ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table

A factored sparse approximate inverse preconditioned conjugate gradient solver on graphics processing units

Graphics Processing Units (GPUs) exhibit significantly higher peak performance than conventional CPUs. However, in general only highly parallel algorithms can exploit their potential. In this scenario, the iterative solution to sparse linear systems of equations could be carried out quite efficiently on a GPU as it requires only matrix-by-vector products, dot products, and vector updates. However, to be really effective, any iterative solver needs to be properly preconditioned and this represents a major bottleneck for a successful GPU implementation. Due to its inherent parallelism, the factored sparse approximate inverse (FSAI) preconditioner represents an optimal candidate for the conjugate gradient-like solution of sparse linear systems. However, its GPU implementation requires a nontrivial recasting of multiple computational steps. We present our GPU version of the FSAI preconditioner along with a set of results that show how a noticeable speedup with respect to a highly tuned CPU counterpart is obtained

Book of Abstracts of the Sixth SIAM Workshop on Combinatorial Scientific Computing

Book of Abstracts of CSC14 edited by Bora UçarInternational audienceThe Sixth SIAM Workshop on Combinatorial Scientific Computing, CSC14, was organized at the Ecole Normale Supérieure de Lyon, France on 21st to 23rd July, 2014. This two and a half day event marked the sixth in a series that started ten years ago in San Francisco, USA. The CSC14 Workshop's focus was on combinatorial mathematics and algorithms in high performance computing, broadly interpreted. The workshop featured three invited talks, 27 contributed talks and eight poster presentations. All three invited talks were focused on two interesting fields of research specifically: randomized algorithms for numerical linear algebra and network analysis. The contributed talks and the posters targeted modeling, analysis, bisection, clustering, and partitioning of graphs, applied in the context of networks, sparse matrix factorizations, iterative solvers, fast multi-pole methods, automatic differentiation, high-performance computing, and linear programming. The workshop was held at the premises of the LIP laboratory of ENS Lyon and was generously supported by the LABEX MILYON (ANR-10-LABX-0070, Université de Lyon, within the program ''Investissements d'Avenir'' ANR-11-IDEX-0007 operated by the French National Research Agency), and by SIAM

Fine-Grained Multithreading for the Multifrontal QR Factorization of Sparse Matrices

International audienceThe advent of multicore processors represents a disruptive event in the history of computer science as conventional parallel programming paradigms are proving incapable of fully exploiting their potential for concurrent computations. The need for different or new programming models clearly arises from recent studies which identify fine-granularity and dynamic execution as the keys to achieving high efficiency on multicore systems. This work presents an approach to the parallelization of the multifrontal method for the $QR$ factorization of sparse matrices specifically designed for multicore based systems. High efficiency is achieved through a fine-grained partitioning of data and a dynamic scheduling of computational tasks relying on a dataflow parallel programming model. Experimental results show that an implementation of the proposed approach achieves higher performance and better scalability than existing equivalent software

High-performance direct solution of finite element problems on multi-core processors

A direct solution procedure is proposed and developed which exploits the parallelism that exists in current symmetric multiprocessing (SMP) multi-core processors. Several algorithms are proposed and developed to improve the performance of the direct solution of FE problems. A high-performance sparse direct solver is developed which allows experimentation with the newly developed and existing algorithms. The performance of the algorithms is investigated using a large set of FE problems. Furthermore, operation count estimations are developed to further assess various algorithms. An out-of-core version of the solver is developed to reduce the memory requirements for the solution. I/O is performed asynchronously without blocking the thread that makes the I/O request. Asynchronous I/O allows overlapping factorization and triangular solution computations with I/O. The performance of the developed solver is demonstrated on a large number of test problems. A problem with nearly 10 million degree of freedoms is solved on a low price desktop computer using the out-of-core version of the direct solver. Furthermore, the developed solver usually outperforms a commonly used shared memory solver.Ph.D.Committee Chair: Will, Kenneth; Committee Member: Emkin, Leroy; Committee Member: Kurc, Ozgur; Committee Member: Vuduc, Richard; Committee Member: White, Donal

Evaluation of Distributed Programming Models and Extensions to Task-based Runtime Systems

