SPICE²: A Spatial, Parallel Architecture for Accelerating the Spice Circuit Simulator

Spatial processing of sparse, irregular floating-point computation using a single FPGA enables up to an order of magnitude speedup (mean 2.8X speedup) over a conventional microprocessor for the SPICE circuit simulator. We deliver this speedup using a hybrid parallel architecture that spatially implements the heterogeneous forms of parallelism available in SPICE. We decompose SPICE into its three constituent phases: Model-Evaluation, Sparse Matrix-Solve, and Iteration Control and parallelize each phase independently. We exploit data-parallel device evaluations in the Model-Evaluation phase, sparse dataflow parallelism in the Sparse Matrix-Solve phase and compose the complete design in streaming fashion. We name our parallel architecture SPICE²: Spatial Processors Interconnected for Concurrent Execution for accelerating the SPICE circuit simulator. We program the parallel architecture with a high-level, domain-specific framework that identifies, exposes and exploits parallelism available in the SPICE circuit simulator. This design is optimized with an auto-tuner that can scale the design to use larger FPGA capacities without expert intervention and can even target other parallel architectures with the assistance of automated code-generation. This FPGA architecture is able to outperform conventional processors due to a combination of factors including high utilization of statically-scheduled resources, low-overhead dataflow scheduling of fine-grained tasks, and overlapped processing of the control algorithms. We demonstrate that we can independently accelerate Model-Evaluation by a mean factor of 6.5X(1.4--23X) across a range of non-linear device models and Matrix-Solve by 2.4X(0.6--13X) across various benchmark matrices while delivering a mean combined speedup of 2.8X(0.2--11X) for the two together when comparing a Xilinx Virtex-6 LX760 (40nm) with an Intel Core i7 965 (45nm). With our high-level framework, we can also accelerate Single-Precision Model-Evaluation on NVIDIA GPUs, ATI GPUs, IBM Cell, and Sun Niagara 2 architectures. We expect approaches based on exploiting spatial parallelism to become important as frequency scaling slows down and modern processing architectures turn to parallelism (\eg multi-core, GPUs) due to constraints of power consumption. This thesis shows how to express, exploit and optimize spatial parallelism for an important class of problems that are challenging to parallelize.</p

ASCR/HEP Exascale Requirements Review Report

This draft report summarizes and details the findings, results, and recommendations derived from the ASCR/HEP Exascale Requirements Review meeting held in June, 2015. The main conclusions are as follows. 1) Larger, more capable computing and data facilities are needed to support HEP science goals in all three frontiers: Energy, Intensity, and Cosmic. The expected scale of the demand at the 2025 timescale is at least two orders of magnitude -- and in some cases greater -- than that available currently. 2) The growth rate of data produced by simulations is overwhelming the current ability, of both facilities and researchers, to store and analyze it. Additional resources and new techniques for data analysis are urgently needed. 3) Data rates and volumes from HEP experimental facilities are also straining the ability to store and analyze large and complex data volumes. Appropriately configured leadership-class facilities can play a transformational role in enabling scientific discovery from these datasets. 4) A close integration of HPC simulation and data analysis will aid greatly in interpreting results from HEP experiments. Such an integration will minimize data movement and facilitate interdependent workflows. 5) Long-range planning between HEP and ASCR will be required to meet HEP's research needs. To best use ASCR HPC resources the experimental HEP program needs a) an established long-term plan for access to ASCR computational and data resources, b) an ability to map workflows onto HPC resources, c) the ability for ASCR facilities to accommodate workflows run by collaborations that can have thousands of individual members, d) to transition codes to the next-generation HPC platforms that will be available at ASCR facilities, e) to build up and train a workforce capable of developing and using simulations and analysis to support HEP scientific research on next-generation systems.Comment: 77 pages, 13 Figures; draft report, subject to further revisio

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.Comment: Submitted as a roadmap article to Modelling and Simulation in Materials Science and Engineering; Address any correspondence to Vikram Gavini ([email protected]) and Danny Perez ([email protected]

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Roadmap on electronic structure codes in the exascale era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry, and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing

