Presentation
Computing with Functions in Spherical and Polar Geometries
2017 SIAM Pacific Northwest Regional Conference
(2017)
Abstract
Spherical and polar geometries are ubiquitous in computational science and engineering, arising in, for example,
weather and climate forecasting, geophysics, and astrophysics. Central to many of these applications is the task
of developing efficient and accurate approximations of functions defined on the surface of the unit sphere or
on the disk. We present a new low rank method for this task by combining an iterative, structure-preserving
variant of Gaussian elimination together with the classic double Fourier sphere method. The resulting scheme
gives a compressed representation functions on the sphere or disk, ameliorates oversampling issues near the
poles of the sphere or origin of the disk, and converges geometrically for sufficiently analytic functions. The low
rank representation makes operations such as function evaluation, differentiation, and integration particularly
efficient. We illustrate the applicability of our method to common computational tasks from data analysis, vector
calculus, and the solution of partial differential equations, which are all implemented in the new Spherefun and
Diskfun features of the Chebfun software system (www.chebfun.org).
Disciplines
Publication Date
October 28, 2017
Location
Corvallis, OR
Citation Information
Grady Wright, Alex Townsend and Heather Wilber. "Computing with Functions in Spherical and Polar Geometries" 2017 SIAM Pacific Northwest Regional Conference (2017) Available at: http://works.bepress.com/grady_wright/36/