N-body method

Load Balancing and Data Locality in Adaptive Hierarchical N-body Methods:Barnes-Hut,Fast Multipole,and Radiosity

Jaswinder Pal Singh,Chris Holt,Takashi Totsuka,

Anoop Gupta and John L.Hennessy

Computer Systems Laboratory

Stanford University

Stanford,CA94305

Abstract

Hierarchical N-body methods,which are based on a fundamental insight into the nature of many physical processes,are increasingly being used to solve large-scale problems in a variety of scientific/engineering

domains.Applications that use these methods are challenging to parallelize effectively,however,owing to

their nonuniform,dynamically changing characteristics and their need for long-range communication.

In this paper,we study the partitioning and scheduling techniques required to obtain effective parallel performance on applications that use a range of hierarchical N-body applications.To obtain representative

coverage,we examine applications that use the three most promising methods used today.Two of these,

the Barnes-Hut method and the Fast Multipole Method,are the best methods known for classical N-body

problems(such as molecular or galactic simulations).The third is a recent hierarchical method for radiosity

calculations in computer graphics,which applies the hierarchical N-body approach to a problem with very

different characteristics.

Wefind that straightforward decomposition techniques which an automatic scheduler might implement do not scale well,because they are unable to simultaneously provide load balancing and data locality.However,

all the applications yield very good parallel performance if appropriate partitioning and scheduling techniques

are implemented by the programmer.For the Barnes-Hut and Fast Multipole applications,we show that simple

yet effective partitioning techniques can be developed by exploiting some key insights into both the solution

methods and the classical problems that they ing a novel partitioning technique,even relatively

small problems achieve45-fold speedups on a48-processor Stanford DASH machine(a cache-coherent,shared

address space multiprocessor)and118-fold speedups on a128-processor simulated architecture.The very

different characteristics of the radiosity application require a different partitioning/scheduling approach to be

used for it;however,it too yields very good parallel performance.

1Introduction

Hierarchical N-body methods,which are based on a fundamental insight into the nature of many physical processes,are increasingly being used to solve a wide variety of scientific and engineering problems.Since these methods also afford substantial parallelism,applications that use them are likely to be among the dominant users of high-performance multiprocessors.Such applications,however,typically have characteristics that make it challenging to partition and schedule them for effective parallel performance.In particular,the workload distribution and communication patterns across the logical units of parallelism(the bodies,for example)are both nonuniform and also change as the computation proceeds,thus complicating the simultaneous incorporation of load balancing and data locality.

In this paper,we study partitioning and scheduling issues in representative applications that use three important hierarchical N-body methods.Two of these methods—the Barnes-Hut method[3]and Greengard and Rokhlin’s Fast Multipole Method(FMM)[15]—are the best methods known for classical N-body problems,such as those in astrophysics,electrostatics and molecular dynamics.In addition to classical problems,the hierarchical