I'm a postdoc at Michigan, collaborating here currently with Shravan Veerapaneni; My work at Michigan currently focuses on numerical methods for inhomogeneous PDEs using fundamental solution techniques: volume and layer potential methods. Specifically we are developing methods for volume potential evaluation in complex geometry for a variety of PDE and non-PDE kernels. Particular applications involve quantifying and optimizing mixing by fluid flows, and we are looking to leverage the basic technology for more complex fluid problems including moving geometries and nonlinear problems.
Before coming here I received my Ph.D. in August 2020 in Applied & Computational Mathematics at Caltech with Oscar Bruno. I am broadly interested in applied mathematics and the practical solution of PDEs with numerical methods for problems of interest in science and engineering. My most recent (computational) work has been in the area of time-domain methods for PDEs using a new frequency/time hybrid approach to that problem that enables efficient long-time simulation. I've recently become more interested in analysis of the wave equation. Past work involves some numerical problems in fluid instabilities, as well as scalable preconditioners for high-order FEM (released in the MFEM library).
T.G. Anderson, M. Bonnet, L.M. Faria, C.P.-Arancibia. High-order numerical evaluation of volume potentials via polynomial density interpolation. September 2022.
T.G. Anderson, M. Bonnet, S. Veerapaneni. Quantifying mixing in arbitrary fluid domains: A Padé approximation approach. June 2022 (accepted, to appear in Numerical Algorithms).
T.G. Anderson, H. Zhu, S. Veerapaneni. A fast, high-order scheme for evaluating volume potentials on complex 2D geometries via area-to-line integral conversion and domain mappings. Mar 2022 (accepted without revision, to appear, in JCP).
T.G. Anderson, O.P. Bruno. "Bootstrap Domain of dependence": Bounds and Time Decay of Solutions of the Wave Equation. Oct 2020.
T.G. Anderson, O.P. Bruno, M. Lyon. High-order, Dispersionless ``Fast-Hybrid'' Wave Equation Solver. Part I: O(1) Sampling Cost via Incident-field Windowing & Recentering SIAM J. Sci. Comput., 42(2), A1348–A1379, (2020).
T.G. Anderson, R. Cimpeanu, D.T. Papageorgiou, P.G. Petropoulos. Electric field stabilization of viscous liquid layers coating the underside of a surface Phys. Rev. Fluids, 2(5), (2017).
T.G. Anderson, E. Mema, L. Kondic, L.J. Cummings. Transitions in Poiseuille flow of nematic liquid crystal Int. J. of Non-Linear Mechanics, 75, (2015).
1. T.G. Anderson, S. Veerapaneni. Fast, adaptive, high-order accurate evaluation of volume potentials in two dimensions.
2. T.G. Anderson, M. Bonnet, S. Veerapaneni. A mix-norm surrogate based on volume potentials.
My thesis (refer to this until these preprints are posted) includes a variety of results which will form the basis for the following additional papers in preparation:
3. High-Order, Dispersionless, ``Fast-Hybrid'' Wave Equation Solver. Part II: Window Tracking and Field Reconstruction in 2D and 3D, General Incident Fields.
4. Hybrid Frequency/Time Methods for Acoustics and Electromagnetics: inhomogeneous, dispersive and attenuating media, and plasmonics.