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ARBOGAST, TODD

Todd J Arbogast

Professor, Core Faculty
Department of Mathematics, Institute for Computational Engineering and Science

W. A. "Tex" Moncrief, Jr. Simulation-Based Engineering and Sciences Professorship I

Numerical Analysis, Partial Differential Equations, Subsurface Modeling

arbogast@ices.utexas.edu

Phone: 512-471-0166

Office Location
RLM 11.162

Postal Address
The University of Texas at Austin
MATHEMATICS
2515 SPEEDWAY, Stop C1200
AUSTIN, TX 78712-1202

Ph.D., University of Chicago (1987)
S.M., University of Chicago (1983)
B.S., University of Minnesota (1981)
B.S., University of Minnesota (1981)

Research Interests

Todd Arbogast's areas of expertise include the numerical analysis of partial differential systems, mathematical modeling, and scientific computation. His research includes the development of a characteristics-mixed scheme for advective flow, the study of cell-centered finite differences (mixed methods) for nonlinear and geometrically irregular problems, the modeling and simulation of flow through fractured and vuggy media, and numerical subgrid upscaling of heterogeneous media and nonlinear problems. He is a member of the Institute for Computational Engineering and Sciences and its Center for Subsurface Modeling at The University of Texas at Austin, and an associated faculty in the Division of Statistics and Scientific Computation.

Publications
(Articles in progress)
[1] T. Arbogast. Composite materials and homogenization. In B. Engquist et al., editor, Encyclopedia of Applied and Computational Mathematics. Springer, 2012, submitted.

[2] T. Arbogast and J. L. Bona. Functional Analysis for the Applied Mathematician. In preparation, 2012.

[3] T. Arbogast, D. Estep, B. Sheehan, and S. Tavener. A-posteriori error estimates for mixed nite element and nite volume methods for problems coupled through a boundary with non-matching grids. Submitted, 2012.

[4] T. Arbogast, M. Juntunen, J. Pool, and M. F. Wheeler. A discontinuous Galerkin method for two-phase ow in a porous medium enforcing H(div) velocity and continuous capillary pressure. Submitted, 2012.

Articles in Journals and Other Refereed Works

[1] T. Arbogast and Hailong Xiao. A multiscale mortar mixed space based on homogenization for heterogeneous elliptic problems. SIAM J. Numer. Anal., 51(1):377{399, 2013.

[2] T. Arbogast, Zhen Tao, and Hailong Xiao. Multiscale mortar mixed methods for heterogeneous elliptic problems. In Hongtao Yang Jichun Li and Eric Machorro, editors, Recent Advances in Scienti c Computing and Applications, volume 586 of Contemporary Mathematics, Providence, Rhode Island, 2013, to appear. American Mathematical Society.

[3] T. Arbogast, Ch.-S. Huang, and Ch.-H. Hung. A fully conservative Eulerian-Lagrangian stream-tube method for advection-di usion problems. SIAM J. Sci. Comput., 34(4):B447{ B478, 2012.

[4] T. Arbogast, Ch.-S. Huang, and T. F. Russell. A locally conservative Eulerian-Lagrangian method for a model two-phase ow problem in a one-dimensional porous medium. SIAM J. Sci. Comput., 34(4):A1950{A1974, 2012.

[5] Ch.-S. Huang, T. Arbogast, and Jianxian Qiu. An Eulerian-Lagrangian WENO nite volume scheme for advection problems. J. Comput. Phys., 231(11):4028{4052, 2012. DOI 10.1016/j.jcp.2012.01.030.

[6] T. Arbogast and Wen-Hao Wang. Stability, monotonicity, maximum and minimum principles, and implementation of the volume corrected characteristic method. SIAM J. Sci. Comput., 33(4):1549{1573, 2011.

  • Fellow of the Society for Industrial and Applied Mathematics, 2018
  • Fellow of the American Mathematical Society, 2012
  • Moncrief Grand Challenge Faculty Award, 2012 (The University of Texas at Austin)
  • ICES Distinguished Research Award, 2011 (The University of Texas at Austin)
  • Frank Gerth III Faculty Fellowship, 2008-2012 (The University of Texas at Austin)
  • The President's Associates Centennial Teaching Fellowship in Mathematics, 1997-1998 (TheUniversity of Texas at Austin)
  • National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship, 1989-1992 (University of Houston and Rice University)
  • Robert R. McCormick Fellowship, 1981-1984 (University of Chicago)
  • Sigma Pi Sigma (physics) and Tau Beta Pi (engineering) honor societies
  • Century Fund Scholarship, 1976-1977 (University of Minnesota