My current research interests are in finite-volume methods for solving hyperbolic, parabolic and elliptic PDEs in complex geometry. In particular, I am interested in methods for structured quadrilateral and hexahedral meshes, uniform Cartesian cut-cell (embedded geometry) methods, adapative mesh refinement methods and numerical methods for solving PDEs on non-Euclidean surfaces.
Application areas in which I have been involved include shallow water wave equations for modeling flooding, volcanic ash dispersion, combustion processes, pattern formation in biology, crystal growth, and modeling of atmospheric flows on the sphere.
Links of particular interest
- ForestClaw : A block-structured approach to AMR using a forest of octrees http://www.forestclaw.org
- A list of available software packages for solving PDEs on logically Cartesian, block-structured adaptive meshes (amr_software)
More details on my research interests
|2016 - present||Associate Professor, Department of Mathematics, Boise State University, Boise, ID.|
|2011 - 2015||Assistant Professor, Department of Mathematics, Boise State University, Boise, ID.|
|Fall 2012||Visiting Fellow, The Isaac Newton Institute (Cambridge, UK) in the program "Multiscale Numerics for the Ocean and Atmosphere".|
|2005 - 2010||Research Scientist at the Commissariat a l'Energie Atomique, Centre de Saclay, France.|
|2004 - 2005||Acting Assistant Professor, Dept. of Mathematics, Univ. of Washington, Seattle, WA.|
|2002 - 2005||Post-doc, Dept. of Applied Mathematics, Univ. of Washington, Seattle, WA.|
|1999 - 2002||Post-doc, Courant Institute of Mathematical Sciences, NYU, New York, NY.|
|1999||PhD, Univ. of Washington, Seattle, WA. Supervisor : Randall J. LeVeque. Title : "A Cartesian grid method for solving the streamfunction-vorticity equations in irregular geometries"|
Selected list of publications
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