Linear/Nonlinear Equations and Multilevel Methods

This project is supported by

• the Army Research Office ,
• the US Army Waterways Experiment Station,
• the National Science Foundation,
• the US Dept of Education GAANN fellowship program, and
• a Cray Fellowship.

The resarch group at NCSU is

• Tim Kelley
• Ph. D. Students
  • Anne Costolanski
  • Kelly Dickson (kidickso@unity.ncsu.edu)
• Alumni
  • Jill Reese (2006) (jreese@scs.fsu.edu)
  • Greg Recine (Postdoc 2004--6) (grecine@stevens-tech.edu)
  • Matthew Lasater (2005) (mslasate@hotmail.com)
  • Chris Kees (Postdoc 2003--4) Christopher.E.Kees@erdc.usace.army.mil
  • Katie Fowler (nee Kavanagh) (2003) kfowler@clarkson.edu
  • Todd Coffey (2002) tscoffe@sandia.gov
  • Lea Jenkins (2000) lea@CLEMSON.EDU
  • Mike Tocci (1998) mtocci@mathworks.com
  • Jim Banoczi (1997) banoczi@erols.com
  • Zhaoqing Xue (1995) zxue@neiddd.com
  • Dongming Hwang (1991) dongming@us.ibm.com
  • Lakshmi Mukundan (1991) Lakshmi_Mukundan@ferris.edu
  • Jim Northrup (1988)

Collaborators at NCSU include Steve Campbell , Pierre Gremaud , Ilse Ipsen, and Carl Meyer.

We collaborate with Cass T. Miller and his group in the Department of Environmental Sciences and Engineering at the University of North Carolina , a large group in the Costal and Hydraulics Laboratory at the US Army Engineer Research and Development Center in Vicksburg Mississippi , Jill Reese at Florida State, Monte Pettit from the University of Houston, Hong-Liang Cui from Stevens Institute, and Dwight Woolard from the Army Research Office .

Publications

• K. I. Dickson, C. T. Kelley, I. C. F. Ipsen, and I. G. Kevrekidis,
  Condition Estimates for Pseudo-Arclength Continuation, SIAM J. Numer. Anal. 45 (2007), 263-276.

• M. S. Lasater, C. T. Kelley, A. Salinger, D. L. Woolard, G. Recine, and P. Zhao,
  Analysis of A Scalable Preconditioner for the Wigner-Poisson Equation Int J. Pure Appl Math., 37 (2007), 247-270.

• L. Qiao, R. Erban, C. T. Kelley, and I. G. Kevrekidis,
  Spatially distributed stochastic systems: equation free and equation assisted preconditioned computation, J. Chem. Phys, 125 (2006), paper 204108, 8 pages.

• M. S. Lasater, C. T. Kelley, A. Salinger, D. L. Woolard, and P. Zhao,
  Parallel Parameter Study of the Wigner-Poisson Equations for RTDs Computers and Mathematics with Applications, 51 (2006), 1677--1688.

• Simulating Non-Darcy Flow through Porous Media using Sundance
  J. P. Reese, Kevin Long, C. T. Kelley, C. T. Miller, and W. G. Gray, Proceedings of Computational Methods in Water Resources XVI, Paper number 256, 8 pages, 2006

• Nonlinear multilevel iterative methods for multiscale models of air/water flow in porous media
  J. P. Reese, Kevin Long, C. T. Kelley, C. T. Miller, and W. G. Gray, Proceedings of Computational Methods in Water Resources XVI, Paper number 148, 8 pages, 2006

• K. R. Kavanagh and C. T. Kelley,
  Pseudo-transient Continuation for Nonsmooth Nonlinear Equations ,
  SIAM J. Numer. Anal., (43) 2005, 1385-1406.
• M. S. Lasater, C. T. Kelley, A. Salinger, D. L. Woolard, and P. Zhao, Parallel Solution of the Wigner-Poisson Equations for RTDs In 2004 International Symposium on Distributed Computing and Applications to Business, Engineering and Science, Wuhan, China, 2004, pp 672--676.

• C. T. Kelley and B. Montgomery Pettitt, A Fast Algorithm for the Ornstein-Zernike Equations,
  Journal of Computational Physics, (197), 2004, 491--501.

  C. T. Kelley, K. R. Kavanagh, and C. E. Kees, Simulation of Nondifferentiable Models for Groundwater Flow and Transport , Proceedings of Computational Methods in Water Resources XV, C. T. Miller, M. W. Farthing, W. G. Gray, and G. F. Pinter, eds, Elsevier, Amsterdam, 2004, pp. 939-952.

• T. Coffey, C. T. Kelley, and D. E. Keyes, Pseudo-Transient Continuation and Differential-Algebraic Equations,
  SIAM J. Sci. Comp. (25), 2003, 553--569.

