Linear and Nonlinear Equations
This is a summary of our activity in equation solving and optimization.
This work involves multilevel methods, Krylov methods, and global convergence.
Some of this activity is related to my work on
porous media flow .
This project is supported by
The resarch group at NCSU is

Tim Kelley
 Ph. D. Students
 Postdocs
 Alumni

Kelly Dickson (2008) (kidickso@unity.ncsu.edu)
 Jill Reese (2006) (jreese@scs.fsu.edu)
 Greg Recine (Postdoc 20046) (grecine@stevenstech.edu)
 Matthew Lasater (2005) (mslasate@hotmail.com)
 Chris Kees (Postdoc 20034) 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,
HongLiang 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 PseudoArclength Continuation,
SIAM J. Numer. Anal. 45 (2007), 263276.

M. S. Lasater, C. T. Kelley, A. Salinger,
D. L. Woolard, G. Recine, and P. Zhao,
Analysis of
A Scalable Preconditioner for the WignerPoisson Equation
Int J. Pure Appl Math., 37 (2007), 247270.

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 WignerPoisson Equations for RTDs
Computers and Mathematics with Applications, 51 (2006), 16771688.

Simulating NonDarcy 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,
Pseudotransient Continuation for Nonsmooth Nonlinear Equations ,
SIAM J. Numer. Anal., (43) 2005, 13851406.

M. S. Lasater, C. T. Kelley, A. Salinger, D. L. Woolard, and P. Zhao,
Parallel Solution of the WignerPoisson Equations for RTDs
In 2004 International Symposium on
Distributed Computing and Applications to
Business, Engineering and Science, Wuhan, China,
2004,
pp 672676.

C. T. Kelley and B. Montgomery Pettitt,
A Fast Algorithm for the OrnsteinZernike Equations,
Journal of Computational Physics, (197), 2004, 491501.
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. 939952.

T. Coffey, C. T. Kelley, and D. E. Keyes,
PseudoTransient Continuation and DifferentialAlgebraic Equations,
SIAM J. Sci. Comp. (25), 2003, 553569.

C. E. Kees, C. T. Miller, E. W. Jenkins, and C. T. Kelley,
Versatile Multilevel Schwarz Preconditioners for Multiphase Flow
Comp. Geo, 7, 2003, 91114.

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, 6981.

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, 247261.

M. I. Lasater, P. Zhao, C. T. Kelley, and D. L. Woolard,
Numerical Tools for the Study of Instabilities within the
PositiveDifferentialResistance Regions of Tunnelling Devices
Proceedings of 2003 IEEE Conference on Nanotechnology,
San Francisco, CA, August 1214, 2003, pp 390393.

C. T. Kelley, D. L. Woolward, P. Zhao, M. Kerr, and M. S. Lasater,
ParallelPlatform Based Numerical Simulation of Instabilities
in Nanoscale Tunneling Devices ,
Proceedings of 2002 2nd IEEE Conference on Nanotechnology,
Washington DC, August 2628, 2002, IEEE, 2002, pp 417421.

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 947954.

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 249256.

E. W. Jenkins, C. T. Kelley, C. T. Miller, and C. E. Kees,
An Aggregationbased
Domain Decomposition Preconditioner for Groundwater Flow
SIAM J. Sci. Comp., (23), 2001, 430441.

P. A. Gremaud, C. T. Kelley, T. A. Royal, and K. A. Coffey,
On a Powder Consolodation Problem
,
SIAM J. Appl. Math., (62), 2001, 120.

W. R. Ferng and C. T. Kelley,
Mesh independence of matrixfree methods for path following
SIAM J. Sci. Comp., (21), 2000, 18351850.

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, 923934.

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 TwoLevel
AggregationBased NewtonKrylovSchwarz Method for Hydrology
in
Parallel Computational Fluid Dynamics 1999,
D. E. Keyes, A. Ecer, J. Periaux, and
N. Satofuka, eds., North Holland, 2000, pp. 257264.

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
ConductiveRadiative Heat Transfer Equations in Two Space
Dimensions,
SIAM J. Sci. Comp., (20), 1999, 12141228.

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, 291310.

Robust Solution of Richards' Equation for NonUniform Porous Media,
(with C. T. Miller, G. A. Williams, and M. D. Tocci),
Water Resources Research, (34) 1998, 25992610.

Convergence Analysis of PseudoTransient Continuation
(with D. E. Keyes),
SIAM J. Numer. Anal, (35) 1998, 508523.

A Fast Multilevel Algorithm for the
Solution of Nonlinear Systems of
ConductiveRadiative Heat Transfer Equations
(with J. M. Banoczi),
SIAM J on Sci. Comp., (19), 1998, 266279.

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, 280290.

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, 114.

GMRES and the Minimal Polynomial,
(with S. L. Campbell, I. C. F. Ipsen, and C. D. Meyer),
BIT, (36), 1996, 664675.

Existence and Uniqueness of Solutions of Nonlinear Systems of
ConductiveRadiative Heat Transfer Equations
Journal of Transport Theory and Stat. Phys., (25), 1996, 249260.

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, 1934.

