SEARCH · Search NASA

Results for “Parallelization efficiency”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

All sources NASA NTRS DOE OSTI

DOE OSTI2014

Collaborating CPU and GPU for large-scale high-order CFD simulations with complex grids on the TianHe-1A supercomputer

Programming and optimizing complex, real-world CFD codes on current many-core accelerated HPC systems is very challenging, especially when collaborating CPUs and accelerators to fully tap the potential of heterogeneous systems. In this paper, with a tri-level hybrid and heterogeneous programming model using MPI + OpenMP + CUDA, we port and optimize our high-order multi-block structured CFD software HOSTA on the GPU-accelerated TianHe-1A supercomputer. HOSTA adopts two self-developed high-order compact definite difference schemes WCNS and HDCS that can simulate flows with complex geometries. We present a dual-level parallelization scheme for efficient multi-block computation on GPUs and perform particular kernel optimizations for high-order CFD schemes. The GPU-only approach achieves a speedup of about 1.3 when comparing one Tesla M2050 GPU with two Xeon X5670 CPUs. To achieve a greater speedup, we collaborate CPU and GPU for HOSTA instead of using a naive GPU-only approach. We present a novel scheme to balance the loads between the store-poor GPU and the store-rich CPU. Taking CPU and GPU load balance into account, we improve the maximum simulation problem size per TianHe-1A node for HOSTA by 2.3×, meanwhile the collaborative approach can improve the performance by around 45% compared to the GPU-only approach. Further, to scale HOSTA on TianHe-1A, we propose a gather/scatter optimization to minimize PCI-e data transfer times for ghost and singularity data of 3D grid blocks, and overlap the collaborative computation and communication as far as possible using some advanced CUDA and MPI features. Scalability tests show that HOSTA can achieve a parallel efficiency of above 60% on 1024 TianHe-1A nodes. With our method, we have successfully simulated an EET high-lift airfoil configuration containing 800M cells and China's large civil airplane configuration containing 150M cells. To our best knowledge, those are the largest-scale CPU–GPU collaborative simulations that solve realistic CFD problems with both complex configurations and high-order schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Parallel-In-Time Magnus Integrators

Magnus integrators are a subset of geometric integration methods for the numerical solution of ordinary differential equations that conserve certain invariants in the numerical solution. Our report explores temporal parallelism of Magnus integrators, particularly in the context of nonlinear problems. The method combines the concurrent computation of matrix commutators and exponentials within a time step with a pipelined iteration applied to multiple time steps in parallel. The accuracy and efficiency of time parallel Magnus methods up to order six are highlighted through numerical examples and demonstrate that critical parallel speedup is possible compared to serial methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Iso-Energy-Efficiency: An Approach to Power Constrained Parallel Computation

Future large scale high performance supercomputer systems require high energy efficiency to achieve exaflops computational power and beyond. Despite the need to understand energy efficiency in high-performance systems, there are few techniques to evaluate energy efficiency at scale. In this paper, we propose a system level iso-energy-efficiency model to analyze, evaluate and predict energy-performance of data intensive parallel applications with various execution patterns running on large scale power-aware clusters. Our analytical model can help users explore the effects of machine and application dependent characteristics on system energy efficiency and isolate efficient ways to scale system parameters (e.g. processor count, CPU power/frequency, workload size and network bandwidth) to balance energy use and performance. We derive our iso-energy-efficiency model and apply it to the NAS Parallel Benchmarks on two power-aware clusters. Our results indicate that the model accurately predicts total system energy consumption within 5% error on average for parallel applications with various execution and communication patterns. We demonstrate effective use of the model for various application contexts and in scalability decision-making.

Song, Shuaiwen↗

DOE OSTI2013

Improving computational efficiency of Monte Carlo simulations with variance reduction

