long

November, 2024

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 für 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 viewpoint, 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. Böhmer).

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. Böhmer).

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 Int’l. 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. Multilevel 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. Böhmer 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, Int’l. 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 Int’l 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 Int’l 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 Int’l. 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. Int’l 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, Int’l. J. High Speed Comp. 2 (1990), pp. 331-334 (with U. Rüde).

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

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 Int’l 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, 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. Nat’l 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 Int’l 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 (aSA), 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 H¹-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. Röhrle).

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. Röhrle, 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. Röhrle).

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 (aSA) 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 (aAMGr), 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).

1435 +6+7 3 .0 ,9 8; :/< > 3 G =0G/ > =0 .9) > 1 EL. G* ? M 􀀀 > N;:*.0 O7,5 P7</QS + @5R; AB=0 AB3 "+ ,2CB!$D;)*: #%@0(*I )/+*EF </T <5=0 ,H!&G* 35. ,0

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 (aSA) 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 Int’l Symp. On Lattice Field Theory, 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. 24 (2017), e2041 (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).

206. Nonsymmetric reduction-based algebraic multigrid, SIAM J. Sci. Comp. 41 (2019), pp. 242-268 (with T. Manteuffel, S. Muenzenmaier, J. Ruge, and B. Southworth).

207. Physics-based preconditioners for fluid-plasma simulations with electromagnetics, Procs. ICOPS (2015) (with K. Beckwith, P. Stolz, and J. Ruge).

208. Discretization-error-accurate mixed-precision multigrid solvers, SIAM J. Sci. Comp. 43 (2021), pp. 420-447 (with J. Benzaken and R. Tamstorf).

209. Algebraic error analysis for mixed-precision multigrid solvers, SIAM J. Sci. Comp. 43 (2021), pp. 392-419 (with J. Benzaken and R. Tamstorf).

210. Nitsche's method for linear Kirchhoff-Love shells: formulation, error analysis, and verification, Comp. Methods Appl. Mech. Eng. 374 (2021), 113544 (with J. Benzaken, J. Evans, and R. Tamstorf).

211. Multigrid methods using block floating point arithmetic, SIAM J. Sci. Comp. 46 (2024), pp. 202-224 (with N. Kohl and R. Tamstorf).

212. Rounding error analysis of multigrid V-cycles, SIAM J. Sci. Comp. 46 (2024), pp. 88-95 (with R. Tamstorf).

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. Röhrle, 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.