GMRES and Integral Operators , (with Z. Q. Xue),
SIAM J. Sci. Comp. (17), 1996, 217226.
 A Fast Multilevel Algorithm for Integral Equations,
SIAM J. Numer. Anal. (32), 1995, 501513.
 Multilevel Source Iteration Accelerators
for the Linear Transport Equation in Slab Geometry,
Trans. Th. Stat. Phys. (24), 1995, 679708.
CRSC
Tech Reports

Condition Estimates for PseudoArclength Continuation
K. I. Dickson, C. T. Kelley, I. C. F. Ipsen, and I. G. Kevrekidis,
March 2006

PseudoTransient Continuation and Optimization
C. T. Kelley, L. Qi, LZ. Liao, J. P. Reese, and C. Winton,
March 2006

CRSCTR0521
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

CRSCTR0510
Simulating Nanoscale Devices ,
M. S. Lasater, C. T. Kelley, A. Salinger,
P. Zhao, and D. L. Woolard,
February, 2005.

CRSCTR0509
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.

CRSCTR0507
Multilevel wavelet solver for the OrnsteinZernike equation,
M. V. Federov, G. N. Chuev, C. T. Kelley, and B. Montgomery Pettitt.

CRSCTR0504
Parallel Parameter Study of the WignerPoisson Equations for RTDs
M. S. Lasater, C. T. Kelley, A. Salinger,
D. L. Woolard, and P. Zhao,

CRSCTR0434
Enhancement of Numerical Computations of the WignerPoisson
Equations for Application to the Simulation of THzFrequency
RTD Oscillators
M. S. Lasater, C. T. Kelley, A. Salinger,
D. L. Woolard, and P. Zhao,
To appear in Proceedings of Optics East 2004.

CRSCTR0410:
NewtonKrylov solvers for timesteppers
C. T. Kelley, I. G. Kevrekidis, and L. Qiao

CRSCTR0347:
Simulation of Nondifferentiable Models for
Groundwater Flow and Transport ,
C. T. Kelley, K. R. Kavanagh, and C. E. Kees, December 2003

CRSCTR0329:
Pseudotransient Continuation for Nonsmooth Nonlinear Equations ,
K. R. Fowler and C. T. Kelley, July 2003
To appear in SIAM J. Numer. Anal.

CRSCTR0323:
Numerical Tools for the Study of Instabilities within the
PositiveDifferentialResistance Regions of Tunnelling Devices,
M. I. Lasater, P. Zhao, C. T. Kelley, and D. L. Woolard,
June, 2003.

CRSCTR0221:
ParallelPlatform 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.

CRSCTR0218:
PseudoTransient Continuation and DifferentialAlgebraic Equations,
T. Coffey, C. T. Kelley, and D. E. Keyes,
July, 2002.

CRSCTR0212:
A Fast Algorithm for the OrnsteinZernike Equations,
C. T. Kelley and B. Montgomery Pettitt,
April, 2002.

CRSCTR0206:
Convergence of Iterative Split Operator Approaches for
Approximating Nonlinear Reactive Transport Problems
J. F. Kanney, C. T. Miller, and C. T. Kelley,
March 2002.

CRSCTR0202:
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

CRSCTR0201:
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

CRSCTR0132:
Versatile Multilevel Schwarz Preconditioners for Multiphase Flow
C. E. Kees, C. T. Miller, E. W. Jenkins, and C. T. Kelley,
December, 2001

CRSCTR0128:
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

CRSCTR0013:
An Aggregationbased
Domain Decomposition Preconditioner for Groundwater Flow
E. W. Jenkins, C. T. Kelley, C. T. Miller, and C. E. Kees, May, 2000.
 CRSCTR9932:
NewtonKrylovSchwarz 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.
 CRSCTR9927:
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.

CRSCTR9925:
A TwoLevel
AggregationBased NewtonKrylovSchwarz 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.

CRSCTR9820:
Mesh independence of matrixfree methods for path following
W. R. Ferng and C. T. Kelley,
May 1998

CRSCTR9811:
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.
 CRSCTR9801:
Transformation Approaches for Simulating Flow in Variably
Saturated Porous Media
G. A. Williams, C. T. Miller, and C. T. Kelley,
January, 1998.

CRSCTR9734:
Robust Solution of Richards' Equation for NonUniform Porous Media,
C. T. Miller, G. A. Williams, C. T. Kelley, and M. D. Tocci,
November, 1997.

CRSCTR9736:
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.
 CRSCTR9715:
A Fast Multilevel Algorithm for the Solution of Nonlinear Systems of
ConductiveRadiative Heat Transfer Equations in Two Space Dimensions
J. M. Banoczi and C. T. Kelley
June, 1997.
 CRSCTR9621:
Convergence Analysis of PseudoTransient Continuation
C. T. Kelley and David K. Keyes
June, 1996.
 CRSCTR9619:
Termination of Newton/Chord Iterations and the Method of Lines
C. T. Kelley, C. T. Miller, and M. D. Tocci
May, 1996.
 CRSCTR9618:
Consistent Initial Conditions for Unstructured Higher Index
DAEs: A Computational Study
S. L. Campbell, C. T. Kelley, and K. D. Yeomans
May, 1996.
 CRSCTR9617:
A Fast Multilevel Algorithm for the
Solution of Nonlinear Systems of
ConductiveRadiative Heat Transfer Equations
J. M. Banoczi and C. T. Kelley, May, 1996.
 CRSCTR9528:
ACCURATE AND ECONOMICAL SOLUTION OF THE PRESSUREHEAD
FORM OF RICHARDS' EQUATION BY THE METHODS OF LINES
M.D. Tocci, C.T. Kelley, and C.T. Miller
August, 1995
 CRSCTR9513:
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
 CRSCTR955 :
EXISTENCE AND UNIQUENESS OF SOLUTIONS OF NONLINEAR SYSTEMS OF
CONDUCTIVERADIATIVE HEAT TRANSFER EQUATIONS
C.T. Kelley
January, 1995
Last modified: August 16, 2008