CCFE perform Monte-Carlo transport simulations on large and complex tokamak models such as ITER. Such simulations are challenging since streaming and deep penetration effects are equally important. In order to make such simulations tractable, both variance reduction (VR) techniques and parallel computing are used. It has been found that the application of VR techniques in such models significantly reduces the efficiency of parallel computation due to 'long histories'. VR in MCNP can be accomplished using energy-dependent weight windows. The weight window represents an 'average behaviour' of particles, and large deviations in the arriving weight of a particle give rise to extreme amounts of splitting being performed and a long history. When running on parallel clusters, a long history can have a detrimental effect on the parallel efficiency - if one process is computing the long history, the other CPUs complete their batch of histories and wait idle. Furthermore some long histories have been found to be effectively intractable. To combat this effect, CCFE has developed an adaptation of MCNP which dynamically adjusts the WW where a large weight deviation is encountered. The method effectively 'de-optimises' the WW, reducing the VR performance but this is offset by a significant increase in parallel efficiency. Testing with a simple geometry has shown the method does not bias the result. This 'long history method' has enabled CCFE to significantly improve the performance of MCNP calculations for ITER on parallel clusters, and will be beneficial for any geometry combining streaming and deep penetration effects. (authors)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Kinetic Simulations of Particle Acceleration at Shocks

Collisionless shocks are mediated by collective electromagnetic interactions and are sources of non-thermal particles and emission. The full particle-in-cell approach and a hybrid approach are sketched, simulations of collisionless shocks are shown using a multicolor presentation. Results for SN 1006, a case involving ion acceleration and B field amplification where the shock is parallel, are shown. Electron acceleration takes place in planetary bow shocks and galaxy clusters. It is concluded that acceleration at shocks can be efficient: >15%; CRs amplify B field via streaming instability; ion DSA is efficient at parallel, strong shocks; ions are injected via reflection and shock drift acceleration; and electron DSA is efficient at oblique shocks.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Massively-parallel electron dynamics calculations in real-time and real-space: Toward applications to nanostructures of more than ten-nanometers in size

A highly efficient program of massively parallel calculations for electron dynamics has been developed in an effort to apply the method to optical response of nanostructures of more than ten-nanometers in size. The approach is based on time-dependent density functional theory calculations in real-time and real-space. The computational code is implemented by using simple algorithms with a finite-difference method in space derivative and Taylor expansion in time-propagation. Since the computational program is free from the algorithms of eigenvalue problems and fast-Fourier-transformation, which are usually implemented in conventional quantum chemistry or band structure calculations, it is highly suitable for massively parallel calculations. Benchmark calculations using the K computer at RIKEN demonstrate that the parallel efficiency of the program is very high on more than 60 000 CPU cores. The method is applied to optical response of arrays of C{sub 60} orderly nanostructures of more than 10 nm in size. The computed absorption spectrum is in good agreement with the experimental observation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Chemoselective, osmium-free, dihydroxylation/oxidative cleavage of heteroaryl isoprenes by a contemporary Malaprade reaction

The methyl ketone is a central synthetic building block for the construction of advanced heteroaryl scaffolds and systems. Reactions, including oxidative cyclization strategies, are often predicated on efficient access to this ubiquitous moiety. In the context of arenes, standard approaches leveraging Markovnikov hydration/oxidation or oxidative cleavage of the C–C π bond often afford satisfactory performance. However, when the substrate contains an electron-deficient heteroaryl core, the traditional Malaprade reaction, and related oxidative-cleavage strategies, frequently result in diminished performance over carbon-based arenes. In this work we present the development and application of an oxidative cleavage reaction of various pyridinyl isoprenes towards accessing the downstream methyl ketone for utilization in advanced cyclizations for the preparation of soft-N-donor complexant scaffolds. Further, this efficient protocol parallels the principles of Green chemistry by exchanging KMnO 4 for the toxic OsO 4 and offers the end-user an efficient, more environmentally friendly option for accessing heteroaryl methyl ketones in one hour of reaction time using potassium permanganate and sodium paraperiodate as a synergistically potent oxidative cleavage system. The wide substrate scope defined access to simple, as well as advanced heteroaryl methyl ketones. Method development, optimization, substrate scope, preliminary mechanistic observations, and a scale up reaction are delineated herein.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Extracting SIMD Parallelism from Recursive Task-Parallel Programs

The pursuit of computational efficiency has led to the proliferation of throughput-oriented hardware, from GPUs to increasingly wide vector units on commodity processors and accelerators. This hardware is designed to efficiently execute data-parallel computations in a vectorized manner. However, many algorithms are more naturally expressed as divide-and-conquer, recursive, task-parallel computations. In the absence of data parallelism, it seems that such algorithms are not well suited to throughput-oriented architectures. This paper presents a set of novel code transformations that expose the data parallelism latent in recursive, task- parallel programs. These transformations facilitate straightforward vectorization of task-parallel programs on commodity hardware. We also present scheduling policies that maintain high utilization of vector resources while limiting space usage. Across several task-parallel benchmarks, we demonstrate both efficient vector resource utilization and substantial speedup on chips using Intel’s SSE4.2 vector units, as well as accelerators using Intel’s AVX512 units. We then show through rigorous sampling that, in practice, our vectorization techniques are effective for a much larger class of programs.