• C. E. Kees, C. T. Miller, E. W. Jenkins, and C. T. Kelley, Versatile Multilevel Schwarz Preconditioners for Multiphase Flow
  Comp. Geo, 7, 2003, 91-114.

• T. S. Coffey, R. J. McMullan, C. T. Kelley, and D. S. McRae, Globally Convergent Algorithms for Nonsmooth Nonlinear Equations in Computational Fluid Dynamics
  J. Comp. Appl. Math., 152, 2003, 69-81.

• J. F. Kanney, C. T. Miller, and C. T. Kelley,
  Convergence of Iterative Split Operator Approaches for Approximating Nonlinear Reactive Transport Problems
  Advances in Water Resources, 26, 2003, 247-261.

• M. I. Lasater, P. Zhao, C. T. Kelley, and D. L. Woolard, Numerical Tools for the Study of Instabilities within the Positive-Differential-Resistance Regions of Tunnelling Devices Proceedings of 2003 IEEE Conference on Nanotechnology, San Francisco, CA, August 12--14, 2003, pp 390-393.

• C. T. Kelley, D. L. Woolward, P. Zhao, M. Kerr, and M. S. Lasater, Parallel-Platform Based Numerical Simulation of Instabilities in Nanoscale Tunneling Devices , Proceedings of 2002 2nd IEEE Conference on Nanotechnology, Washington DC, August 26-28, 2002, IEEE, 2002, pp 417--421.

• K. R. Kavanagh, C. T. Kelley, R. C. Berger, J. P. Hallberg, and Stacy E. Howington,
  Nonsmooth Nonlinearities and Temporal Integration of Richards' Equation ,
  Proceedings of the XIV International Conference on Computational Methods in Water Resources, S. Majid Hassanizadeh, Ruud J. Schotting, W. G. Gray, and G. F. Pinder, editors, 2002, pp 947-954.
• C. T. Miller and M. W. Farthing and C. E. Kees and C. T. Kelley,
  Higher Order, Locally Conservative, Temporal Integration Methods for Multiphase Flow in Porous Media,
  Proceedings of the XIV International Conference on Computational Methods in Water Resources, S. Majid Hassanizadeh, Ruud J. Schotting, W. G. Gray, and G. F. Pinder, editors, 2002, pp 249-256.
• E. W. Jenkins, C. T. Kelley, C. T. Miller, and C. E. Kees,
  An Aggregation-based Domain Decomposition Preconditioner for Groundwater Flow
  SIAM J. Sci. Comp., (23), 2001, 430-441.
• P. A. Gremaud, C. T. Kelley, T. A. Royal, and K. A. Coffey, On a Powder Consolodation Problem ,
  SIAM J. Appl. Math., (62), 2001, 1-20.

• W. R. Ferng and C. T. Kelley, Mesh independence of matrix-free methods for path following
  SIAM J. Sci. Comp., (21), 2000, 1835--1850.

• G. A. Williams, C. T. Miller, and C. T. Kelley, Transformation Approaches for Simulating Flow in Variably Saturated Porous Media, Water Resources Research, (36), 2000, 923-934.

• E. W. Jenkins, R. C. Berger, J. P. Hallberg, S. E. Howington, C. T. Kelley, J. H. Schmidt, A. K. Stagg, and M. D. Tocci, A Two-Level Aggregation-Based Newton-Krylov-Schwarz Method for Hydrology in Parallel Computational Fluid Dynamics 1999, D. E. Keyes, A. Ecer, J. Periaux, and N. Satofuka, eds., North Holland, 2000, pp. 257--264.

• C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, no. 16 in SIAM Frontiers in Applied Mathematics. SIAM, Philadelphia, 1995.
• J. M. Banoczi and C. T. Kelley, A Fast Multilevel Algorithm for the Solution of Nonlinear Systems of Conductive-Radiative Heat Transfer Equations in Two Space Dimensions, SIAM J. Sci. Comp., (20), 1999, 1214--1228.
• M. D. Tocci, C. T. Kelley, C. T. Miller, and C. E. Kees, Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions,
  Computational Geosciences, (2), 1998, 291-310.
• Robust Solution of Richards' Equation for Non-Uniform Porous Media, (with C. T. Miller, G. A. Williams, and M. D. Tocci), Water Resources Research, (34) 1998, 2599-2610.
• Convergence Analysis of Pseudo-Transient Continuation (with D. E. Keyes), SIAM J. Numer. Anal, (35) 1998, 508-523.
• A Fast Multilevel Algorithm for the Solution of Nonlinear Systems of Conductive-Radiative Heat Transfer Equations (with J. M. Banoczi), SIAM J on Sci. Comp., (19), 1998, 266-279.
• Termination of Newton/Chord Iterations and the Method of Lines , (with M.D. Tocci and C.T. Miller), SIAM J on Sci. Comp., (19), 1998, 280-290.
• Accurate and Economical Solution of the Pressure Head Form of Richards' Equation by the Method of Lines , (with M.D. Tocci and C.T. Miller), Advances in Water Resources, (20), 1997, 1-14.
• GMRES and the Minimal Polynomial, (with S. L. Campbell, I. C. F. Ipsen, and C. D. Meyer), BIT, (36), 1996, 664-675.
• Existence and Uniqueness of Solutions of Nonlinear Systems of Conductive-Radiative Heat Transfer Equations Journal of Transport Theory and Stat. Phys., (25), 1996, 249-260.
• Convergence Estimates for Solution of Integral Equations with GMRES, (with S. L. Campbell, I. C. F. Ipsen, C. D. Meyer, and Z. Q. Xue) Journal of Integral Equations and Applications, (8), 1996, 19-34.
• GMRES and Integral Operators , (with Z. Q. Xue), SIAM J. Sci. Comp. (17), 1996, 217-226.
• A Fast Multilevel Algorithm for Integral Equations, SIAM J. Numer. Anal. (32), 1995, 501-513.
• Multilevel Source Iteration Accelerators for the Linear Transport Equation in Slab Geometry,
  Trans. Th. Stat. Phys. (24), 1995, 679-708.

