An asynchronous parallel multilevel fast multipole algorithm

The multilevel fast multipole algorithm (MLFMA) has gained substantial interest as a method to accelerate the matrix-vector product in the iterative solving of electromagnetic scattering problems. Its complexity of O(N) or 0(N log N) allows for the simulation of very large scale problems when sufficient computational resources such as parallel computers are available. However, the derivation of a parallel variant of the MLFMA is a non-trivial assignment due to the intense communication between the nodes required at each iterative step. This becomes especially true when considering distributed memory machines where the processors only have fast access to their own local memory. For communication, they rely on message passing through an interconnection network which speed determines to a great extent the parallel efficiency that can be obtained. Previous efforts at parallel MLFMA focused essentially on the scattering from a single three-dimensional perfect electric conductor (PEC) [1, 2]. In this contribution, we propose a novel asynchronous parallel algorithm. When considering parallel algorithms, the term asynchronous denotes that different processors can perform different types of operations at a given time, e.g. while some nodes are calculating, others could be communicating. This has two major advantages. First, by distributing communication in time, communication congestion is avoided and the need for a fast and hence expensive interconnection network is alleviated. This allows for parallel MLFMA on very low-cost non-dedicated parallel systems such as GRID computers or clusters of workstations. Second, the asynchronous algorithm allows for an efficient parallelization strategy when different dielectric objects are considered. This will be further explained in the next section. The parallel algorithm makes no assumptions about the kernel used or the dimensionality of the problem and is implemented on a method of moment discretization of a two-dimensional TM elect- romagnetic scattering problem.