Recursive Programs, task parallelism, vectorizatio↗

DOE OSTI2016

TU-AB-BRC-12: Optimized Parallel MonteCarlo Dose Calculations for Secondary MU Checks

Purpose: Secondary MU checks are an important tool used during a physics review of a treatment plan. Commercial software packages offer varying degrees of theoretical dose calculation accuracy, depending on the modality involved. Dose calculations of VMAT plans are especially prone to error due to the large approximations involved. Monte Carlo (MC) methods are not commonly used due to their long run times. We investigated two methods to increase the computational efficiency of MC dose simulations with the BEAMnrc code. Distributed computing resources, along with optimized code compilation, will allow for accurate and efficient VMAT dose calculations. Methods: The BEAMnrc package was installed on a high performance computing cluster accessible to our clinic. MATLAB and PYTHON scripts were developed to convert a clinical VMAT DICOM plan into BEAMnrc input files. The BEAMnrc installation was optimized by running the VMAT simulations through profiling tools which indicated the behavior of the constituent routines in the code, e.g. the bremsstrahlung splitting routine, and the specified random number generator. This information aided in determining the most efficient compiling parallel configuration for the specific CPU’s available on our cluster, resulting in the fastest VMAT simulation times. Our method was evaluated with calculations involving 10{sup 8} – 10{sup 9} particle histories which are sufficient to verify patient dose using VMAT. Results: Parallelization allowed the calculation of patient dose on the order of 10 – 15 hours with 100 parallel jobs. Due to the compiler optimization process, further speed increases of 23% were achieved when compared with the open-source compiler BEAMnrc packages. Conclusion: Analysis of the BEAMnrc code allowed us to optimize the compiler configuration for VMAT dose calculations. In future work, the optimized MC code, in conjunction with the parallel processing capabilities of BEAMnrc, will be applied to provide accurate and efficient secondary MU checks.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2013

Hierarchical Petascale Simulation Framework For Stress Corrosion Cracking

A number of major accomplishments resulted from the project. These include: • Data Structures, Algorithms, and Numerical Methods for Reactive Molecular Dynamics. We have developed a range of novel data structures, algorithms, and solvers (amortized ILU, Spike) for use with ReaxFF and charge equilibration. • Parallel Formulations of ReactiveMD (Purdue ReactiveMolecular Dynamics Package, PuReMD, PuReMD-GPU, and PG-PuReMD) for Messaging, GPU, and GPU Cluster Platforms. We have developed efficient serial, parallel (MPI), GPU (Cuda), and GPU Cluster (MPI/Cuda) implementations. Our implementations have been demonstrated to be significantly better than the state of the art, both in terms of performance and scalability. • Comprehensive Validation in the Context of Diverse Applications. We have demonstrated the use of our software in diverse systems, including silica-water, silicon-germanium nanorods, and as part of other projects, extended it to applications ranging from explosives (RDX) to lipid bilayers (biomembranes under oxidative stress). • Open Source Software Packages for Reactive Molecular Dynamics. All versions of our soft- ware have been released over the public domain. There are over 100 major research groups worldwide using our software. • Implementation into the Department of Energy LAMMPS Software Package. We have also integrated our software into the Department of Energy LAMMPS software package.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Identification of 2-Hydroxyacyl-CoA Synthases with High Acyloin Condensation Activity for Orthogonal One-Carbon Bioconversion

