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A large number of scientific and engineering problems require the rapid solution of large systems of simultaneous equations. The performance of parallel computers in this area now dwarfs traditional vector computers by nearly an order of magnitude. This talk describes the major issues involved in parallel equation solvers with particular emphasis on the Intel Paragon, IBM SP-1 and SP-2 processors.
NASA's OpenMDAO framework facilitates constructing complex models and computing their derivatives for multidisciplinary design optimization. Decomposing a model into components that follow a prescribed interface enables OpenMDAO to assemble multidisciplinary derivatives from the component derivatives using what amounts to the adjoint method, direct method, chain rule, global sensitivity equations, or any combination thereof, using the MAUD architecture. OpenMDAO also handles the distribution of processors among the disciplines by hierarchically grouping the components, and it automates the data transfer between components that are on different processors. These features have made OpenMDAO useful for applications in aircraft design, satellite design, wind turbine design, and aircraft engine design, among others. This paper presents new algorithms for OpenMDAO that enable reconfigurable model execution. This concept refers to dynamically changing, during execution, one or more of: the variable sizes, solution algorithm, parallel load balancing, or set of variables-i.e., adding and removing components, perhaps to switch to a higher-fidelity sub-model. Any component can reconfigure at any point, even when running in parallel with other components, and the reconfiguration algorithm presented here performs the synchronized updates to all other components that are affected. A reconfigurable software framework for multidisciplinary design optimization enables new adaptive solvers, adaptive parallelization, and new applications such as gradient-based optimization with overset flow solvers and adaptive mesh refinement. Benchmarking results demonstrate the time savings for reconfiguration compared to setting up the model again from scratch, which can be significant in large-scale problems. Additionally, the new reconfigurability feature is applied to a mission profile optimization problem for commercial aircraft where both the parametrization of the mission profile and the time discretization are adaptively refined, resulting in computational savings of roughly 10% and the elimination of oscillations in the optimized altitude profile.
Gas turbines can experience significant unsteady loading during operation which can cause damage such as blade cracking or bearing wear. While computational fluid dynamics (CFD) modeling of full three-dimensional gas turbine flow to verify meanline design performance is standard practice within the industry, the use of time-accurate CFD makes it possible to assess the unsteady loading which can be especially problematic at operating conditions where unsteady fluid loading aligns with structural modes. The Fluid Dynamics branch (ER42) at NASA Marshall Space Flight Center has developed a time-accurate CFD analysis methodology using the unstructured, density-based, Loci-CHEM solver which is capable of simulating the relative motion required for turbomachinery applications through sliding interface meshes. The highly-parallel unstructured solver allows for full three-dimensional, time-accurate simulation of turbines including upstream and downstream components such as manifolds, nozzles, and stators, any of which could excite a turbine structural mode. Recently, Loci-CHEM was used to analyze the FASTRAC supersonic turbine to assess the loading on the rotor. Overall performance and time-averaged loading on the rotor was computed, including the axial force over the entire rotor disk which is required for force balance calculations on the turbopump. The FASTRAC turbine has supersonic nozzles upstream of the rotor that result in significant unsteady loading on the rotor blades at multiples of the nozzle pass frequency. The unsteady blade pressure loading was decomposed into the frequency domain for direct use in structural forced response analysis. Utilizing this type of CFD analysis coupled with structural analysis has proven to be a valuable tool in identifying structural modes that are being excited by unsteady fluid loading.
Gas turbines can experience significant unsteady loading during operation which can cause damage such as blade cracking or bearing wear. While computational fluid dynamics (CFD) modeling of full three-dimensional gas turbine flow to verify meanline design performance is standard practice within the industry, the use of time-accurate CFD makes it possible to assess the unsteady loading which can be especially problematic at operating conditions where unsteady fluid loading aligns with structural modes. The Fluid Dynamics branch (ER42) at NASA Marshall Space Flight Center has developed a time-accurate CFD analysis methodology using the unstructured, density-based, Loci-CHEM solver which is capable of simulating the relative motion required for turbomachinery applications through sliding interface meshes. The highly-parallel unstructured solver allows for full three-dimensional, time-accurate simulation of turbines including upstream and downstream components such as manifolds, nozzles, and stators, any of which could excite a turbine structural mode. Recently, Loci-CHEM was used to analyze the FASTRAC supersonic turbine to assess the loading on the rotor. Overall performance and time-averaged loading on the rotor was computed, including the axial force over the entire rotor disk which is required for force balance calculations on the turbopump. The FASTRAC turbine has supersonic nozzles upstream of the rotor that result in significant unsteady loading on the rotor blades at multiples of the nozzle pass frequency. The unsteady blade pressure loading was decomposed into the frequency domain for direct use in structural forced response analysis. Utilizing this type of CFD analysis coupled with structural analysis has proven to be a valuable tool in identifying structural modes that are being excited by unsteady fluid loading.
