Computing with functions in the ball
arXiv:1911.00114 · doi:10.1137/19M1297063
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.
arXiv comment23 pages, 9 figures
References in corpus (6)
- Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
- The automatic solution of partial differential equations using a global spectral method
- Toroidal and poloidal energy in rotating Rayleigh-Bénard convection
- Extension of Chebfun to periodic functions
- Poloidal-toroidal decomposition in a finite cylinder. II. Discretization, regularization and validation
- Poloidal-toroidal decomposition in a finite cylinder. I. Influence matrices for the magnetohydrodynamic equations