One-carbon (C1) compounds are emerging as cost-effective and potentially carbon-negative feedstocks for biomanufacturing, which require efficient, versatile metabolic platforms for the synthesis of value-added products. Synthetic formyl-CoA elongation (FORCE) pathways allow diverse product synthesis from C1 compounds via iterative C1 elongation, operating independently from the host metabolism with reduced engineering complexity and improved theoretical yields. However, a major bottleneck was identified as the suboptimal kinetics of the core C1–C1 condensation enzyme, 2-hydroxyacyl-CoA synthase (HACS), catalyzing the acyloin condensation reaction between formaldehyde and formyl-CoA. Furthermore, we used a combinatorial approach of bioprospecting and rational protein engineering to identify multiple HACS variants with significantly improved activities toward C1 substrates. Sequence and structure alignment of the active variants elucidated the key regions for the catalytic function, which were targeted for mutagenesis, leading to improved catalytic efficiency. In parallel, a consecutive round of bioprospecting for homologs with high similarity with active variants revealed a highly active HACS variant exhibiting up to 7-fold improvement in catalytic efficiency (k cat /K M ) and 14-fold improvement in the FORCE pathway flux in vivo compared to the previous reports. Upon further optimization of the downstream pathway, the orthogonal C1-to-product bioconversion system showed a metabolic flux of up to 700 μM glycolate OD –1 h –1 (2.1 mmol gDCW –1 h –1 ) and an industrially relevant glycolate titer, rate, and yield of 5.2 g L –1 (67.8 mM), 0.22 g L –1 h –1 , and 94% carbon yield, respectively.

2-hydroxyacyl-CoA synthase↗

DOE OSTI2017

EvoGraph: On-The-Fly Efficient Mining of Evolving Graphs on GPU

With the prevalence of the World Wide Web and social networks, there has been a growing interest in high performance analytics for constantly-evolving dynamic graphs. Modern GPUs provide massive AQ1 amount of parallelism for efficient graph processing, but the challenges remain due to their lack of support for the near real-time streaming nature of dynamic graphs. Specifically, due to the current high volume and velocity of graph data combined with the complexity of user queries, traditional processing methods by first storing the updates and then repeatedly running static graph analytics on a sequence of versions or snapshots are deemed undesirable and computational infeasible on GPU. We present EvoGraph, a highly efficient and scalable GPU- based dynamic graph analytics framework.

dynamic graphs↗

DOE OSTI2017

Extreme scale unstructured adaptive CFD for aerodynamic flow control

Understanding the flow of fluid, either liquid or gas, through and around solid bodies has challenged man since the dawn of scientific inquiry. Many of the great minds of science and mathematics have progressively built up a hierarchy of fluid models since fluid flow impacts our lives in so many fundamental ways - from the early days of flow of water in viaducts to cities, to today's flight of planes. This chapter is concerned with the computational modeling of turbulent flow around aerodynamic bodies such as planes and wind turbines. In this case, viscous effects near the solid bodies create very thin boundary layers that yield highly anisotropic (gradients normal to the surface may be 10 6 larger than gradients along the surface) solutions to the governing non-linear partial differential equations (PDE); the Navier-Stokes equations. Furthermore, turbulent flows develop extremely broad ranges of length and time scales motivating the use of discretization methods capable of employing adaptivity and implicit time integration. The combination of these features - non-linear, anisotropy, adaptivity, and implicit - dramatically raise the complexity of the discretization, posing large challenges to efficient scalable parallel implementation. However, through careful design, the more complex algorithms can provide great reductions in computational cost relative to simpler methods (e.g., Cartesian grids with explicit time integration) that are easier to mate efficiently to hardware. In this chapter, we not only describe our approach but we also address the fact that while complex algorithms may never be as efficient flop-for-flop as simple methods, in the important measure of science-per-core-hour, they can still win big by making complex features like adaptivity and implicit methods as efficient and scalable as possible.

42 ENGINEERING↗

DOE OSTI2017

Energy Efficiency Roadmap for Uganda, Making Energy Efficiency Count. Executive Summary

Like many countries in Sub-Saharan Africa, Uganda has focused its energy sector investments largely on increasing energy access by increasing energy supply. The links between energy efficiency and energy access, the importance of energy efficiency in new energy supply, and the multiple benefits of energy efficiency for the level and quality of energy available, have been largely overlooked. Implementing energy efficiency in parallel with expanding both the electricity grid and new clean energy generation reduces electricity demand and helps optimize the power supply so that it can serve more customers reliably at minimum cost. Ensuring efficient appliances are incorporated into energy access efforts provides improved energy services to customers. Energy efficiency is an important contributor to access to modern energy. This Energy Efficiency Roadmap for Uganda (Roadmap) is a response to the important role that electrical energy efficiency can play in meeting Uganda’s energy goals. Power Africa and the United Nations Sustainable Energy for All (SEforALL) initiatives collaborated with more than 24 stakeholders in Uganda to develop this document. The document estimates that if the most efficient technologies on the market were adopted, 2,224 gigawatt hours could be saved in 2030 across all sectors, representing 31% of the projected load. This translates into 341 megawatts of peak demand reductions, energy access to an additional 6 million rural customers and reduction of carbon dioxide emissions by 10.6 million tonnes in 2030. The Roadmap also finds that 91% of this technical potential is cost-effective, and 47% is achievable under conservative assumptions. The Roadmap prioritizes recommendations for implementing energy efficiency and maximizing benefits to meet the goals and priorities established in Uganda’s 2015 SEforALL Action Agenda. One important step is to create and increase demand for efficiency through long-term enabling policies and financial incentives combined with development of technical expertise in the labor force to allow for the promotion of new business models, such as energy service companies. A combination of enabling policies, financial schemes, regulations, enforcement, and skill development are needed to open the energy efficiency market.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2017