High Performance Computing (HPC) has always been a key foundation for scientific simulation and discovery. And more recently, deep learning models\u27 training have further accelerated the demand of computational power and lower precision arithmetic. In this era following the end of Dennard\u27s Scaling and when Moore\u27s Law seemingly still holds true to a lesser extent, it is not a coincidence that HPC systems are equipped with multi-cores CPUs and a variety of hardware accelerators that are all massively parallel. Coupling this with interconnect networks\u27 speed improvements lagging behind those of computational power increases, the current state of HPC systems is heterogeneous and extremely complex. This was heralded as a great challenge to the software stacks and their ability to extract performance from these systems, but also as a great opportunity to innovate at the programming model level to explore the different approaches and propose new solutions. With usability, portability, and performance as the main factors to consider, this dissertation first evaluates some of the widely used parallel programming models (MPI, MPI+OpenMP, and task-based runtime systems) ability to manage the load imbalance among the processes computing the LU factorization of a large dense matrix stored in the Block Low-Rank (BLR) format. Next I proposed a number of optimizations and implemented them in PaRSEC\u27s Dynamic Task Discovery (DTD) model, including user-level graph trimming and direct Application Programming Interface (API) calls to perform data broadcast operation to further extend the limit of STF model. On the other hand, the Parameterized Task Graph (PTG) approach in PaRSEC is the most scalable approach for many different applications, which I then explored the possibility of combining both the algorithmic approach of Communication-Avoiding (CA) and the communication-computation overlapping benefits provided by runtime systems using 2D five-point stencil as the test case. This broad programming models evaluation and extension work highlighted the abilities of task-based runtime system in achieving scalable performance and portability on contemporary heterogeneous HPC systems. Finally, I summarized the profiling capability of PaRSEC runtime system, and demonstrated with a use case its important role in the performance bottleneck identification leading to optimizations

Methodology for malleable applications on distributed memory systems

A la portada logo BSC(English) The dominant programming approach for scientific and industrial computing on clusters is MPI+X. While there are a variety of approaches within the node, denoted by the ``X'', Message Passing interface (MPI) is the standard for programming multiple nodes with distributed memory. This thesis argues that the OmpSs-2 tasking model can be extended beyond the node to naturally support distributed memory, with three benefits: First, at small to medium scale the tasking model is a simpler and more productive alternative to MPI. It eliminates the need to distribute the data explicitly and convert all dependencies into explicit message passing. It also avoids the complexity of hybrid programming using MPI+X. Second, the ability to offload parts of the computation among the nodes enables the runtime to automatically balance the loads in a full-scale MPI+X program. This approach does not require a cost model, and it is able to transparently balance the computational loads across the whole program, on all its nodes. Third, because the runtime handles all low-level aspects of data distribution and communication, it can change the resource allocation dynamically, in a way that is transparent to the application. This thesis describes the design, development and evaluation of OmpSs-2@Cluster, a programming model and runtime system that extends the OmpSs-2 model to allow a virtually unmodified OmpSs-2 program to run across multiple distributed memory nodes. For well-balanced applications it provides similar performance to MPI+OpenMP on up to 16 nodes, and it improves performance by up to 2x for irregular and unbalanced applications like Cholesky factorization. This work also extended OmpSs-2@Cluster for interoperability with MPI and Barcelona Supercomputing Center (BSC)'s state-of-the-art Dynamic Load Balance (DLB) library in order to dynamically balance MPI+OmpSs-2 applications by transparently offloading tasks among nodes. This approach reduces the execution time of a microscale solid mechanics application by 46% on 64 nodes and on a synthetic benchmark, it is within 10% of perfect load balancing on up to 8 nodes. Finally, the runtime was extended to transparently support malleability for pure OmpSs-2@Cluster programs and interoperate with the Resources Management System (RMS). The only change to the application is to explicitly call an API function to control the addition or removal of nodes. In this regard we additionally provide the runtime with the ability to semi-transparently save and recover part of the application status to perform checkpoint and restart. Such a feature hides the complexity of data redistribution and parallel IO from the user while allowing the program to recover and continue previous executions. Our work is a starting point for future research on fault tolerance. In summary, OmpSs-2@Cluster expands the OmpSs-2 programming model to encompass distributed memory clusters. It allows an existing OmpSs-2 program, with few if any changes, to run across multiple nodes. OmpSs-2@Cluster supports transparent multi-node dynamic load balancing for MPI+OmpSs-2 programs, and enables semi-transparent malleability for OmpSs-2@Cluster programs. The runtime system has a high level of stability and performance, and it opens several avenues for future work.(Español) El modelo de programación dominante para clusters tanto en ciencia como industria es actualmente MPI+X. A pesar de que hay alguna variedad de alternativas para programar dentro de un nodo (indicado por la "X"), el estandar para programar múltiples nodos con memoria distribuida sigue siendo Message Passing Interface (MPI). Esta tesis propone la extensión del modelo de programación basado en tareas OmpSs-2 para su funcionamiento en sistemas de memoria distribuida, destacando 3 beneficios principales: En primer lugar; a pequeña y mediana escala, un modelo basado en tareas es más simple y productivo que MPI y elimina la necesidad de distribuir los datos explícitamente y convertir todas las dependencias en mensajes. Además, evita la complejidad de la programacion híbrida MPI+X. En segundo lugar; la capacidad de enviar partes del cálculo entre los nodos permite a la librería balancear la carga de trabajo en programas MPI+X a gran escala. Este enfoque no necesita un modelo de coste y permite equilibrar cargas transversalmente en todo el programa y todos los nodos. En tercer lugar; teniendo en cuenta que es la librería quien maneja todos los aspectos relacionados con distribución y transferencia de datos, es posible la modificación dinámica y transparente de los recursos que utiliza la aplicación. Esta tesis describe el diseño, desarrollo y evaluación de OmpSs-2@Cluster; un modelo de programación y librería que extiende OmpSs-2 permitiendo la ejecución de programas OmpSs-2 existentes en múltiples nodos sin prácticamente necesidad de modificarlos. Para aplicaciones balanceadas, este modelo proporciona un rendimiento similar a MPI+OpenMP hasta 16 nodos y duplica el rendimiento en aplicaciones irregulares o desbalanceadas como la factorización de Cholesky. Este trabajo incluye la extensión de OmpSs-2@Cluster para interactuar con MPI y la librería de balanceo de carga Dynamic Load Balancing (DLB) desarrollada en el Barcelona Supercomputing Center (BSC). De este modo es posible equilibrar aplicaciones MPI+OmpSs-2 mediante la transferencia transparente de tareas entre nodos. Este enfoque reduce el tiempo de ejecución de una aplicación de mecánica de sólidos a micro-escala en un 46% en 64 nodos; en algunos experimentos hasta 8 nodos se pudo equilibrar perfectamente la carga con una diferencia inferior al 10% del equilibrio perfecto. Finalmente, se implementó otra extensión de la librería para realizar operaciones de maleabilidad en programas OmpSs-2@Cluster e interactuar con el Sistema de Manejo de Recursos (RMS). El único cambio requerido en la aplicación es la llamada explicita a una función de la interfaz que controla la adición o eliminación de nodos. Además, se agregó la funcionalidad de guardar y recuperar parte del estado de la aplicación de forma semitransparente con el objetivo de realizar operaciones de salva-reinicio. Dicha funcionalidad oculta al usuario la complejidad de la redistribución de datos y las operaciones de lectura-escritura en paralelo, mientras permite al programa recuperar y continuar ejecuciones previas. Este es un punto de partida para futuras investigaciones en tolerancia a fallos. En resumen, OmpSs-2@Cluster amplía el modelo de programación de OmpSs-2 para abarcar sistemas de memoria distribuida. El modelo permite la ejecución de programas OmpSs-2 en múltiples nodos prácticamente sin necesidad de modificarlos. OmpSs-2@Cluster permite además el balanceo dinámico de carga en aplicaciones híbridas MPI+OmpSs-2 ejecutadas en varios nodos y es capaz de realizar maleabilidad semi-transparente en programas OmpSs-2@Cluster puros. La librería tiene un niveles de rendimiento y estabilidad altos y abre varios caminos para trabajos futuro.Arquitectura de computador

