Donald L. Brown

University of Nottingham, UK


PhD in Applied Mathematics.
Texas A&M University, August, 2012
Dissertation Title:“ Multiscale Methods in Fluid-Structure Interaction” Advisor: Yalchin Efendiev (Math), Co-Advisor: Akhil Datta-Gupta (PeEng) GPA (3.75/4.0)

BA in Mathematical Sciences
University of Cincinnati, June, 2007 High Honors in Mathematical Sciences GPA (3.54/4.0)

Research interests:

Multiscale modeling and simulation of porous media with a focus on geoscience applications. Effective equations and modelling of mechanics in porous media applications. Multiscale finite element methods, multilevel upscaling in heterogeneous media. Data integration via reduced models.

Grants & Awards:

PI: Subsurface mechanical-chemical interactions Co-PI Veerle Vandiginste UofN , Chemistry Research Priority Area Grant Fund
University of Nottingham (Summer 2016, £6k)

Hausdorff Postdoctoral Fellowship University of Bonn, Germany (May 2014-September 2015)

Interpore-Fraunhofer Award for Young Researchers Fraunhofer Institute for Industrial and Appl. Math, Kaiserslautern, Germany (Summer 2013)

Institute for Applied Mathematics and Computational Science Fellowship Texas A&M University, College Station, TX via. KAUST grant (2010-2012)

L.F. Guseman Prize in Mathematics Texas A&M University, College Station, TX (May 2012)

National Science Foundation, East Asia Pacific Summer Institute Grant Nanyang Technological University, Singapore (Summer 2010)

National Science Foundation, IGERT Graduate Fellowship “Next-generation Computational and Analytical Tools for Materials” Texas A&M University, College Station TX (2007-2009)

Refereed journal publications:

Published or Submitted

”Homogenization of Stokes Flow in Slowly Varying Media with Application to Fluid-Structure Interaction”, 2011 Int. J. of Geomathematics Vol. 2, Iss. 2, D.L. Brown, P. Popov, Y. Efendiev

”An Efficient Hierarchical Multiscale Finite Element Method for Stokes Equations in Slowly Varying Media”, 2013 SIAM MMS 11-1 , pp. 30-58, D.L. Brown, V. H. Hoang, Y. Efendiev

”Effective Equations for Fluid-Structure Interaction with Applications to Poroelasticity”, 2013 Applicable Analysis 93-4, pp. 771-790, D.L. Brown, P. Popov, Y. Efendiev

”Homogenization of Brinkmann equations with High-Contrast Coefficients”, 2014, Multiscale Model. Simul., 13(2), 472490, D.L. Brown, G. Li, V.L. Savatorova, Y. Efendiev

”An Energy-Stable Convex Splitting for the Phase-Field Crystal Equation”, Computers & Structures Volume 158, 1 October 2015, Pages 355-368, P. Vignal, N. Collier, L. Dalcin, D.L. Brown, V. Calo

”Generalized Multiscale Finite Element Method for Poroelasticity Equations I: Linear Problems”, Journal of Computational and Applied Mathematics 294 Issue C, March 2016, 372-388. D.L. Brown, M. Vasilyeva

”Generalized Multiscale Finite Element Method for Poroelasticity Equations II: Nonlinear Coupling” Journal of Computational and Applied Mathematics 297 , 2016, 132-146. D.L. Brown, M. Vasilyeva

”On Multiscale Finite Elements for Neumann Problems in Porous Domains”, 2016, Disc. and Cont. Dyn. Sys Series S. 9(5), 1299-1326, V. Taralova, D.L. Brown

”A Multiscale Method for Porous Microstructures” 2016, Multiscale Model. Simul., 14(3), 11231152., D.L. Brown, D. Peterseim

”Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Me- dia”, 2017, Geofluids, Volume 2017, J. Li, D.L. Brown.

”Effective equations governing an active poroelastic medium”, 2017, Proceedings of the Royal Society A. Volume 473, Issue 2198, J. Collis, D.L. Brown, O. Reuben, M. Hubbard

”An energy-stable time-integrator for phase-field models”, 2017, Computer Methods in Applied Mechanics and Engineering. 316, 11791214, P. Vignal, N. Collier, L. Dalcin, D.L. Brown, V. Calo

”Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations” arXiv:1511.09244, (in press, LNCSE ), D. L. Brown, D. Gallistl, and D. Peterseim

”A Hierarchical Finite Element Monte Carlo Method for Stochastic Two-Scale Elliptic Equa- tions”, (in revision), D.L. Brown, V.H. Hoang

”Multiscale Method for High-Frequency Elastodynamics with Wavenumber Explicit Bounds”, arXiv:1608.04243, (submitted), D. L. Brown, D. Gallistl

Conference proceedings:

”On Two-Scale Convergence of Fluid-Structure Interaction Problems with Applications to Poroelasticity” 2017, Poromechanics VI, BIOT6 Poromechanics Conference Proceedings, Paris, France, J. Fellerman, D.L. Brown, M. Vasilyeva.

”Lattice Boltzmann Flow Simulations With Applications of Reduced Order Modeling Tech- niques.”, January 2014, 7th International Petroleum Technology Conference, Doha, Qatar, D.L. Brown, J.Li, V. Calo, M. Ghommem, Y. Efendiev

”On Multiscale Lattice Boltzmann Method for flow Simulations in Highly Heterogenous Porous Media.”, September 2013, SPE Reservoir Simulation Conference and Exhibition, Abu Dhabi, UAE, J. Li, D.L. Brown, V. Calo, Y. Efendiev, O. Iliev

”Multiscale Modeling of High Contrast Brinkman Equations with Applications to Deformable Porous Media”, July 2013, Poromechanics V, BIOT5 Poromechanics Conference, Vienna, Austria, D.L. Brown., G. Li, V.L. Savatorova, Y. Efendeiv, P. Popov

”Homogenization of High-Contrast Brinkman” February 2013, extended abstract, ”Mini Sym- posium” Numerical Upscaling for Media with Deterministic and Stochastic Heterogeneity”, Oberwolfach, Germany, D.L. Brown., G. Li, V.L. Savatorova, Y. Efendeiv