SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page C169-C191, January 2020.
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 decompositions of a vector field defined on the ball.

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SIAM科学计算杂志，第42卷，第4期，第C169-C191页，2020年1月。
描述了面向对象MATLAB中的算法集合，这些数据用于在Chebfun软件中使用定义在单位球上的平滑函数进行数值计算。通过使用三维傅里叶球体方法的三维类似物来形成“ Ballfun”对象，数字地和自适应地将函数解析为基本的机械精度，例如函数求值，微分，积分，由欧拉角快速旋转和亥姆霍兹的操作我们的算法对于矢量微积分运算特别有效，并且我们描述了如何计算在球上定义的矢量场的极-环和亥姆霍兹-霍奇分解。