Task-Based FMM for Multicore Architectures

Abstract

International audienceFast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and hardware. In this paper, we propose a new approach that achieves high performance across architectures. Our method consists of expressing the FMM algorithm as a task flow and employing a state- of-the-art runtime system, StarPU, to process the tasks on the different computing units. We carefully design the task flow, the mathematical operators, their implementations as well as scheduling schemes. Potentials and forces on 200 million particles are computed in 42.3 seconds on a homogeneous 160 cores SGI Altix UV 100 and good scalability is shown

An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles

“…The idea is to map 3D points in the octree to those in a 1D array based on the z-value of each point, and then to partition all points based on the index of their 1D representation. After partitioning, local points are inserted into the octree on each processor, and each processor then performs FMM and communicates with other processors 36 . This strategy consumes less memory than the previous two methods, but its implementation is more involved.…”

Asynchronous Task Scheduling of the Fast Multipole Method Using Various Runtime Systems

“…By contrast, datadriven approaches seem promising to address these issues, such as the ones in Refs. [23]- [25], and the several versions to be discussed in Section IV.…”

An embedded corrector problem for homogenization. Part II: Algorithms and discretization

“…for d linearly independent vectors p of R d (Problems (2) are complemented by geometric constraints on w, such as ∇w is quasi-periodic or random stationary, that we do not detail further). Note that the problems (2) are posed on the whole space R d .…”

“…for d linearly independent vectors p of R d (Problems (2) are complemented by geometric constraints on w, such as ∇w is quasi-periodic or random stationary, that we do not detail further). Note that the problems (2) are posed on the whole space R d . In practice, approximate corrector problems, defined on a sequence of increasing truncated domains with appropriate boundary conditions (typically periodic boundary conditions), are often considered to obtain a convergent sequence of approximate homogenized matrices [7,16].…”

“…Note that integral equations have already been introduced in the context of homogenization in [11]. In this article, the authors consider the (standard) corrector problem (2), posed on a truncated domain and complemented by periodic boundary conditions. The problem is next recast in a boundary integral formulation (which is different from ours since the PDE of interest is different).…”