Parallel algorithms for computational fluid dynamics on unstructured meshes

La simulació numèrica directa (DNS) de fluxos complexes és actualment una utopia per la majoria d'aplicacions industrials ja que els requeriments computacionals son massa elevats. Donat un flux, la diferència entre els recursos computacionals necessaris i els disponibles és cobreix mitjançant la modelització/simplificació d'alguns termes de les equacions originals que regeixen el seu comportament. El creixement continuat dels recursos computacionals disponibles, principalment en forma de super-ordinadors, contribueix a reduir la part del flux que és necessari aproximar. De totes maneres, obtenir la eficiència esperada dels nous super-ordinadors no és una tasca senzilla i, per aquest motiu, part de la recerca en el camp de la Mecànica de Fluids Computacional es centra en aquest objectiu. En aquest sentit, algunes contribucions s'han presentat en el marc d'aquesta tesis. El primer objectiu va ser el desenvolupament d'un codi de CFD de propòsit general i paral·lel, basat en la metodologia de volums finits en malles no estructurades, per resoldre problemes de multi-física. Aquest codi, anomenat TermoFluids (TF), té un disseny orientat a objectes i pensat per ser usat de forma altament eficient en els super-ordinadors actuals. Amb el temps, ha esdevingut pel grup una eina fonamental en projectes tant de recerca bàsica com d'interès industrial. En el context d'aquesta tesis, el treball s'ha focalitzat en el desenvolupament de dos de les llibreries més bàsiques de TermoFluids: i) La Basics Objects Library (BOL), que es una plataforma de software sobre la qual estan programades la resta de llibreries del codi, i que conté els mètodes algebraics i geomètrics fonamentals per la implementació paral·lela dels algoritmes de discretització, ii) la Linear Solvers Library (LSL), que conté un gran nombre de mètodes per resoldre els sistemes d'equacions lineals derivats de les discretitzacions. El primer capítol d'aquesta tesi conté les principals idees subjacents al disseny i la implementació de la BOL i la LSL, juntament amb alguns exemples i algunes aplicacions industrials. En els capítols posteriors hi ha una explicació detallada de solvers específics per algunes aplicacions concretes. En el segon capítol, es presenta un solver paral·lel i directe per la resolució de l'equació de Poisson per casos en els quals una de les direccions del domini té condicions d'homogeneïtat. En la simulació de fluxos incompressibles, l'equació de Poisson es resol almenys una vegada en cada pas de temps, convertint-se en una de les parts més costoses i difícils de paral·lelitzar del codi. El mètode que proposem és una combinació d'una descomposició directa de Schur (DDS) i una diagonalització de Fourier. La darrera descompon el sistema original en un conjunt de sub-sistemes 2D independents que es resolen mitjançant l'algorisme DDS. Atès que no s'imposen restriccions a les direccions no periòdiques del domini, aquest mètode és aplicable a la resolució de problemes discretitzats mitjançat l'extrusió de malles 2D no estructurades. L'escalabilitat d'aquest mètode ha estat provada amb èxit amb un màxim de 8192 CPU per malles de fins a ~10⁹ volums de control. En el darrer capitol capítol, es presenta un mètode de resolució per l'equació de Transport de Boltzmann (BTE). La estratègia emprada es basa en el mètode d'Ordenades Discretes i pot ser aplicat en discretitzacions no estructurades. El flux per a cada ordenada angular es resol amb un mètode de substitució equivalent a la resolució d'un sistema lineal triangular. La naturalesa seqüencial d'aquest procés fa de la paral·lelització de l'algoritme el principal repte. Diversos algorismes de substitució han estat analitzats, esdevenint una de les heurístiques proposades la millor opció en totes les situacions analitzades, amb excel·lents resultats. Els testos d'eficiència paral·lela s'han realitzat usant fins a 2560 CPU.Direct Numerical Simulation (DNS) of complex flows is currently an utopia for most of industrial applications because computational requirements are too high. For a given flow, the gap between the required and the available computing resources is covered by modeling/simplifying of some terms of the original equations. On the other hand, the continuous growth of the computing power of modern supercomputers contributes to reduce this gap, reducing hence the unresolved physics that need to be attempted with approximated models. This growth, widely relies on parallel computing technologies. However, getting the expected performance from new complex computing systems is becoming more and more difficult, and therefore part of the CFD research is focused on this goal. Regarding to it, some contributions are presented in this thesis. The first objective was to contribute to the development of a general purpose multi-physics CFD code. referred to as TermoFluids (TF). TF is programmed following the object oriented paradigm and designed to run in modern parallel computing systems. It is also intensively involved in many different projects ranging from basic research to industry applications. Besides, one of the strengths of TF is its good parallel performance demonstrated in several supercomputers. In the context of this thesis, the work was focused on the development of two of the most basic libraries that compose TF: I) the Basic Objects Library (BOL), which is a parallel unstructured CFD application programming interface, on the top of which the rest of libraries that compose TF are written, ii) the Linear Solvers Library (LSL) containing many different algorithms to solve the linear systems arising from the discretization of the equations. The first chapter of this thesis contains the main ideas underlying the design and the implementation of the BOL and LSL libraries, together with some examples and some industrial applications. A detailed description of some application-specific linear solvers included in the LSL is carried out in the following chapters. In the second chapter, a parallel direct Poisson solver restricted to problems with one uniform periodic direction is presented. The Poisson equation is solved, at least, once per time-step when modeling incompressible flows, becoming one of the most time consuming and difficult to parallelize parts of the code. The solver here proposed is a combination of a direct Schur-complement based decomposition (DSD) and a Fourier diagonalization. The latter decomposes the original system into a set of mutually independent 2D sub-systems which are solved by means of the DSD algorithm. Since no restrictions are imposed in the non-periodic directions, the overall algorithm is well-suited for solving problems discretized on extruded 2D unstructured meshes. The scalability of the solver has been successfully tested using up to 8192 CPU cores for meshes with up to 10 9 grid points. In the last chapter, a solver for the Boltzmann Transport Equation (BTE) is presented. It can be used to solve radiation phenomena interacting with flows. The solver is based on the Discrete Ordinates Method and can be applied to unstructured discretizations. The flux for each angular ordinate is swept across the computational grid, within a source iteration loop that accounts for the coupling between the different ordinates. The sequential nature of the sweep process makes the parallelization of the overall algorithm the most challenging aspect. Several parallel sweep algorithms, which represent different options of interleaving communications and calculations, are analyzed. One of the heuristics proposed consistently stands out as the best option in all the situations analyzed. With this algorithm, good scalability results have been achieved regarding both weak and strong speedup tests with up to 2560 CPUs

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing