### About

I am a Postdoctoral Associate at the Courant Institute, working with Benjamin Peherstorfer.

Previously, I was a Chu Assistant Professor at Columbia University. I received a PhD in applied math from the University of Washington, advised by Randall J. LeVeque and Gunther Uhlmann.

[CV, updated 2019/07/01].

### Research Interests

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

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

### Publications / Preprints / Software

**Manifold Approximations via Transported Subspaces: Model reduction for transport-dominated problems**

D. Rim, B. Peherstorfer, K.T. Mandli

*Preprint*
(2019) | [arXiv]

**Exact and fast inversion of the approximate discrete Radon transform from partial data**

D. Rim

*Appl. Math.*
**102** 106159 (2020) | [doi][arXiv]

**The Effects of Earthquake Kinematics on Tsunami Propagation**

A. Williamson, D. Melgar, D. Rim

*J. Geophys. Res. Solid Earth*
**124** (2019) | [doi]

**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.*
**40** (6), A4184–A4207 (2018) | [doi][arXiv]

**Displacement interpolation using monotone rearrangement**

D. Rim and K.T. Mandli

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

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

F. Monard and D. Rim

*Inverse Probl.*
**34** (7), 075005 (2018) | [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*
**6** (1), 118-150 (2018) | [doi][arXiv]

**An elementary proof that symplectic matrices have determinant one**

D. Rim

*Adv. Dyn. Syst. Appl.*
**12** (1), 15-20 (2017) | [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.*
173: 3671 (2016) | [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** no. 4, 337-353 (2012) | [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

_{Email: dr1653@nyu.edu}