Hybrid collocation perturbation for PDEs with random domains

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by $N$ random variables. The random domain is split into large and small variations contributions. The large variations are approximated by applying a sparse grid stochastic collocation method. The small variations are approximated with a stochastic collocation-perturbation method. Convergence rates for the variance of the QoI are derived and compared to those obtained in numerical experiments. Our approach significantly reduces the dimensionality of the stochastic problem. The computational cost of this method increases at most quadratically with respect to the number of dimensions of the small variations. Moreover, for the case that the small and large variations are independent the cost increases linearly

A Domain-Specific Language and Editor for Parallel Particle Methods

Domain-specific languages (DSLs) are of increasing importance in scientific high-performance computing to reduce development costs, raise the level of abstraction and, thus, ease scientific programming. However, designing and implementing DSLs is not an easy task, as it requires knowledge of the application domain and experience in language engineering and compilers. Consequently, many DSLs follow a weak approach using macros or text generators, which lack many of the features that make a DSL a comfortable for programmers. Some of these features---e.g., syntax highlighting, type inference, error reporting, and code completion---are easily provided by language workbenches, which combine language engineering techniques and tools in a common ecosystem. In this paper, we present the Parallel Particle-Mesh Environment (PPME), a DSL and development environment for numerical simulations based on particle methods and hybrid particle-mesh methods. PPME uses the meta programming system (MPS), a projectional language workbench. PPME is the successor of the Parallel Particle-Mesh Language (PPML), a Fortran-based DSL that used conventional implementation strategies. We analyze and compare both languages and demonstrate how the programmer's experience can be improved using static analyses and projectional editing. Furthermore, we present an explicit domain model for particle abstractions and the first formal type system for particle methods.Comment: Submitted to ACM Transactions on Mathematical Software on Dec. 25, 201

RTSim: A cycle-accurate simulator for racetrack memories

Racetrack memories (RTMs) have drawn considerable attention from computer architects of late. Owing to the ultra-high capacity and comparable access latency to SRAM, RTMs are promising candidates to revolutionize the memory subsystem. In order to evaluate their performance and suitability at various levels in the memory hierarchy, it is crucial to have RTM-specific simulation tools that accurately model their behavior and enable exhaustive design space exploration. To this end, we propose RTSim, an open source cycle-accurate memory simulator that enables performance evaluation of the domain-wall-based racetrack memories. The skyrmions-based RTMs can also be modeled with RTSim because they are architecturally similar to domain-wall-based RTMs. RTSim is developed in collaboration with physicists and computer scientists. It accurately models RTM-specific shift operations, access ports management and the sequence of memory commands beside handling the routine read/write operations. RTSim is built on top of NVMain2.0, offering larger design space for exploration

Shiftsreduce: Minimizing shifts in racetrack memory 4.0

Racetrack memories (RMs) have significantly evolved since their conception in 2008, making them a serious contender in the field of emerging memory technologies. Despite key technological advancements, the access latency and energy consumption of an RM-based system are still highly influenced by the number of shift operations. These operations are required to move bits to the right positions in the racetracks. This article presents data-placement techniques for RMs that maximize the likelihood that consecutive references access nearby memory locations at runtime, thereby minimizing the number of shifts. We present an integer linear programming (ILP) formulation for optimal data placement in RMs, and we revisit existing offset assignment heuristics, originally proposed for random-access memories. We introduce a novel heuristic tailored to a realistic RM and combine it with a genetic search to further improve the solution. We show a reduction in the number of shifts of up to 52.5%, outperforming the state of the art by up to 16.1%

A language and development environment for parallel particle methods

We present the Parallel Particle-Mesh Environment (PPME), a domain-specific language (DSL) and development environment for numerical simulations using particles and hybrid particle-mesh methods. PPME is the successor of the Parallel Particle-Mesh Language (PPML), a Fortran-based DSL that provides high-level abstrac- tions for the development of distributed-memory particle-mesh simulations. On top of PPML, PPME provides a complete development environment for particle-based simu- lations usin state-of-the-art language engineering and compiler construction techniques. Relying on a novel domain metamodel and formal type system for particle methods, it enables advanced static code correctness checks at the level of particle abstractions, com- plementing the low-level analysis of the compiler. Furthermore, PPME adopts Herbie for improving the accuracy of floating-point expressions and supports a convenient high-level mathematical notation for equations and differential operators. For demonstration purposes, we discuss an example from Discrete Element Methods (DEM) using the classic Silbert model to simulate granular flows

Automatic Creation of High-Bandwidth Memory Architectures from Domain-Specific Languages: The Case of Computational Fluid Dynamics

Numerical simulations can help solve complex problems. Most of these algorithms are massively parallel and thus good candidates for FPGA acceleration thanks to spatial parallelism. Modern FPGA devices can leverage high-bandwidth memory technologies, but when applications are memory-bound designers must craft advanced communication and memory architectures for efficient data movement and on-chip storage. This development process requires hardware design skills that are uncommon in domain-specific experts. In this paper, we propose an automated tool flow from a domain-specific language (DSL) for tensor expressions to generate massively-parallel accelerators on HBM-equipped FPGAs. Designers can use this flow to integrate and evaluate various compiler or hardware optimizations. We use computational fluid dynamics (CFD) as a paradigmatic example. Our flow starts from the high-level specification of tensor operations and combines an MLIR-based compiler with an in-house hardware generation flow to generate systems with parallel accelerators and a specialized memory architecture that moves data efficiently, aiming at fully exploiting the available CPU-FPGA bandwidth. We simulated applications with millions of elements, achieving up to 103 GFLOPS with one compute unit and custom precision when targeting a Xilinx Alveo U280. Our FPGA implementation is up to 25x more energy efficient than expert-crafted Intel CPU implementations

Magnetic racetrack memory: from physics to the cusp of applications within a decade

Racetrack memory (RTM) is a novel spintronic memory-storage technology that has the potential to overcome fundamental constraints of existing memory and storage devices. It is unique in that its core differentiating feature is the movement of data, which is composed of magnetic domain walls (DWs), by short current pulses. This enables more data to be stored per unit area compared to any other current technologies. On the one hand, RTM has the potential for mass data storage with unlimited endurance using considerably less energy than today's technologies. On the other hand, RTM promises an ultrafast nonvolatile memory competitive with static random access memory (SRAM) but with a much smaller footprint. During the last decade, the discovery of novel physical mechanisms to operate RTM has led to a major enhancement in the efficiency with which nanoscopic, chiral DWs can be manipulated. New materials and artificially atomically engineered thin-film structures have been found to increase the speed and lower the threshold current with which the data bits can be manipulated. With these recent developments, RTM has attracted the attention of the computer architecture community that has evaluated the use of RTM at various levels in the memory stack. Recent studies advocate RTM as a promising compromise between, on the one hand, power-hungry, volatile memories and, on the other hand, slow, nonvolatile storage. By optimizing the memory subsystem, significant performance improvements can be achieved, enabling a new era of cache, graphical processing units, and high capacity memory devices. In this article, we provide an overview of the major developments of RTM technology from both the physics and computer architecture perspectives over the past decade. We identify the remaining challenges and give an outlook on its future