Computing with functions in the ball
Numerical Analysis
2020-09-29 v1 Numerical Analysis
Abstract
A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine precision by using a three-dimensional analogue of the double Fourier sphere method to form "ballfun" objects. Operations such as function evaluation, differentiation, integration, fast rotation by an Euler angle, and a Helmholtz solver are designed. Our algorithms are particularly efficient for vector calculus operations, and we describe how to compute the poloidal-toroidal and Helmholtz--Hodge decomposition of a vector field defined on the ball.
Cite
@article{arxiv.1911.00114,
title = {Computing with functions in the ball},
author = {Nicolas Boullé and Alex Townsend},
journal= {arXiv preprint arXiv:1911.00114},
year = {2020}
}
Comments
23 pages, 9 figures