# 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 Equ**ations* 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.