What are standard non-uniform spatial domain decomposition methods in parallel programming?

Question

Motivating example: I am trying to implement a land-only infection simulation in parallel based on the UK map.

I sample points uniformly spread over the land area and determine its infection status at each time step, which depends on the previous status of its neighbouring points (SIR model). The country is irregularly shaped, and so cartesian coordinates do not load-balance well - what are more efficient decomposition methods I should consider as standard?

Many thanks.

Answer 1

An excellent article (Seal & Aluru, 2001) outlining methods of

• Orthogonal Recursive Bisection
• Space Filling Curves
• Octrees and Compressed Octrees

and a further paper (Aluru & Sevilgen) focussing on Space Filling Curves.

Answer 2

deLaunay meshes are another standard decomposition for irregular objects.

You should consider how such meshes are load balanced; here's a sample article.