Abstract
A collection of algorithms is described for numerically computing with smooth functions defined on the unit disk. Low rank approximations to functions in polar geometries are formed by synthesizing the disk analogue of the double Fourier sphere method with a structure-preserving variant of iterative Gaussian elimination that is shown to converge geometrically for certain analytic functions. This adaptive procedure is near-optimal in its sampling strategy, producing approximants that are stable for differentiation and facilitate the use of FFT-based algorithms in both variables. The low rank form of the approximants is especially useful for operations such as integration and differentiation, reducing them to essentially 1D procedures, and it is also exploited to formulate a new fast disk Poisson solver that computes low rank approximations to solutions. This work complements a companion paper (Part I) on computing with functions on the surface of the unit sphere.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
