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Department of Mathematics College of Liberal Arts and Sciences

Research & Students

My research is focused on the design and analysis of efficient and accurate numerical methods for nonlinear and multiscale partial differential equations and eigenvalue problems.

My research on accelerating low-memory iterative methods for eigenvalue problems is funded by a CAREER award from the National Science Foundation, DMS 2045059: Extrapolation methods for matrix and tensor eigenvalue problems. This work includes theoretical and practical advances in momentum methods and polynomial acceleration.

My ongoing work on nonlinear PDE includes design and analysis of extrapolation methods and acceleration for nonlinear problems, quantifying the behavior of numerical algorithms in the preasymptotic regime. My recent work includes methods for PDE constrained optimal control. My research in these areas has been supported by a collaborative grant from the National Science Foundation, DMS 2011519, with Leo Rebholz from Clemson University, a single PI grant from the NSF, DMS-1852876, 2018-2020 (previously DMS-1719849, 2017-2018), and Air Force Research Labs FA8651-25-1-0002 with PI Anil Rao of UF MAE.

I also have a continuing interest in computational geometry, which started from my undergraduate research project. I have worked on developing robust algorithms for inverse-kinematic loop closure, and on characterizing the solution space and singularities of both the geometrical and computational problems.

keywords:
nonlinear partial differential equations, eigenvalue problems, extrapolation, Anderson acceleration, momentum methods, finite element analysis, nonsymmetric problems, nonmonotone problems, multiscale methods, discrete comparison principles, uniqueness of discrete solutions, adaptive methods, regularization, goal oriented methods, inverse-kinematics.

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