squidpack

Spherical Quadrature on Icosahedral Domains

This repository contains the code for SQUIDpack, first presented at the 2019 PDEs on the Sphere conference held in Montréal, Québec.

The included python modules are:

• quadfuncs.py -- computes a normalized linear combination of (x, y, and z) monomials, such that the resulting functions are approximately orthogonal over a small region near the north pole of a sphere.

• calcquad.py -- Computes a quadrature rule for a grid of spherical hexagons/pentagons

• prec_quadrature.ipynb -- A Jupyter notebook which uses the above modules to compute quadrature rules for a selection of progressively refined icosahedral grids; it generates the figures used in the aformentioned presentation.

The core Python modules require:

• Numpy, for high-performance Python numerical arrays
• Sympy, for symbolic/algebraic routines used to generate the orthogonal moment functions
• Mpmath, for high-precision floating point objects used in some intermediate calculations

And the Jupyter notebook additionally requires:

• Scipy, for its spatial submodule used to generate and manipulate the convex hull given scattered gridpoints
• iModel by Pedro Peixoto, for the repository of pre-generated grids used (see its getgridsfromserver.sh)
• ipyparallel, for parallel processing of elements (it is optionally used by calcquad). This dependency could be made optional with minor changes to the notebook.