The results of a detailed investigation of the distribution of stresses in aluminum and composite panels subjected to uniform end shortening are presented. The focus problem is a rectangular panel with two longitudinal stiffeners, and an inner stiffener discontinuous at a central hole in the panel. The influence of the stiffeners on the stresses is evaluated through a two-dimensional global finite element analysis in the absence or presence of the hole. Contrary to the physical feel, it is found that the maximum stresses from the glocal analysis for both stiffened aluminum and composite panels are greater than the corresponding stresses for the unstiffened panels. The inner discontinuous stiffener causes a greater increase in stresses than the reduction provided by the two outer stiffeners. A detailed layer-by-layer study of stresses around the hole is also presented for both unstiffened and stiffened composite panels. A parallel equation solver is used for the global system of equations since the computational time is far less than that using a sequential scheme. A parallel Choleski method with up to 16 processors is used on Flex/32 Multicomputer at NASA Langley Research Center. The parallel computing results are summarized and include the computational times, speedups, bandwidths, and their inter-relationships for the panel problems. It is found that the computational time for the Choleski method decreases with a decrease in bandwidth, and better speedups result as the bandwidth increases.
Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.
This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear solvers, nonlinear solvers, and time integrators that may be used in application codes written in Fortran, C, C++, and Python. PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or dbx, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than \rolling them" yourself.
The Lanczos algorithm for the solution of generalized eigen-problem has been receiving a lot of attention in recent years due to its computational efficiency. The focus of this paper is to develop a Lanczos algorithm which can exploit both the parallel and vector capabilities provided by modern high-performance computers. A partial restoring orthogonality scheme is also developed and incorporated into the basic Lanczos algorithm. The numerical performance in terms of accuracy and efficiency of the proposed parallel-vector Lanczos algorithm is demonstrated by solving for the frequencies and mode shapes of structural problems on multiprocessor supercomputers.
A new class of distance-two interpolation methods for algebraic multigrid (AMG) that can be formulated in terms of sparse matrix-matrix multiplications is presented and analyzed. Compared with similar distance-two prolongation operators, the proposed algorithms exhibit improved efficiency and portability to various computing platforms, since they allow one to easily exploit existing high-performance sparse matrix kernels. The new interpolation methods have been implemented in hypre, a widely used parallel multigrid solver library. With the proposed interpolations, the overall time of hypre's BoomerAMG setup can be considerably reduced, while sustaining equivalent, sometimes improved, convergence rates. Numerical results for a variety of test problems on parallel machines are presented that support the superiority of the proposed interpolation operators over the existing ones in hypre.
A Choleski method used to solve linear systems of equations that arise in large scale structural analyses is described. The method uses a novel variable-band storage scheme and is structured to exploit fast local memory caches while minimizing data access delays between main memory and vector registers. Several parallel implementations of this method are described for the CRAY-2 and CRAY Y-MP computers demonstrating the use of microtasking and autotasking directives. A portable parallel language, FORCE, is also used for two different parallel implementations, demonstrating the use of CRAY macrotasking. Results are presented comparing the matrix factorization times for three representative structural analysis problems from runs made in both dedicated and multi-user modes on both the CRAY-2 and CRAY Y-MP computers. CPU and wall clock timings are given for the various parallel methods and are compared to single processor timings of the same algorithm. Computation rates over 1 GIGAFLOP (1 billion floating point operations per second) on a four processor CRAY-2 and over 2 GIGAFLOPS on an eight processor CRAY Y-MP are demonstrated as measured by wall clock time in a dedicated environment. Reduced wall clock times for the parallel methods relative to the single processor implementation of the same Choleski algorithm are also demonstrated for runs made in multi-user mode.
