Parallel Support Set Searches for Meshfree Methods

We describe the implementation of a parallel algorithm that solves a computational geometry problem arising in meshfree methods. We solve the following problem: Given a collection of N d-rectangles Si and Q points xk in Rd, compute Ik = { i | xk \in Si }. This task is necessary for computing values of the meshfree basis functions Psii (xk) and can be used to efficiently compute the mass and stiffness matrices for the meshfree Galerkin method.