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At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Parallel-in-Time Multigrid Methods for Hyperbolic Problems, with a Focus on the Shallow Water Equations

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations, 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 problems of programmatic interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic problems on future architectures. The difficulty lies in the fact that hyperbolic problems are well-known to be difficult for parallel-in-time methods, with the most common parallel-in-time method, Parareal, diverging in many cases. Here, the chosen methodology for scalably solving these hyperbolic space-time equations is multigrid-reductionin-time (MGRIT), because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. To further research in this area, this project will explore a model hyperbolic problem (the shallow water equations) in the context of recent advances (e.g., by Wingate and Haut) in constructing improved coarse time-grid time-propagators by using the slow asymptotic structure of the equations. In particular, we will investigate if such coarse time-propagators offer significant advantages in an MGRIT setting, and explore any broader insights gained into parallel-in-time for hyperbolic problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The effects of multispecies Hohlraum walls on stimulated Brillouin scattering, Hohlraum dynamics, and beam propagation

We report experiments and simulations have been conducted to investigate the efficacy of Ta 2 O 5 -lined Hohlraum walls at reducing stimulated Brillouin backscattering (SBS) as well as any subsequent effects on the Hohlraum dynamics and capsule implosions in indirect drive experiments at the National Ignition Facility. Using a 1.1 MJ 400 TW, 351 nm, shaped laser pulse, we measure a 5× reduction in SBS power in the peak of the pulse from the wall on the outer 50° cone beams. The SBS spectrum indicates a reduction in the high-Z spectral signature when using multispecies wall materials. Detailed hydrodynamic simulations were performed using different heat conduction models with flux limiters. Additional simulations were performed on the plasma maps using the 3D parallel paraxial code pF3D to compare backscatter powers between the pure Au and Ta 2 O 5 -lined Hohlraums. Further analysis, using hydrodynamically equivalent plasmas, shows that the SBS reduction is clearly a result of the added ion Landau damping caused by the oxygen ions and not from differences in plasma conditions. The experimental and simulation results also show an increase in the wall plasma expansion when using the Ta 2 O 5 liner leading to a 70% more oblate implosion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

In situ Parallel Training of Analog Neural Network Using Electrochemical Random-Access Memory

In-memory computing based on non-volatile resistive memory can significantly improve the energy efficiency of artificial neural networks. However, accurate in situ training has been challenging due to the nonlinear and stochastic switching of the resistive memory elements. One promising analog memory is the electrochemical random-access memory (ECRAM), also known as the redox transistor. Its low write currents and linear switching properties across hundreds of analog states enable accurate and massively parallel updates of a full crossbar array, which yield rapid and energy-efficient training. While simulations predict that ECRAM based neural networks achieve high training accuracy at significantly higher energy efficiency than digital implementations, these predictions have not been experimentally achieved. In this work, we train a 3 × 3 array of ECRAM devices that learns to discriminate several elementary logic gates (AND, OR, NAND). We record the evolution of the network’s synaptic weights during parallel in situ (on-line) training, with outer product updates. Due to linear and reproducible device switching characteristics, our crossbar simulations not only accurately simulate the epochs to convergence, but also quantitatively capture the evolution of weights in individual devices. The implementation of the first in situ parallel training together with strong agreement with simulation results provides a significant advance toward developing ECRAM into larger crossbar arrays for artificial neural network accelerators, which could enable orders of magnitude improvements in energy efficiency of deep neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Temporal Properties of Compressible Magnetohydrodynamic Turbulence

Describing the temporal properties of compressible magnetohydrodynamic (MHD) turbulence is a fundamental problem that has important implications for particle acceleration and transport in astrophysical plasmas. Here, by carefully analyzing the spatial and temporal properties of compressible MHD turbulence, we derive a new spectral power density function that is supported by simulations. This new function reveals that the low-frequency fluctuations are dominated by modes with small parallel wavenumbers with respect to the mean background magnetic field. Furthermore, for fluctuations with dynamically significant parallel wavenumbers, broadening around their eigenfrequencies is described by this function, which is in close agreement with simulations. We use this formalism to present the scaling properties of individual MHD modes. Such broadening is a direct consequence of nonlinear processes and is different for the three fundamental MHD modes. Our results provide a new window to investigate the temporal properties of turbulence and will enable further studies on the interaction between compressible MHD turbulence and energetic plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Transferring ecosystem simulation codes to supercomputers

