Publications
(many available in Postscript
and PDF
formats):
Publications in peer-reviewed journals:
-
Analytical Solution of Hermite Collocation Discretization
of the Transient Convection-Diffusion Equation
by Stephen H. Brill
In preparation.
-
Optimal Hermite Collocation Applied to a One-Dimensional Convection-Diffusion
Equation Using an Adaptive Hybrid Optimization Algorithm
by Karen L. Ricciardi and Stephen H. Brill
Journal of
Optimization Theory and Applications, submitted 25 January 2007.
-
Optimal Collocation
Solution of the One-Dimensional Steady-State Convection-Diffusion Equation
with Variable Coefficients
by Stephen H. Brill
International Journal of Computational and
Numerical Analysis and Applications, Vol. 6, No. 3, pp 257-283, 2004.
-
Analytical Upstream Collocation Solution of a Forced
One-Dimensional Steady-State Convection-Diffusion
Equation
by Stephen H. Brill
International Journal of Differential Equations and Applications,
Vol. 7, No. 1, pp. 69-99, 2003.
-
Optimal Upstream Collocation Solution of the
One-Dimensional Steady-State Convection-Diffusion
Equation
by Stephen H. Brill
International Journal of Applied Mathematics,
Vol. 10, No. 2, pp. 197-215, 2002.
-
Analytical Solution of Hermite Collocation Discretization
of Self-Adjoint Ordinary Differential Equations
by Stephen H. Brill
International Journal of Differential Equations and
Applications,
Vol. 6, No. 1, pp. 1-18, 2002.
-
Parallel Implementation of the Bi-CGSTAB Method with
Block Red-Black Gauss-Seidel Preconditioner Applied
to the Hermite Collocation Discretization of
Partial Differential Equations
by Stephen H. Brill and George F. Pinder
Parallel Computing, Vol. 28, pp. 399-414, 2002.
-
Analytical Solution of Hermite Collocation Discretization
of the Steady-State Convection-Diffusion Equation
by Stephen H. Brill
International Journal of Differential Equations and
Applications,
Vol. 4, No. 2, pp. 141-155, 2002.
-
Analysis of a Block Red-Black
Preconditioner Applied to the
Hermite Collocation Discretization of
a Model Parabolic Equation
by Stephen H. Brill and George F. Pinder
Numerical Methods for Partial Differential Equations,
Vol. 17, No. 6, pp. 584-606, November 2001.
-
Eigenvalue Analysis of a Block Red-Black
Gauss-Seidel Preconditioner Applied to the
Hermite Collocation Discretization of
Poisson's Equation
by Stephen H. Brill and George F. Pinder
Numerical Methods for Partial
Differential Equations,
Vol. 17, No. 3, pp. 204-228, May 2001.
-
Hermite Collocation Solution of Partial Differential
Equations via Preconditioned Krylov Methods
by Stephen H. Brill
Numerical Methods for Partial
Differential Equations,
Vol. 17, No. 2, pp. 120-136, March 2001.
*********************************************************************************************************
Publications in conference proceedings, etc.:
-
A Family of Solutions for the One-Dimensional Transport Equation
by Stephen H. Brill
Proceedings of the
XVI International Conference on
Computational Methods in Water Resources, 2006.
-
Optimal Collocation Applied to a One-Dimensional Convection-Diffusion
Equation Using a Hybrid Optimization Algorithm
by Karen L. Ricciardi and Stephen H. Brill
Proceedings of the
XVI International Conference on
Computational Methods in Water Resources, 2006.
-
Optimal Upstream Collocation: A Survey of Recent Results
by Stephen H. Brill
Proceedings of the
XV International Conference on
Computational Methods in Water Resources, 2004.
-
The Analytical Solution of the Hermite Collocation Discretization
of the One-Dimensional Steady-State Convection-Diffusion Equation:
A Survey of Recent Results
by Stephen H. Brill
INRA/INEEL Subsurface Science Symposium,
2002.
-
Optimal Hermite Collocation
Solution of a Forced Convection-Diffusion Equation
by Stephen H. Brill and V.K. Stepanyan
Proceedings of the
XIV International Conference on
Computational Methods in Water Resources, 2002.
-
Optimal Upstream Collocation Solution of a Convection-Diffusion Equation
by Stephen H. Brill
INRA/INEEL Subsurface Science Symposium,
2001.
-
Solving Multiphase Equations from a Dynamical Systems
Point of View
by Stephen H. Brill
Proceedings of the
XIII International Conference on
Computational Methods in Water Resources,
2000.
-
The Bi-CGTAB Method with Red-Black
Gauss-Seidel Preconditioner
Applied to the Hermite Collocation
Discretization
of Subsurface Multiphase Flow and
Transport Problems
by Stephen H. Brill, Joseph F. Guarnaccia,
and George F. Pinder
Proceedings of the
XII International Conference on
Computational Methods in Water Resources,
1998.
-
Documentation for Collocation Software
by Stephen H. Brill
RCGRD Publication #98-01,
Research Center for Groundwater Remediation Design,
University of Vermont, Burlington, Vermont,
1998.
-
The Solution of Two-Dimensional Partial Differential Equations via Hermite
Collocation with Block Red-Black Gauss-Seidel Preconditioner
by Stephen H. Brill
Ph.D. dissertation,
University of Vermont, Burlington, Vermont,
1998.
-
A Parallel Preconditioned
Bi-Conjugate Gradient Algorithm
for Two-Dimensional Elliptic and Parabolic
Equations Using Hermite Collocation
by Stephen H. Brill and George F. Pinder
Proceedings of the Eighth SIAM Conference
on Parallel Processing for Scientific Computing,
1997.
-
A Block Red-Black SOR Method for a Two-Dimensional
Parabolic Equation Using Hermite Collocation
by Stephen H. Brill and George F. Pinder
The Mathematics of Finite Elements
and Applications
John Wiley & Sons Ltd., 1997.
This page was most recently updated on 16 November 2007.