### About

I am a Chu Assistant Professor of Applied Mathematics at Columbia University.

Previously, I was a PhD student at the University of Washington, advised by Randall J. LeVeque and Gunther Uhlmann.

[CV, updated 2019/01/20].

### Research Interests

My interests are in the numerical analysis of partial differential equations (PDEs) and inverse problems

- Model reduction of parametrized nonlinear hyperbolic systems of conservation laws
- Uncertainty quantification (UQ) and inverse problems involving nonlinear hyperbolic PDEs
- Approximate discrete Radon transform (ADRT) and its applications
- Applications in geophysics and medical imaging: probabilistic tsunami hazard assessment, storm surge prediction, coupled-physics imaging

### Publications, Preprints and Numerical Software

**Model reduction of a parametrized scalar hyperbolic conservation law using displacement interpolation**

D. Rim and K.T Mandli

*Preprint*
(*2018*)
[arXiv] [github]

**Dimensional splitting of hyperbolic partial differential equations using the Radon transform**

D. Rim

*SIAM J. Sci. Comput.*
(*2018*)
* 40 (6), A4184–A4207.* [doi][arXiv]

**Displacement interpolation using monotone rearrangement**

D. Rim and K.T Mandli

*SIAM/ASA J. Uncertainty Quantification*
(*2018*)
* 6 (4), 1503-1531* [doi][arXiv] [github]

**Imaging of isotropic and anisotropic conductivities from power densities in three dimensions**

F. Monard and D. Rim

*Inverse Probl.*
(*2018*)
* 34 (7), 075005* [doi][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**

D. Rim

*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]

### More Numerical Software

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)*.

### Contact

_{500 W. 120th St 200 S.W. Mudd
Mail Code: 4701
Applied Physics and Applied Mathematics
Columbia University
New York, NY, USA, 10027-6623
Email: dr2965@columbia.edu }