Sci. Comp. 33 (2011), pp. 1-24 (with J. Adler, T. Manteuffel, J. Nolting, J. Ruge, and L. Tang).

194. *Adaptive
multigrid algorithm for the lattice Wilson-Dirac operator*, Physical
Review Letters 105 (2010), pp. 1-4 (with R. Babich, J. Brannick,
R. Brower, M. Clark, T. Manteuffel, J. Osborn, and C.
Rebbi).

195.* Relaxation-corrected bootstrap algebraic
multigrid*, J. Num. Lin. Alg. Appl. 19 (2012), pp.
178-193 (with M. Brezina, C. Ketelsen,
M. Park, T. Manteuffel, and J. Ruge).

196. *Parallel
adaptive mesh refinement for first-order system least squares*, J. Num.
Lin. Alg. Appl. 19 (2012), pp. 343-366 (with M. Brezina, J. Garcia, T. Manteuffel,
J. Ruge, and
L. Tang).

197. *Hybrid first-order
system least squares finite element methods with application to Stokes
equations*, SIAM J. Num. Anal. 51 (2013), pp. 2214-2237
(with K. Liu, T. Manteuffel, J. Ruge,
and L. Tang).

198. *Island coalescence using
parallel first-order system least squares on incompressible resistive **magnetohydrodynamics*, SIAM
J. Sci. Comp. 35 (2013), pp. 171-191
(with J.
Adler, M. Brezina, T. Manteuffel,
J. Nolting, J. Ruge, and L.
Tang).

199. *Algebraic multigrid domain
and range decomposition (AMG-DD/AMG-RD)*, SIAM J.
Sci. Comp. 37
(2015), pp. 113-136 (with R. Bank, R. Falgout, T. Jones, T. Manteuffel,
and J. Ruge).

200. *Smoothed
aggregation algebraic multigrid for SPDE problems with layered materials**, *J. Num. Lin. Alg. Appl. 21 (2013), pp.
239-255 (with M. Brezina, A. Doostan,
T. Manteuffel, and J. Ruge).

201. *Fully
implicit ultrascale physics solvers and application
to ion source modelling, *IEEE Transactions on Plasma Science 4
(2015), pp. 957-964 (with K. Beckwith, J. Calhoun, L. Olson, J. Ruge, and S. Veitzer).

202. *Hybrid first-order system least (FOSLS/FOSLL*)*, Proceedings of the 11^{th}
International Conference on Numerical Analysis and Applied Mathematics, ICNAAM
2013, Rhodes, Greece, September 21-27, 2013 (with K. Liu, T. Manteuffel, J. Ruge, and L. Tang).

203. *Smoothed aggregation multigrid for cloth simulation*, ACM
Trans. Graph. 34 (2015) (with R. Tamstorf and
T. Jones).

204. *A low communication, parallel algorithm for solving
PDEs based on range decomposition*, J. Num.
Lin. Alg. Appl. (2016), to appear (with
D. Appelhans, T. Manteuffel,
and J. Ruge).

205. *Fully implicit solution methods for fluid plasma
equations with physics-based preconditioning*, Procs. ICOPS (2014) (with K. Beckwith,
E. Hallman, J. King, and J. Ruge).

**PH. D. STUDENTS**

1979 D. Longsine, *Simultaneous
optimization of the Rayleigh quotient for Ax = **lBx*

1981 J. Ruge, *Multigrid for eigenproblems, variational problems, and multigrid simulation*

1982 S. Schaffer, *Higher-order
multigrid methods*

1989 C. Liu, *Multilevel
adaptive methods in computational fluid dynamics*

1990 Z. Cai, *A theoretical foundation for the finite
volume element method*

1993 Z. Liu, *Multilevel
methods for flow transition*

1993 D. Quinlan, *Adaptive
mesh refinement for distributed parallel architectures*

1995 J. Jones, *Multilevel
methods for mixed finite element applications*

1996 B. Lee, *Multilevel
methods for first-order system least squares*

1999 M. Berndt, *Parallel
multilevel adaptive methods*

2001 A. Codd,
*First-order system least squares (FOSLS)
for elliptic grid generation (EGG)*

2001 T. Chartier,
*Algebraic multigrid based on element
interpolation (AMGe) and spectral AMGe*

2001 B. Philip, *Asynchronous fast adaptive composite grid
methods for elliptic problems on adaptively-refined curvilinear grids*

2001 H. MacMillan, *First-order system least squares for
electrical impedance tomography* (Co-advisor)

2003 L. Olson, *Least-squares methods for hyperbolic
problems *(Co-advisor)

2004 S. MacLachlan,
*Adaptive algebraic multigrid methods and
homogenization*

2004 C. Westphal,
*Least-squares methods for nonlinear
elasticity *(Co-advisor)

2004 O. Ršhrle, *Multilevel
first-order system least squares for nonlinear PDEs*

2005 J. Brannick, *Adaptive algebraic multigrid methods*

2010 M. Park, *Relaxation-corrected bootstrap algebraic multigrid (**rBAMG**)*

2014 T.
Jones, *Algebraic multigrid domain
and range decomposition (AMG-DD/AMG-RD)*

**RESEARCH INTERESTS**

Multilevel methods, partial differential equations, integral equations, computational fluid dynamics, adaptive mesh refinement methods, iterative schemes in general, least squares problems, eigenvalue problems, image reconstruction, human organ simulation, math software, vector and parallel supercomputing, inverse problems, particle transport, structural analysis, plasma physics, combustion, and quantum chromdynamics.