11 citations · 30 across the 19 of their papers we have counts for
21 papers
A frequency-independent solver for systems of first order linear ordinary differential equations
Tony Hu, James Bremer
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillat…
The Levin approach to the numerical calculation of phase functions
Murdock Aubry, James Bremer
The solutions of scalar ordinary differential equations become more complex as their coefficients increase in magnitude. As a consequence, when a standard solver is applied to such…
Phase function methods for second order inhomogeneous linear ordinary differential equations
Kirill Serkh, James Bremer
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underl…
On the adaptive Levin method
Shukui Chen, Kirill Serkh, James Bremer
The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antider…
Phase function methods for second order linear ordinary differential equations with turning points
James Bremer
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of th…
An algorithm for the numerical evaluation of the Sturm-Liouville eigenvalues of the spheroidal wave functions of order zero
Rafeh Rehan, James Bremer
In addition to being the eigenfunctions of the restricted Fourier operator, the angular spheroidal wave functions of the first kind of order zero and nonnegative integer characteri…
On the numerical evaluation of the prolate spheroidal wave functions of order zero
James Bremer
We describe a method for the numerical evaluation of the angular prolate spheroidal wave functions of the first kind of order zero. It is based on the observation that underlies th…
Rapid Application of the Spherical Harmonic Transform via Interpolative Decomposition Butterfly Factorization
James Bremer, Ze Chen, Haizhao Yang
We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse ass…
A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential
James Bremer
Standard solvers for the variable coefficient Helmholtz equation in two spatial dimensions have running times which grow quadratically with the wavenumber . Here, we describe a…
An O(1) Algorithm for the Numerical Evaluation of the Prolate Spheroidal Wave Functions of Order 0
Xinge Zhang, James Bremer
The standard algorithm for the numerical evaluation of the prolate spheroidal wave function of order , bandlimit and characteristic…
Fast Algorithms for the Multi-dimensional Jacobi Polynomial Transform
James Bremer, Qiyuan Pang, Haizhao Yang
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algori…
Fast algorithms for Jacobi expansions via nonoscillatory phase functions
James Bremer, Haizhao Yang
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadratur…
An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order
James Bremer
We describe a method for the numerical evaluation of normalized versions of the associated Legendre functions and of degrees and orde…
An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments
James Bremer
We describe a method for the rapid numerical evaluation of the Bessel functions of the first and second kinds of nonnegative real orders and positive arguments. Our algorithm makes…
On the nonoscillatory phase function for Legendre's differential equation
James Bremer, Vladimir Rokhlin
We express a certain complex-valued solution of Legendre's differential equation as the product of an oscillatory exponential function and an integral involving only nonoscillatory…
On the numerical calculation of the roots of special functions satisfying second order ordinary differential equations
James Bremer
We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solu…
Improved estimates for nonoscillatory phase functions
James Bremer, Vladimir Rokhlin
Recently, it was observed that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase f…
On the existence of nonoscillatory phase functions for second order differential equations in the high-frequency regime
Jhu Heitman, James Bremer, Vladimir Rokhlin
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In ad…
On the numerical solution of second order differential equations in the high-frequency regime
James Bremer
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the…
On the asymptotics of Bessel functions in the Fresnel regime
Jhu Heitman, James Bremer, Vladimir Rokhlin +1
We introduce a version of the asymptotic expansions for Bessel functions , that is valid whenever (which is deep in the Fresnel regime), as opposed to th…
A high-order accurate accelerated direct solver for acoustic scattering from surfaces
James Bremer, Adrianna Gillman, Per-Gunnar Martinsson
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth paramete…