James Bremer

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.

Recent Grants

NSF DMS-2012487, 2020-2023
NSF DMS-1818820, 2018-2021
UC Davis Chancellor's Fellowship, 2016-2021
NSF DMS-1418723, 2014-2017
Sloan Research Fellowship, 2012-2014

Preprints and Publications

James Bremer, Ze Chen and Haizhao Yan, Rapid Application of the Spherical Harmonic Transform via Interpolative Decomposition Butterfly Factorization [Download PDF]

James Bremer, A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential. Journal of Computational Physics, to appear. [Download PDF]

Xinge Zhang and James Bremer, An O(1) algorithm for the numerical evaluation of the prolate spheroidal wave functions of order 0 [arXiv:1905.04415] [Download PDF]

James Bremer, Qiyuan Pang, Haizhao Yang, Fast Algorithms for the Multi-dimensional Jacobi Polynomial Transform. Applied and Computational Harmonic Analysis, to appear. [Download PDF]

James Bremer and Haizhao Yang, Fast algorithms for Jacobi expansions via nonoscillatory phase functions, IMA Journal of Numerical Analysis, to appear. [Download PDF]

James Bremer, On the numerical solution of second order differential equations in the high-frequency regime. Applied and Computational Harmonic Analysis 44 (2018), 312-349. [Journal Link] [Download PDF]

James Bremer, An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order. Journal of Computational Physics 360 (2018), 15-38. [Journal Link] [Download PDF]

James Bremer, An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments. Advances in Computational Mathematics, to appear. [Journal Link] [Download PDF]

James Bremer and Vladimir Rokhlin, On the nonoscillatory phase function for Legendre's differential equation Journal of Computational Physics 350 (2017), 326-342. [Journal Link] [Download PDF]

James Bremer, On the numerical calculation of the roots of special functions satisfying second order ordinary differential equations. SIAM Journal on Scientific Computing 39 (2017), A55-A82. [Journal Link] [Download PDF]

James Bremer and Vladimir Rokhlin, Improved estimates for nonoscillatory phase functions Discrete and Continuous Dynamical Systems, Series A 36 (2016), 4101-4131. [Journal Link] [Download PDF]

Zhu Heitman, James Bremer and Vladimir Rokhlin. On the existence of nonoscillatory phase functions for second order differential equations in the high-frequency regime. Journal of Computational Physics 290 (2015), 1-27. [Journal Link] [Download PDF]

James Bremer, Bogdan Vioreanu, Zhu Heitman and Vladimir Rokhlin, On the asymptotics of Bessel functions in the Fresnel regime. Applied and Computational Harmonic Analysis, 39 (2015), 347-356. [Journal Link] [Download PDF]

James Bremer, Adrianna Gillmann and Gunnar Martinsson, A high-order accurate accelerated direct solver for acoustic scattering from surfaces. BIT Numerical Mathematics 55 (2015), 367-397. [Journal Link] [Download PDF]

James Bremer and Zydrunas Gimbutas, On the numerical evaluation of the singular integrals of scattering theory. Journal of Computational Physics 251 (2013), 327-343. [Journal Link] [Download PDF]

James Bremer and Zydrunas Gimbutas, A Nyström method for weakly singular integral operators on surfaces. Journal of Computational Physics, 231 (2012), 4885-4903 [Journal Link] [Download PDF]

James Bremer, A fast direct solver for the integral equations of scattering theory on planar curves with corners. Journal of Computational Physics, 231 (2012), 1879-1899. [Journal Link] [Download PDF]

James Bremer, On the Nyström discretization of integral equations on planar curves with corners. Applied and Computational Harmonic Analysis, 32 (2012), 45-64. [Journal Link] [Download PDF]

W.Y. Kong, James Bremer, and Vladimir Rokhlin, An adaptive fast direct solver for boundary integral equations in two dimensions. Applied and Computational Harmonic Analysis, 31 (2011), 346-369. [Journal Link] [Download PDF]

James Bremer, Vladimir Rokhlin and Ian Sammis, Universal quadratures for boundary integral equations on two-dimensional domains with corners. Journal of Computational Physics, 229 (2010), 8259-8280. [Journal Link] [Download PDF]

James Bremer, Zydrunas Gimbutas and Vladimir Rokhlin, A nonlinear optimization procedure for generalized Gaussian quadratures. SIAM Journal of Scientific Computing, 32 (2010), 1761-1788. [Journal Link] [Download PDF]

James Bremer and Vladimir Rokhlin, Efficient discretization of Laplace boundary integral equations on polygonal domains. Journal of Computational Physics, 229 (2010), 2507-2525. [Journal Link] [Download PDF]

Mauro Maggioni, James Bremer, Arthur Szlam and R.R. Coifman Diffusion wavelet packets Applied and Computational Harmonic Analysis, 21 (2006), 95-112. [Journal Link] [Download PDF]

Mauro Maggioni, James Bremer, Arthur Szlam and R.R. Coifman Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs. SPIE Wavelet XI, August 2005.