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
Displacement interpolation using monotone rearrangement
D. Rim and K.T Mandli
Preprint (2017) [arXiv]
Dimensional splitting of hyperbolic partial differential equations using the Radon transform
Preprint. (2017) [arXiv]
Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
F. Monard and D. Rim
Accepted to Inverse Probl. (2017) [arXiv] [github]
Transport reversal for model reduction of hyperbolic partial differential equations
D. Rim, S. Moe, and R. J. LeVeque
SIAM/ASA J. Uncertainty Quantification (2018) 6 (1), 118-150 [doi][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 [doi] [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, 10027-6623