Appointment

Associate Professor of Mathematics, University of California, Davis

Education

Ph.D., Mathematics, Yale University, 2007. Advisor: R.R. Coifman.
B.S., Mathematics, University of Maryland, College Park, 2001.
B.S., Computer Science, University of Maryland, College Park, 2001.

Research interests

Numerical analysis, particularly the development of fast and highly accurate solvers for partial differential equations.

Recent grants

UC Davis Chancellor's Fellowship, 2017-2022
NSF DMS-1418723, 2014-2017.
Sloan Research Fellowship, 2012-2014.
ONR N00014-12-1-0117, 2011-2014 (co-PI with Naoki Saito).
ONR N00014-09-1-0318, 2008-2011 (co-PI with Naoki Saito).

Preprints and Publications

19. An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order. arXiv:1707.03287.
18. An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments arxiv.org:1705.07820.
17. On the nonoscillatory phase function for Legendre's differential equation (with V. Rokhlin).
Journal of Computational Physics, to appear. Download.
16. On the numerical calculation of the roots of special functions satisfying second order ordinary differential
equations. SIAM Journal on Scientific Computing 39 (2017), pp A55-A82. Download.
15. On the numerical solution of second order differential equations in the high-frequency regime.
Applied and Computational Harmonic Analysis, to appear. Download.
14. Improved estimates for nonoscillatory phase functions (with V. Rokhlin).
Discrete and Continuous Dynamical Systems, Series A 36 (2016), pp. 4101-4131. Download.
13. On the existence of nonoscillatory phase functions for second order differential equations
in the high-frequency regime (with V. Rokhlin and Z. Heitman).
Journal of Computational Physics 290 (2015), pp. 1-27. Download.
12. On the asymptotics of Bessel functions in the Fresnel regime (with Z. Heitman, V. Rokhlin, and B. Vioreanu).
Applied and Computational Harmonic Analysis, 39 (2015), pp. 347-356. Download.
11. A high-order accelerated direct solver for integral equations on curved surfaces (with A. Gillman and P.-G. Martinsson ).
BIT Numerical Mathematics 55 (2015), pp. 367-397. Download.
10. On the numerical evaluation of the singular integrals of scattering theory (with Z. Gimbutas).
Journal of Computational Physics 251 (2013), pp. 327-343. Download.
9. A Nyström method for weakly singular integral operators on surfaces (with Z. Gimbutas).
Journal of Computational Physics, 231 (2012), pp. 4885-4903. Download.
8. A fast direct solver for the integral equations of scattering theory on planar curves with corners.
Journal of Computational Physics, 231 (2012), pp. 1879-1899. Download.
7. On the Nyström discretization of integral equations on planar curves with corners.
Applied and Computational Harmonic Analysis, 32 (2012), pp. 45-64. Download.
6. An adaptive fast direct solver for boundary integral equations in two dimensions (with W. Y. Kong and V. Rokhlin).
Applied and Computational Harmonic Analysis, 31 (2011), pp. 346-369. Download.
5. Universal quadratures for boundary integral equations on two-dimensional domains with corners (with V. Rokhlin and I. Sammis).
Journal of Computational Physics, 229 (2010), pp. 8259-8280. Download.
4. A nonlinear optimization procedure for generalized Gaussian quadratures (with V. Rokhlin and Z. Gimbutas).
SIAM Journal of Scientific Computing, 32 (2010), pp. 1761-1788. Download.
3. Efficient discretization of Laplace boundary integral equations on polygonal domains (with V. Rokhlin).
Journal of Computational Physics, 229 (2010), pp. 2507-2525. Download.
2. Diffusion wavelet packets (with R.R. Coifman, M. Maggioni and A. Szlam).
Applied and Computational Harmonic Analysis, 21 (2006), pp. 95-112. Download.
1. Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs (with R.R. Coifman, M. Maggioni and A. Szlam).
SPIE Wavelet XI, August 2005. Download.