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A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential

https://doi.org/10.1016/j.jcp.2020.109401

Bremer, James (June 2020, Journal of Computational Physics)

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Fast algorithms for Jacobi expansions via nonoscillatory phase functions

https://doi.org/10.1093/imanum/drz016

Bremer, James; Yang, Haizhao (April 2019, IMA Journal of Numerical Analysis)
null (Ed.)
Abstract We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm–Liouville eigentransforms and calculating Gauss–Jacobi quadrature rules. Our approach, which applies in the case in which both of the parameters $$\alpha $$ and $$\beta $$ in Jacobi’s differential equation are of magnitude less than $1/2$, is based on the well-known fact that in this regime Jacobi’s differential equation admits a nonoscillatory phase function that can be loosely approximated via an affine function over much of its domain. We illustrate this with several numerical experiments, the source code for which is publicly available.
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An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments

https://doi.org/10.1007/s10444-018-9613-9

Bremer, James (February 2019, Advances in Computational Mathematics)
null (Ed.)
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An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order

https://doi.org/10.1016/j.jcp.2018.01.014

Bremer, James (May 2018, Journal of Computational Physics)
null (Ed.)
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On the numerical solution of second order ordinary differential equations in the high-frequency regime

https://doi.org/10.1016/j.acha.2016.05.002

Bremer, James (March 2018, Applied and Computational Harmonic Analysis)
null (Ed.)
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