Many ecosystem simulation computer codes have been developed in the last twenty-five years. This development took place initially on main-frame computers, then mini-computers, and more recently, on micro-computers and workstations. Supercomputing platforms (both parallel and distributed systems) have been largely unused, however, because of the perceived difficulty in accessing and using the machines. Also, significant differences in the system architectures of sequential, scalar computers and parallel and/or vector supercomputers must be considered. We have transferred a grassland simulation model (developed on a VAX) to a Cray Y-MP/C90. We describe porting the model to the Cray and the changes we made to exploit the parallelism in the application and improve code execution. The Cray executed the model 30 times faster than the VAX and 10 times faster than a Unix workstation. We achieved an additional speedup of 30 percent by using the compiler's vectoring and 'in-line' capabilities. The code runs at only about 5 percent of the Cray's peak speed because it ineffectively uses the vector and parallel processing capabilities of the Cray. We expect that by restructuring the code, it could execute an additional six to ten times faster.

Skiles, J. W.↗
DOE OSTI2023

Insights on the dissolution of water in an albite melt at high pressures and temperatures from a direct structural analysis

The water dissolution mechanism in silicate melts under high pressures is not well understood. Here we present the first direct structure investigation of a water-saturated albite melt to monitor the interactions between water and the network structure of silicate melt at the molecular level. In situ high-energy X-ray diffraction was carried out on the NaAlSi 3 O 8 -H 2 O system at 800 °C and 300 MPa, at the Advanced Photon Source synchrotron facility. The analysis of the X-ray diffraction data was augmented with classical Molecular Dynamics simulations of a hydrous albite melt, incorporating accurate water-based interactions. The results show that metal–oxygen bond breaking at the bridging sites occurs overwhelmingly at the Si site upon reaction with H 2 O, with subsequent Si–OH bond formation and negligible Al–OH formation. Furthermore, we see no evidence for the dissociation of the Al 3+ ion from the network structure upon breaking of the Si–O bond in the hydrous albite melt. The results also indicate that the Na + ion is an active participant in the modifications of the silicate network structure of the albite melt upon water dissolution at high P–T conditions. We do not find evidence for the Na + ion dissociating from the network structure upon depolymerization and subsequent formation of NaOH complexes. Instead, our results show that the Na + ion persists as a structure modifier with a shift away from Na–BO bonding to an increase in the extent of Na-NBO bonding, in parallel with pronounced depolymerization of the network. Our MD simulations show that the Si–O and Al–O bond lengths are expanded by about 6% in the hydrous albite melt compared to those of the dry melt at high P–T conditions. The changes in the network silicate structure of a hydrous albite melt at high pressure and temperature, as revealed in this study, must be considered in the advancement of water dissolution models of hydrous granitic (or alkali aluminosilicate) melts.

36 MATERIALS SCIENCE↗
NASA NTRS2012

Algorithm for Simulating Atmospheric Turbulence and Aeroelastic Effects on Simulator Motion Systems

Atmospheric turbulence produces high frequency accelerations in aircraft, typically greater than the response to pilot input. Motion system equipped flight simulators must present cues representative of the aircraft response to turbulence in order to maintain the integrity of the simulation. Currently, turbulence motion cueing produced by flight simulator motion systems has been less than satisfactory because the turbulence profiles have been attenuated by the motion cueing algorithms. This report presents a new turbulence motion cueing algorithm, referred to as the augmented turbulence channel. Like the previous turbulence algorithms, the output of the channel only augments the vertical degree of freedom of motion. This algorithm employs a parallel aircraft model and an optional high bandwidth cueing filter. Simulation of aeroelastic effects is also an area where frequency content must be preserved by the cueing algorithm. The current aeroelastic implementation uses a similar secondary channel that supplements the primary motion cue. Two studies were conducted using the NASA Langley Visual Motion Simulator and Cockpit Motion Facility to evaluate the effect of the turbulence channel and aeroelastic model on pilot control input. Results indicate that the pilot is better correlated with the aircraft response, when the augmented channel is in place.

