@inproceedings{a6708afbf87740ad89ac62aa8ea4a6f5,

title = "Distributed decomposition over hyperspherical domains",

abstract = "We are motivated by an optimization problem arising in computational scaling for optical lithography that reduces to finding the point of minimum radius that lies outside of the union of a set of diamonds centered at the origin of Euclidean space of arbitrary dimension. A decomposition of the feasible region into convex regions suggests a heuristic sampling approach to finding the global minimum. We describe a technique for decomposing the surface of a hypersphere of arbitrary dimension, both exactly and approximately, into a specific number of regions of equal area and small diameter. The decomposition generalizes to any problem posed on a spherical domain where regularity of the decomposition is an important concern. We specifically consider a storage-optimized decomposition and analyze its performance. We also show how the decomposition can parallelize the sampling process by assigning each processor a subset of points on the hypersphere to sample. Finally, we describe a freely available C++ software package that implements the storage-optimized decomposition.",

author = "Aron Ahmadia and Keyes, {David Elliot} and David Melville and Alan Rosenbluth and Kehan Tian",

year = "2009",

month = oct,

day = "12",

doi = "10.1007/978-3-642-02677-5_27",

language = "English (US)",

isbn = "9783642026768",

series = "Lecture Notes in Computational Science and Engineering",

pages = "251--258",

booktitle = "Domain Decomposition Methods in Science and Engineering XVIII",

note = "18th International Conference of Domain Decomposition Methods ; Conference date: 12-01-2008 Through 17-01-2008",

}