The Simulation EnviRonment for Geomorphology, Hydrodynamics, and Ecohydrology in Integrated form (SERGHEI) is a multi-dimensional, multi-domain, and multi-physics model framework for environmental and landscape simulation, designed with an outlook towards Earth system modelling. At the core of SERGHEI's innovation is its performance-portable high-performance parallel-computing (HPC) implementation, built from scratch on the Kokkos portability layer, allowing SERGHEI to be deployed, in a performance-portable fashion, in graphics processing unit (GPU)-based heterogeneous systems. In this work, we explore combinations of MPI and Kokkos using OpenMP and CUDA backends. In this contribution, we introduce the SERGHEI model framework and present with detail its first operational module for solving shallow-water equations (SERGHEI-SWE) and its HPC implementation. This module is designed to be applicable to hydrological and environmental problems including flooding and runoff generation, with an outlook towards Earth system modelling. Its applicability is demonstrated by testing several well-known benchmarks and large-scale problems, for which SERGHEI-SWE achieves excellent results for the different types of shallow-water problems. Finally, SERGHEI-SWE scalability and performance portability is demonstrated and evaluated on several TOP500 HPC systems, with very good scaling in the range of over 20 000 CPUs and up to 256 state-of-the art GPUs.
The popular QR algorithm for solving all eigenvalues of an unsymmetric matrix is reviewed. Among the basic components in the QR algorithm, it was concluded from this study, that the reduction of an unsymmetric matrix to a Hessenberg form (before applying the QR algorithm itself) can be done effectively by exploiting the vector speed and multiple processors offered by modern high-performance computers. Numerical examples of several test cases have indicated that the proposed parallel-vector algorithm for converting a given unsymmetric matrix to a Hessenberg form offers computational advantages over the existing algorithm. The time saving obtained by the proposed methods is increased as the problem size increased.
The current computing environment that most researchers are using for the calculation of 3D unsteady Computational Fluid Dynamic (CFD) results is a super-computer class machine. The Massively Parallel Processors (MPP's) such as the 160 node IBM SP2 at NAS and clusters of workstations acting as a single MPP (like NAS's SGI Power-Challenge array) provide the required computation bandwidth for CFD calculations of transient problems. Work is in progress on a set of software tools designed specifically to address visualizing 3D unsteady CFD results in these super-computer-like environments. The visualization is concurrently executed with the CFD solver. The parallel version of Visual3, pV3 required splitting up the unsteady visualization task to allow execution across a network of workstation(s) and compute servers. In this computing model, the network is almost always the bottleneck so much of the effort involved techniques to reduce the size of the data transferred between machines.
With the renewed interest in Cartesian gridding methodologies for the ease and speed of gridding complex geometries in addition to the simplicity of the control volumes used in the computations, it has become important to investigate ways of extending the existing Cartesian grid solver functionalities. This includes developing methods of modeling the viscous effects in order to utilize Cartesian grids solvers for accurate drag predictions and addressing the issues related to the distributed memory parallelization of Cartesian solvers. This research presents advances in two areas of interest in Cartesian grid solvers, viscous effects modeling and MPI parallelization. The development of viscous effects modeling using solely Cartesian grids has been hampered by the widely varying control volume sizes associated with the mesh refinement and the cut cells associated with the solid surface. This problem is being addressed by using physically based modeling techniques to update the state vectors of the cut cells and removing them from the finite volume integration scheme. This work is performed on a new Cartesian grid solver, NASCART-GT, with modifications to its cut cell functionality. The development of MPI parallelization addresses issues associated with utilizing Cartesian solvers on distributed memory parallel environments. This work is performed on an existing Cartesian grid solver, CART3D, with modifications to its parallelization methodology.