Extreme Scale Unstructured Adaptive CFD: From Multiphase Flow to Aerodynamic Flow Control

Understanding the flow of fluid, either liquid or gas, through and around solid bodies has challenged man since the dawn of scientific inquiry. Many of the great minds of science and math have progressively built up a hierarchy of fluid models. This report is concerned with the computational modeling of turbulent flow around aerodynamic bodies such as planes and wind turbines. In this case, viscous effects near the solid bodies create very thin boundary layers that yield highly anisotropic (gradients normal to the surface may be 10^6 times larger than gradients along the surface) solutions to the governing non-linear partial differential equations (PDE); the Navier-Stokes equations. Furthermore, turbulent flows develop extremely broad ranges of length and time scales.This disparity motivates the use of discretization methods capable of employing adaptivity and implicit time integration. The combination of these features (non-linear, anisotropy, adaptivity, andimplicit) dramatically raise the complexity of the discretization, posing large challenges to efficient scalable parallel implementation. However, through careful design, the more complex algorithms can provide great reductions in computational cost relative to simpler methods (e.g., Cartesian grids with explicit time integration) that are easier to mate efficiently to hardware. In this report, we not only describe our approach but we also address the fact that while complex algorithms may never be as efficient flop-for-flop as simple methods, in the important measure of science-per-core-hour, they can still win big by making complex features like adaptivity and implicit methods as efficient and scalable as possible.

42 ENGINEERING↗

DOE OSTI2022

Parallel Multigrid in Time and Space for Extreme-Scale Computational Science: Chaotic and Hyperbolic Problems

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallelin-time methods, with the most common method, parareal, diverging in many cases. The current stateof-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, we take inspiration from the Least Squares Shadowing (LSS by Wang) approach for solving chaotic problems. Here, an optimization approach is able to find “well-conditioned” shadow trajectories/solutions to the original “ill-conditioned” chaotic problem. Thus, the new multigrid methods researched here also arise in an optimization context.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multigrid Reduction in Time for Chaotic and Hyperbolic Problems (Final Report)

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallelin-time methods, with the most common method, parareal, diverging in many cases. The current state-of-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, this work shall continue researching the directions from the current collaboration with Dr. Falgout, which are laid out in the work Toward Parallel in Time for Chaotic Dynamical Systems and showed the first known results of a parallel-in-time speedup for a chaotic problem. This work outlines two key improvements to XBraid for chaotic problems, the so-called “theta” and “delta-correction” methods. Here, these two improvements will be implemented in a high-performance but general way in XBraid and explored for more complicated problems. We will additionally research, as time allows, improvements to these techniques, as well as multigrid relaxation techniques based on Least Squares Shadowing (LSS by Wang) and a nonintrusive block tridiagonal solver based on MGRIT, called TriMGRIT.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Multigrid Reduction in Time for Chaotic and Hyperbolic Problems (Final Report)

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallel-in-time methods, with the most common method, parareal, diverging in many cases. The current state of-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, this work shall continue researching the directions from the current collaboration with Dr. Falgout, which are laid out in the work Toward Parallel in Time for Chaotic Dynamical Systems and showed the first known results of a parallel-in-time speedup for a chaotic problem. This work outlines two key improvements to XBraid for chaotic problems, the so-called “theta” and “delta-correction” methods. Here, these two improvements will be further researched and improved (including with a new relaxation method inspired by on Least Squares Shadowing (LSS)) and explored for more complicated problems.

97 MATHEMATICS AND COMPUTING↗