Productivity from day one on supercomputers that leverage new technologies requires significant preparation. An institution that procures a novel system architecture often lacks sufficient institutional knowledge and skills to prepare for it. Thus, the "Center of Excellence" (CoE) concept has emerged to prepare for systems such as Summit and Sierra, currently the top two systems in the Top 500. This paper documents CoE experiences that prepared a workload of diverse applications and math libraries for a heterogeneous system. We describe our approach to this preparation, including our management and execution strategies, and detail our experiences with and reasons for using different programming approaches. Our early science and performance results show that the project enabled significant early seismic science with up to a l4X throughput increase over Cori. In addition to our successes, we discuss our challenges and failures so others may benefit from our experience.

Summary Stencils are commonly used to implement efficient on‐the‐fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend the software to enable stencil computations of more complex problems and methods such as inf‐sup‐stable Stokes discretizations and mixed finite element discretizations.

Hybrid MPI + OpenMP is a popular means of programming modern machines that feature substantial parallelism both off-node and on-node. Determining the right mix of the two programming models to use, however, is not as straightforward as simply using exclusively OpenMP on-node and limiting MPI to only inter-node communication. We present a step-by-step methodology to help make the decision of which mix of the two programming models to use. It starts with an estimate of the performance of a generic hybrid application on a given machine and incorporates additional available information about the specific application and the machine to provide guidance for selecting effective mixes of MPI processes and OpenMP threads to use when running that application on the machine in question. We validate our approach on four different applications on an IBM Blue Gene/Q, a Cray XK7, and a Cray XC30.

Algebraic Multigrid (AMG) is a linear solver, well known for its linear computational complexity and excellent parallelization scalability. As a result, AMG is expected to be a solver of choice for emerging extreme scale systems capable of delivering hundred Pflops and beyond. While node level performance of AMG is generally limited by memory bandwidth, achieving high bandwidth efficiency is challenging due to highly sparse irregular computation, such as triple sparse matrix products, sparse-matrix dense-vector multiplications, independent set coarsening algorithms, and smoothers such as Gauss-Seidel. We develop and analyze a highly optimized AMG implementation, based on the well-known HYPRE library. Compared to the HYPRE baseline implementation, our optimized implementation achieves 2.0x speedup on a recent Intel® Xeon® Haswell processor. Combined with our other multi-node optimizations, this translates into similarly high speedups when weak-scaled multiple nodes. In addition, our implementation achieves 1.3x speedup compared to AmgX, NVIDIA's high-performance implementation of AMG, running on K40c.

The rise of multicore cluster architectures has led to intense interest in using a combination of MPI and OpenMP to more effectively program these machines. We present a performance model for hybrid implementation of the solve cycle of algebraic multigrid (AMG), a popular iterative solver for large sparse linear systems and a key component of many scientific simulations. We validate the model on two leading parallel platforms, and discuss implications for applications programmed in a hybrid model on future machines.

Scientists across a wide range of domains increasingly rely on computer simulation for their investigations. Such simulations often spend a majority of their run-times solving large systems of linear equations that require vast amounts of computational power and memory. It is hence critical to design solvers in a highly efficient and scalable manner. Hypre is a high performance, scalable software library that offers several optimized linear solver routines and pre-conditioners. In this paper, we study the characteristics of Hypre's Preconditioned Conjugate Gradient (PCG) solver algorithm. The PCG routine is known to spend a majority of its communication time in the MPI All reduce operation to compute a global summation during the inner product operation. The MPI All reduce is a blocking operation, whose latency is often a limiting factor to the overall efficiency of the PCG solver routine, and correspondingly the performance of simulations that rely on this solver. Hence, hiding the latency of the MPI All reduce operation is critical towards scaling the PCG solver routine and improving the performance of many simulations. The upcoming revision of MPI, MPI-3, will provide support for non-blocking collective communication to enable latency-hiding. The latest Infini Band adapter from Mellanox, ConnectX-2, enables offloading of generalized lists of communication operations to the network interface. Such an interface can be leveraged to design non-blocking collective operations. In this paper, we design fully functional, scalable algorithms for the MPI Iall reduce operation, based on the network offload technology. To the best of our knowledge, these network offload-based algorithms are the first to be presented for the MPI Iall reduce operation. Our designs scale beyond 512 processes and we achieve near perfect communication/computation overlap. We also re-design the PCG solver routine to leverage our proposed MPI Iall reduce operation to hide the latency of the global reduction operations. We observe up to 21% improvements in the run-times of the PCG routine, when compared to the default PCG implementation in Hypre. We also note that about 16% of the overall benefits are due to overlapping the All reduce operations.

Now that the performance of individual cores has plateaued, future supercomputers will depend upon increasing parallelism for performance. Processor counts are now in the hundreds of thousands for the largest machines and will soon be in the millions. There is an urgent need to model application performance at these scales and to understand what changes need to be made to ensure continued scalability. This paper considers algebraic multigrid (AMG), a popular and highly efficient iterative solver for large sparse linear systems that is used in many applications. We discuss the challenges for AMG on current parallel computers and future exascale architectures, and we present a performance model for an AMG solve cycle as well as performance measurements on several massively-parallel platforms.

Algebraic multigrid (AMG) is a popular solver for large-scale scientific computing and an essential component of many simulation codes. AMG has shown to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore architectures, we face new challenges that can significantly deteriorate AMG's performance. We examine its performance and scalability on three disparate multicore architectures: a cluster with four AMD Opteron Quad-core processors per node (Hera), a Cray XT5 with two AMD Opteron Hex-core processors per node (Jaguar), and an IBM Blue Gene/P system with a single Quad-core processor (Intrepid). We discuss our experiences on these platforms and present results using both an MPI-only and a hybrid MPI/OpenMP model. We also discuss a set of techniques that helped to overcome the associated problems, including thread and process pinning and correct memory associations.

The software library hypre provides high-performance preconditioners and solvers for the solution of large, sparse linear systems on massively parallel computers as well as conceptual interfaces that allow users to access the library in the way they naturally think about their problems. These interfaces include a stencil-based structured interface (Struct); a semistructured interface (semiStruct), which is appropriate for applications that are mostly structured, for example, block structured grids, composite grids in structured adaptive mesh refinement applications, and overset grids; and a finite element interface (FEI) for unstructured problems, as well as a conventional linear-algebraic interface (IJ). It is extremely important to provide an efficient, scalable implementation of these interfaces in order to support the scalable solvers of the library, especially when using tens of thousands of processors. This article describes the data structures, parallel implementation, and resulting performance of the IJ, Struct and semiStruct interfaces. It investigates their scalability, presents successes as well as pitfalls of some of the approaches and suggests ways of dealing with them.

In this paper, we give an overview of the Cedar multiprocessor and present recent performance results. These include the performance of some computational kernels and the Perfect Benchmarks. We also present a methodology for judging parallel system performance and apply this methodology to Cedar, Cray YMP-8, and Thinking Machines CM-5.