CRSC Tech Reports

• Condition Estimates for Pseudo-Arclength Continuation
  K. I. Dickson, C. T. Kelley, I. C. F. Ipsen, and I. G. Kevrekidis, March 2006

• Pseudo-Transient Continuation and Optimization
  C. T. Kelley, L. Qi, L-Z. Liao, J. P. Reese, and C. Winton, March 2006

• CRSC-TR05-21 A Scalable Preconditioner for a Parametric Study of the {W}igner-{P}oisson Equations for Resonant Tunneling Diodes ,
  P. Zhao, D. L. Woolard, M. S. Lasater, and C. T. Kelley, April, 2005

• CRSC-TR05-10 Simulating Nanoscale Devices ,
  M. S. Lasater, C. T. Kelley, A. Salinger, P. Zhao, and D. L. Woolard, February, 2005.

• CRSC-TR05-09 Steady state determination of chemical process plants by legacy dynamic process models,
  A. Kavouras, C. Georgakis, I. G. Kevrekidis, and C. T. Kelley, January, 2005.

• CRSC-TR05-07 Multilevel wavelet solver for the Ornstein-Zernike equation,
  M. V. Federov, G. N. Chuev, C. T. Kelley, and B. Montgomery Pettitt.
  

• CRSC-TR05-04 Parallel Parameter Study of the Wigner-Poisson Equations for RTDs
  M. S. Lasater, C. T. Kelley, A. Salinger, D. L. Woolard, and P. Zhao,
  

• CRSC-TR04-34 Enhancement of Numerical Computations of the Wigner-Poisson Equations for Application to the Simulation of THz-Frequency RTD Oscillators
  M. S. Lasater, C. T. Kelley, A. Salinger, D. L. Woolard, and P. Zhao,
  To appear in Proceedings of Optics East 2004.

