Professor Allen is UW’s Vice President for Academic Affairs.  In this role, Professor Allen is the university's chief academic officer, responsible for the university's academic budget, academic planning, curriculum, outreach mission, and academic personnel decisions, including hiring, reappointment, tenure, and promotion.

His mathematical interests include numerical analysis, mathematical modeling, and fluid mechanics in porous media. Applications of these areas include the analysis and prediction of contaminant flows in groundwater aquifers and flows of native and injected fluids in oil and gas reservoirs.

Flows of this type obey a remarkable variety of partial differential equations, including equations of elliptic, parabolic, and hyperbolic type as well as nonlinear, coupled systems having mixed type. The equations generally require numerical solution. Numerical methods of interest include mixed finite elements, cell-centered finite-differences, Eulerian- Lagrangian methods such as the modified method of characteristics, streamline diffusion methods, and finite-volume methods.

All of these discrete approximation schemes yield large, sparse matrix equations. Solving them involves numerical linear algebra, including gradient-based methods, preconditioning, multigrid methods, and domain decomposition. Often accompanying the linear algebraic issues is the question of how best to exploit advanced and emerging computer architectures, such as massively parallel machines.

To model porous-media flows found in nature, one must address some physical issues that cause severe numerical difficulties. First, The equations are often nonlinear, so one must devise sensitive iterative schemes based, for example, on Newton's method. Second, the equations often have solutions with steep gradients, near which most numerical methods yield poor approximate solutions. Third, the equations sometimes include chemical or biological reactions, which involve complicated thermodynamic constraints or reaction-diffusion structures, such as traveling waves. Fourth, to accommodate natural geologic heterogeneity, one must account for differences in scale between the measurements used to determine model inputs and the computational grids used to solve the problems.

Representative Publications (from a total of over 60 scientific articles and 4 books):

A.S. Telyakovskiy and M.B. Allen, "Polynomial approximate solutions to the Boussinesq equation," Advances in Water Resources 29 (2006), 1767-1779.

A. Telyakovskiy and M.B. Allen, “Solving thermodynamic equilibrium constraints for vapor-liquid flows in porous media,” in Proceedings, XIV International Conference on Computational Methods in Water Resources, Delft, Netherlands, 23-28 June 2002, ed. by S.M. Hassanizadeh et al, Balkema, Rotterdam, 2002, 265-272.

L. Wu and M.B. Allen, "Two-grid method for mixed finite-element solution of coupled reaction-diffusion systems,"Numerical Methods for Partial Differential Equations 15 (1999), 589-604.

L. Wu and M.B. Allen, "A two-grid method for mixed finite-element solution of reaction-diffusion equations," Numerical Methods for Partial Differential Equations 15 (1999), 317-332.

M.B. Allen and E.L. Isaacson, Numerical Analysis for Applied Science, John Wiley and Sons, New York, 1998 (492 pages).

B.J. Suchomel, B.M. Chen, and M.B. Allen, Network model of flow, transport, and biofilm effects in porous media, Transport in Porous Media 30 (1998), 1-23.

M.B. Allen and F. Furtado, "Computational methods for porous-media flows," Chapter 6, Advances in Fluid Mechanics: Fluid Transport in Porous Media, ed. by J.P. du Plessis, Computational Mechanics Publications, Southampton, UK, 1997, pp. 255-302 (see www.witpress.com/acatalog/429X.html).

Other Activities

* Supervised 12 M.S students and 6 Ph.D. students to completion

* Served as Department Head in Mathematics, 1992 - 1998

* Served on 4 NSF panels from 2002 - 2007

* Received the Humphrey Award. (UW's highest faculty award)

* Serve on two international editorial boards

* Continue to teach a mathematics course each fall semester

* Volunteer as a ski patroller (National Appointment 10216), serving as instructor in outdoor emergency care, avalanche, and mountain travel and rescue