2D Static Resource Allocation for Compressed Linear Algebra and Communication Constraints

International audienceThis paper adresses static resource allocation problems for irregular distributed parallel applications. More precisely, we focus on two classical tiled linear algebra kernels: the Matrix Multiplication (MM) and the LU decomposition (LU) algorithms on large linear systems. In the context of parallel distributed platforms, data exchanges can dramatically degrade the performance of linear algebra kernels and in this context, compression techniques such as Block Low Rank (BLR) compression techniques are good candidates both for limiting data storage on each processor and data exchanges between processors. On the other hand, the use of BLR representation makes the static allocation problem of tiles to processors more complex. Indeed, the load associated to each tile depends on its compression factor, which induces an heterogeneous load balancing problem. In turn, solving this load balancing problem optimally might lead to complex allocation schemes, where the tiles allocated to a given processor are scattered all over the matrix. This in turn induces communication costs, since matrix multiplication and LU decompositions heavily rely on broadcasting operations along rows and columns of processors, so that the communication volume is minimized when the maximal number of different processors on any row and column is minimized. In the fully homogeneous case, 2D Block Cyclic (BC) allocation solves both load balancing and communication minimization issues simultaneously , but it might lead to bad load balancing in the heterogeneous case. Our goal in this paper is to propose data allocation schemes dedicated to BLR format and to prove that it is possible to obtain good performance on makespan when simultaneously balancing the load and minimizing the maximal number of different processor in any row or column

Software Support for Irregular and Loosely Synchronous Problems

A large class of scientific and engineering applications may be classified as irregular and loosely synchronous from the perspective of parallel processing. We present a partial classification of such problems. This classification has motivated us to enhance Fortran D to provide language support for irregular, loosely synchronous problems. We present techniques for parallelization of such problems in the context of Fortran D