Travis Askham

About

askham [at] njit [dot] edu

I am an associate professor in the Department of Mathematical Sciences at NJIT. I teach applied mathematics courses (linear algebra, partial differential equations, vector analysis, etc.) and conduct research in scientific computing and numerical analysis. My primary research interests are in fast and high-order accurate numerical methods for the PDEs of mathematical physics and optimization algorithms for inverse problems.

Publications

Journal Articles

Travis Askham, Carlos Borges, Reconstructing the shape and material parameters of dissipative obstacles using an impedance model. Inverse Problems, Accepted 2024. accepted manuscript
Travis Askham, Carlos Borges, Jeremy Hoskins, and Manas Rachh, Random walks in frequency and the reconstruction of obstacles with cavities from multi-frequency data. Journal of Scientific Computing, 98(1) 15, 2023. accepted manuscript
Ruqi Pei, Travis Askham, Leslie Greengard, and Shidong Jiang, A fast method for imposing periodic boundary conditions on arbitrarily-shaped lattices in two dimensions. Journal of Computational Physics, 474:111792, 2023. accepted manuscript
Travis Askham, Peng Zheng, Aleksandr Aravkin, and J Nathan Kutz, Robust and scalable methods for the dynamic mode decomposition. SIAM Journal on Applied Dynamical Systems, 21(1):60–79, 2022. accepted manuscript
Ludvig af Klinteberg, Travis Askham, and Mary Catherine Kropinski, A fast integral equation method for the two-dimensional navier-stokes equations. Journal of Computational Physics, 409:109353, 2020. accepted manuscript
Travis Askham and Manas Rachh, A boundary integral equation approach to computing eigenvalues of the stokes operator. Advances in Computational Mathematics, 46(2):1–42, 2020. accepted manuscript
Niall M Mangan, Travis Askham, Steven L Brunton, J Nathan Kutz, and Joshua L Proctor, Model selection for hybrid dynamical systems via sparse regression. Proceedings of the Royal Society A, 475(2223):20180534, 2019. accepted manuscript
Peng Zheng, Travis Askham, Steven L Brunton, J Nathan Kutz, and Aleksandr Y Aravkin, A unified framework for sparse relaxed regularized regression: SR3. IEEE Access, 7:1404–1423, 2019. accepted manuscript
Travis Askham, A stabilized separation of variables method for the modified biharmonic equation. Journal of Scientific Computing, 76(3):1674–1697, 2018. accepted manuscript
Travis Askham and J Nathan Kutz, Variable projection methods for an optimized dynamic mode decomposition. SIAM Journal on Applied Dynamical Systems, 17(1):380–416, 2018. accepted manuscript
Emily Clark, Travis Askham, Steven L Brunton, and J Nathan Kutz, Greedy sensor placement with cost constraints. IEEE Sensors Journal, 19(7):2642–2656, 2018. accepted manuscript
Manas Rachh and Travis Askham, Integral equation formulation of the biharmonic dirichlet problem. Journal of Scientific Computing, 75(2):762–781, 2018. accepted manuscript
Chang Sun, Travis Askham, and J Nathan Kutz, Stability and dynamics of microring combs: elliptic function solutions of the Lugiato–Lefever equation. JOSA B, 35(6):1341–1353, 2018. accepted manuscript
Travis Askham and Antoine J Cerfon, An adaptive fast multipole accelerated poisson solver for complex geometries. Journal of Computational Physics, 344:1–22, 2017. accepted manuscript
Travis Askham and Leslie Greengard, Norm-preserving discretization of integral equations for elliptic pdes with internal layers I: The one-dimensional case. SIAM Review, 56(4):625–641, 2014. accepted manuscript

Software

Maintainer

chunkie A MATLAB package for integral equations in two dimensions.
optdmd A MATLAB package for computing optimized dynamic mode decompositions.

Contributor

fmm2d A Fortran package with wrappers in higher level languages for fast multipole calculations in two dimensions.
FMM3D A Fortran package with wrappers in higher level languages for fast multipole calculations in three dimensions.
fmm3dbie A Fortran package with wrappers in higher level languages for solving integral equations in three dimensions.