• CRSC-TR04-10: Newton-Krylov solvers for time-steppers
  C. T. Kelley, I. G. Kevrekidis, and L. Qiao
• CRSC-TR03-47: Simulation of Nondifferentiable Models for Groundwater Flow and Transport ,
  C. T. Kelley, K. R. Kavanagh, and C. E. Kees, December 2003
• CRSC-TR03-29: Pseudo-transient Continuation for Nonsmooth Nonlinear Equations ,
  K. R. Fowler and C. T. Kelley, July 2003
  To appear in SIAM J. Numer. Anal.
• CRSC-TR03-23: Numerical Tools for the Study of Instabilities within the Positive-Differential-Resistance Regions of Tunnelling Devices,
  M. I. Lasater, P. Zhao, C. T. Kelley, and D. L. Woolard, June, 2003.
• CRSC-TR02-21: Parallel-Platform Based Numerical Simulation of Instabilities in Nanoscale Tunneling Devices,
  C. T. Kelley, D. L. Woolward, P. Zhao, M. Kerr, and M. S. Lasater, July, 2002.
• CRSC-TR02-18: Pseudo-Transient Continuation and Differential-Algebraic Equations,
  T. Coffey, C. T. Kelley, and D. E. Keyes, July, 2002.
• CRSC-TR02-12: A Fast Algorithm for the Ornstein-Zernike Equations,
  C. T. Kelley and B. Montgomery Pettitt, April, 2002.
• CRSC-TR02-06: Convergence of Iterative Split Operator Approaches for Approximating Nonlinear Reactive Transport Problems
  J. F. Kanney, C. T. Miller, and C. T. Kelley, March 2002.
• CRSC-TR02-02: Higher Order, Locally Conservative, Temporal Integration Methods for Multiphase Flow in Porous Media
  C. T. Miller, M. W. Farthing, C. E. Kees, and C. T. Kelley, February, 2002
• CRSC-TR02-01: Nonsmooth Nonlinearities and Temporal Integration of Richards' Equation
  K. R. Kavanagh, C. T. Kelley, R. C. Berger, J. P. Hallberg, and Stacy E. Howington, January, 2002
• CRSC-TR01-32: Versatile Multilevel Schwarz Preconditioners for Multiphase Flow
  C. E. Kees, C. T. Miller, E. W. Jenkins, and C. T. Kelley, December, 2001
• CRSC-TR01-28: Globally Convergent Algorithms for Nonsmooth Nonlinear Equations in Computational Fluid Dynamics T. S. Coffey, R. J. McMullan, C. T. Kelley, and D. S. McRae, October, 2001
• CRSC-TR00-13: An Aggregation-based Domain Decomposition Preconditioner for Groundwater Flow
  E. W. Jenkins, C. T. Kelley, C. T. Miller, and C. E. Kees, May, 2000.
• CRSC-TR99-32: Newton-Krylov-Schwarz Methods for Richards' Equation
  E. W. Jenkins, R. C. Berger, J. P. Hallberg, S. E. Howington, E. W. Jenkins, C. T. Kelley, J. H. Schmidt, A. K. Stagg, and M. D. Tocci, October 1999.
• CRSC-TR99-27: A Model to Simulate the Interaction between Groundwater and Surface Water
  S. E. Howington, R. C. Berger, J. P. Hallberg, J. F. Peters, A. K. Stagg, E. W. Jenkins, and C. T. Kelley, August 1999.
• CRSC-TR99-25: A Two-Level Aggregation-Based Newton-Krylov-Schwarz Method for Hydrology
  E. W. Jenkins, R. C. Berger, J. P. Hallberg, S. E. Howington, C. T. Kelley, J. H. Schmidt, A. K. Stagg, and M. D. Tocci, August, 1999.
• CRSC-TR98-20: Mesh independence of matrix-free methods for path following
  W. R. Ferng and C. T. Kelley, May 1998
• CRSC-TR98-11: Efficient and Robust Numerical Modeling of Variably Saturated flow in Layered Porous Media
  C. T. Miller, G. A. Williams, and C. T. Kelley, March, 1998.
• CRSC-TR98-01: Transformation Approaches for Simulating Flow in Variably
  Saturated Porous Media
  G. A. Williams, C. T. Miller, and C. T. Kelley, January, 1998.

• CRSC-TR97-34: Robust Solution of Richards' Equation for Non-Uniform Porous Media,
  C. T. Miller, G. A. Williams, C. T. Kelley, and M. D. Tocci, November, 1997.

• CRSC-TR97-36: Inexact Newton methods and the method of lines for solving
  Richards' equation in two space dimensions,
  M. D. Tocci, C. T. Kelley, C. T. Miller, and C. E. Kees, November, 1997.

• CRSC-TR97-15: A Fast Multilevel Algorithm for the Solution of Nonlinear Systems of Conductive-Radiative Heat Transfer Equations in Two Space Dimensions
  J. M. Banoczi and C. T. Kelley
  June, 1997.

• CRSC-TR96-21: Convergence Analysis of Pseudo-Transient Continuation
  C. T. Kelley and David K. Keyes
  June, 1996.
  

• CRSC-TR96-19: Termination of Newton/Chord Iterations and the Method of Lines
  C. T. Kelley, C. T. Miller, and M. D. Tocci
  May, 1996.
  

• CRSC-TR96-18: Consistent Initial Conditions for Unstructured Higher Index DAEs: A Computational Study
  S. L. Campbell, C. T. Kelley, and K. D. Yeomans
  May, 1996.

• CRSC-TR96-17: A Fast Multilevel Algorithm for the Solution of Nonlinear Systems of Conductive-Radiative Heat Transfer Equations
  J. M. Banoczi and C. T. Kelley, May, 1996.
  

• CRSC-TR95-28: ACCURATE AND ECONOMICAL SOLUTION OF THE PRESSURE-HEAD FORM OF RICHARDS' EQUATION BY THE METHODS OF LINES
  M.D. Tocci, C.T. Kelley, and C.T. Miller
  August, 1995

• CRSC-TR95-13: CONVERGENCE ESTIMATES FOR SOLUTION OF INTEGRAL EQUATIONS WITH GMRES
  S.L. Campbell, I.C.F. Ipsen, C.T. Kelley, C.D. Meyer and Z.Q. Xue
  March, 1995

• CRSC-TR95-5 : EXISTENCE AND UNIQUENESS OF SOLUTIONS OF NONLINEAR SYSTEMS OF CONDUCTIVE-RADIATIVE HEAT TRANSFER EQUATIONS
  C.T. Kelley
  January, 1995