Stephen H. Brill

Publications in peer-reviewed journals:

Analytical Upstream Collocation Solution of a Quadratically Forced Steady-State Convection-Diffusion Equation by Stephen Brill and Eric Smith. International Journal of Numerical Methods for Heat and Fluid Flow Vol. 22, No. 4, pp. 436-457, 2012. Color figures in pdf

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. International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 19, No. 7, pp. 874-893, 2009.

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.

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.

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.