I am a Chu Assistant Professor of Applied Mathematics at Columbia University.
My interests are in the numerical analysis of partial differential equations (PDEs) and inverse problems
- Uncertainty quantification (UQ) concerning nonlinear hyperbolic systems of conservation laws, via reduced order models (ROMs).
- Target applications are geophysical problems: probabilistic tsunami hazard assessment (PTHA) and statistical tsunami source inversion.
- Inverse anisotropic conductivity from power densities in dimension three.
Publications and Preprints
Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
F. Monard and D. Rim
Preprint (2017) [arXiv]
Dimensional splitting of hyperbolic partial differential equations using the Radon transform
Preprint. (2017) [arXiv]
Transport reversal for model reduction of hyperbolic partial differential equations
D. Rim, S. Moe, and R. J. LeVeque
Accepted, SIAM/ASA J. Uncertainty Quantification (2017) [arXiv]
An elementary proof that symplectic matrices have determinant one
Adv. Dyn. Syst. Appl. (2017) 12 (1), 15-20 [arXiv]
Generating random earthquake events for probabilistic tsunami hazard assessment (PTHA)
R. J. LeVeque, K. Waagan, F. I. Gonzalez, D. Rim, and G. Lin
Pure Appl. Geophys. (2016) 173: 3671 [doi][arXiv]
Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods
C. Carstensen, J. Gedicke, and D. Rim
J. Comput. Math. 30 (2012) no. 4, 337-353 [Preprint]
For a full list of relevant numerical softwares,
please visit my github page.
See also: Top ten reasons to not share your code (and why you should anyway).
500 W. 120th St 200 S.W. Mudd
Mail Code: 4701
Applied Physics and Applied Mathematics
New York, NY, USA