The popularity of crystal plasticity finite element method (CPFEM) models is increasing due to their ability to predict the mechanical response of crystalline materials such as metals and metal alloys more accurately than traditional continuum mechanics models. This is since the crystal plasticity models consider the effect of atomic structure, microstructural morphology, and properties of individual grains. These CPFEM models use a large number of material parameters in order to capture the mesoscale physics which comes with the downside of the tedious calibration process. In this paper, a CPFEM code was developed to include the twinning induced grain reorientation and subsequent crystallographic slip for HPC material. The developed code is incorporated in a large-scale, parallelized nonlinear solver WARP3D. Further, a sensitivity analysis with respect to 22 material parameters was then conducted using single crystal and polycrystal representative volume element (RVE) of Zircaloy material. Loading was applied along five different crystallographic orientations for single crystal RVE and along three directions namely, rolling (RD), transverse (TD), and normal (ND) direction for polycrystal RVE. Results obtained from the sensitivity analysis were used for the calibration of material parameters for Zircaloy. Finally, developed code along with calibrated material parameters was used to investigate the effect of the hydride phase formation in Zircaloy which is a typical case observed for nuclear applications. It was found that the volume fraction of the hydride phase has a significant impact on the mechanical properties of Zircaloy.
3D image registration is one of the most fundamental and computationally expensive operations in medical image analysis. Here, we present a mixed-precision, Gauss–Newton–Krylov solver for diffeomorphic registration of two images. Our work extends the publicly available CLAIRE library to GPU architectures. Despite the importance of image registration, only a few implementations of large deformation diffeomorphic registration packages support GPUs. Our contributions are new algorithms to significantly reduce the run time of the two main computational kernels in CLAIRE: calculation of derivatives and scattered-data interpolation. Additionally, we deploy (i) highly-optimized, mixed-precision GPU-kernels for the evaluation of scattered-data interpolation, (ii) replace Fast-Fourier-Transform (FFT)-based first-order derivatives with optimized 8th-order finite differences, and (iii) compare with state-of-the-art CPU and GPU implementations. As a highlight, we demonstrate that we can register clinical images in less than 6 s on a single NVIDIA Tesla V100. This amounts to over 20 speed-up over the current version of CLAIRE and over 30 speed-up over existing GPU implementations.
We developed and verified a high-performance open-source discrete element method (DEM) solver with simultaneously-supported feedstock-specific interaction models, including bonded-sphere, liquid bridge, cohesion, and non-linear contact models. Our solver uses parallel data structures on hybrid central and graphics processing unit (CPU/GPU) architectures, with favorable strong scaling performance observed for large problem sizes comprised of (100 M particles), and 4X single-node GPU speedup. The particles for corn stover feedstock were conceptualized and calibrated based on experimental measurements and results. Sensitivity analyses demonstrate that the mass flow rate from a wedge hopper is governed primarily by moisture content, friction coefficient, and cohesion energy density. The model is used to reproduce experimentally observed hopper jamming results, highlighting that the experimental no-flow trends can only be achieved by using non-spherical particles, liquid bridge and cohesion models, highlighting the importance of using concurrent feedstock specialized models for the effective representation of biomass material handling problems.
For high-performance computing (HPC) system designers and users, meeting the myriad challenges of next-generation exascale supercomputing systems requires rethinking their approach to application and system software design. Among these challenges, providing resiliency and stability to the scientific applications in the presence of high fault rates requires new approaches to software architecture and design. As HPC systems become increasingly complex, they require intricate solutions for detection and mitigation for various modes of faults and errors that occur in these large-scale systems, as well as solutions for failure recovery. These resiliency solutions often interact with and affect other system properties, including application scalability, power and energy efficiency. Therefore, resilience solutions for HPC systems must be thoughtfully engineered and deployed.In previous work, we developed the concept of resilience design patterns, which consist of templated solutions based on well-established techniques for detection, mitigation and recovery. In this paper, we use these patterns as the foundation to propose new approaches to designing runtime systems for HPC systems. The instantiation of these patterns within a runtime system enables flexible and adaptable end-to-end resiliency solutions for HPC environments. The paper describes the architecture of the runtime system, named Plexus, and the strategies for dynamically composing and adapting pattern instances under runtime control. This runtime-based approach enables actively balancing the cost-benefit trade-off between performance overhead and protection coverage of the resilience solutions. Based on a prototype implementation of PLEXUS, we demonstrate the resiliency and performance gains achieved by the pattern-based runtime system for a parallel linear solver application.