Hierarchical Parallelisation of Functional Renormalisation Group Calculations -- hp-fRG

The functional renormalisation group (fRG) has evolved into a versatile tool in condensed matter theory for studying important aspects of correlated electron systems. Practical applications of the method often involve a high numerical effort, motivating the question in how far High Performance Computing (HPC) can leverage the approach. In this work we report on a multi-level parallelisation of the underlying computational machinery and show that this can speed up the code by several orders of magnitude. This in turn can extend the applicability of the method to otherwise inaccessible cases. We exploit three levels of parallelisation: Distributed computing by means of Message Passing (MPI), shared-memory computing using OpenMP, and vectorisation by means of SIMD units (single-instruction-multiple-data). Results are provided for two distinct High Performance Computing (HPC) platforms, namely the IBM-based BlueGene/Q system JUQUEEN and an Intel Sandy-Bridge-based development cluster. We discuss how certain issues and obstacles were overcome in the course of adapting the code. Most importantly, we conclude that this vast improvement can actually be accomplished by introducing only moderate changes to the code, such that this strategy may serve as a guideline for other researcher to likewise improve the efficiency of their codes

Programming distributed memory architectures using Kali

Programming nonshared memory systems is more difficult than programming shared memory systems, in part because of the relatively low level of current programming environments for such machines. A new programming environment is presented, Kali, which provides a global name space and allows direct access to remote data values. In order to retain efficiency, Kali provides a system on annotations, allowing the user to control those aspects of the program critical to performance, such as data distribution and load balancing. The primitives and constructs provided by the language is described, and some of the issues raised in translating a Kali program for execution on distributed memory systems are also discussed

Efficient Generation of Parallel Spin-images Using Dynamic Loop Scheduling

High performance computing (HPC) systems underwent a significant increase in their processing capabilities. Modern HPC systems combine large numbers of homogeneous and heterogeneous computing resources. Scalability is, therefore, an essential aspect of scientific applications to efficiently exploit the massive parallelism of modern HPC systems. This work introduces an efficient version of the parallel spin-image algorithm (PSIA), called EPSIA. The PSIA is a parallel version of the spin-image algorithm (SIA). The (P)SIA is used in various domains, such as 3D object recognition, categorization, and 3D face recognition. EPSIA refers to the extended version of the PSIA that integrates various well-known dynamic loop scheduling (DLS) techniques. The present work: (1) Proposes EPSIA, a novel flexible version of PSIA; (2) Showcases the benefits of applying DLS techniques for optimizing the performance of the PSIA; (3) Assesses the performance of the proposed EPSIA by conducting several scalability experiments. The performance results are promising and show that using well-known DLS techniques, the performance of the EPSIA outperforms the performance of the PSIA by a factor of 1.2 and 2 for homogeneous and heterogeneous computing resources, respectively

Parallel language constructs for tensor product computations on loosely coupled architectures

Distributed memory architectures offer high levels of performance and flexibility, but have proven awkard to program. Current languages for nonshared memory architectures provide a relatively low level programming environment, and are poorly suited to modular programming, and to the construction of libraries. A set of language primitives designed to allow the specification of parallel numerical algorithms at a higher level is described. Tensor product array computations are focused on along with a simple but important class of numerical algorithms. The problem of programming 1-D kernal routines is focused on first, such as parallel tridiagonal solvers, and then how such parallel kernels can be combined to form parallel tensor product algorithms is examined

Distributed memory compiler methods for irregular problems: Data copy reuse and runtime partitioning

Outlined here are two methods which we believe will play an important role in any distributed memory compiler able to handle sparse and unstructured problems. We describe how to link runtime partitioners to distributed memory compilers. In our scheme, programmers can implicitly specify how data and loop iterations are to be distributed between processors. This insulates users from having to deal explicitly with potentially complex algorithms that carry out work and data partitioning. We also describe a viable mechanism for tracking and reusing copies of off-processor data. In many programs, several loops access the same off-processor memory locations. As long as it can be verified that the values assigned to off-processor memory locations remain unmodified, we show that we can effectively reuse stored off-processor data. We present experimental data from a 3-D unstructured Euler solver run on iPSC/860 to demonstrate the usefulness of our methods