Ercole, Anthony V.↗
NASA NTRS2001

Molecular Simulations in Astrobiology

One of the main goals of astrobiology is to understand the origin of cellular life. In the absence of any record of the earliest ancestors of contemporary cells, protocells, the most direct way to test our understanding of their characteristics is to construct laboratory models of protocells. Such efforts, currently underway in the NASA Astrobiology Program, are accompanied by computational studies aimed at explaining self-organization of simple molecules into ordered structures and developing designs of molecules that are capable of performing protocellular functions. Many of these functions, such as importing nutrients, capturing and storing energy, and responding to changes in the environment, are carried out by proteins bound to membranes. We use computer simulations to address the following, questions about these proteins: (1) How do small proteins (peptides) organize themselves into ordered structures at water-membrane interfaces and insert into membranes? (2) How do peptides aggregate to form membrane-spannin(y structures (e.g., channels)? (3) By what mechanisms do such aggregates perform their functions? The simulations are performed using the molecular dynamics (MD) method. In this method, Newton's equations of motion for each atom in the system are solved iteratively. At each time step, the forces exerted on each atom by the remaining atoms are evaluated by dividing them into two parts. Short-range forces are calculated directly in real space while long-range forces are evaluated in reciprocal space, usually using a particle-mesh algorithm which is of order O(NlnN). Currently, a time step of 2 femtoseconds is typically used, thereby making studies of problems occurring on multi-nanosecond time scales (10(exp 6) - 10(exp 8) time steps) accessible. To address a broader range of problems, simulations need to be extended by three orders of magnitude. Such an extension requires both algorithmic improvements and codes scalable to a large number of parallel processors. Work in this direction is in progress. Two specific series of simulations that demonstrate how peptides self-organize and function in membranes are discussed. In one series of simulations, it was shown that nonpolar peptides, disordered in water, translocate to the nonpolar interior of the membrane and, simultaneously, fold into two different helical structures, which remain in equilibrium. Once in the membrane, the peptides can readily change their orientation, especially in response to local electric fields. This structural and orientational flexibility of peptides with changing conditions may have provided a mechanism of transmitting signals between the environment and the interior of the protocell. In another series of simulations, the mechanism by which a simple protein channel efficiently mediates proton transport across membranes was investigated. This process is a key step in cellular bioenergetics. In the channel under study, proton transport is gated by four histidines that occlude the channel pore. The simulations demonstrate that protons move through the gate by a "shuttle" mechanism, wherein one histidine is protonated on the extracellular side and, subsequently, the proton bound on the opposite side is released.

Pohorille, Andrew↗
DOE OSTI2026

Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2004

Magnetospheric Magnetic Reconnection with Southward IMF by a 3D EMPM Simulation

We report our new simulation results on magnetospheric magnetic reconnection with southward IMF using a 3D EMPM model, with greater resolution and more particles using the parallelized 3D HPF TRISTAN code on VPP5000 supercomputer. Main parameters used in the new simulation are: domain size is 215 x 145 x 145, grid size = 0.5 Earth radius, initial particle number is 16 per cell, the IMF is southward. Arrival of southward IMF will cause reconnection in the magnetopause, thus allowing particles to enter into the inner magnetosphere. Sunward and tailward high particle flow are observed by satellites, and these phenomena are also observed in the simulation near the neutral line (X line) of the near-Earth magnetotail. This high particle flow goes along with the reconnected island. The magnetic reconnection process contributes to direct plasma entry between the magnetosheath to the inner magnetosphere and plasma sheet, in which the entry process eats the magnetosheath plasma to plasma sheet temperatures. We investigate magnetic, electric fields, density, and current during this magnetic reconnection with southward IMF. Further investigation with this simulation will provide insight into unsolved problems, such as the triggering of storms and substorms, and the storm-substorm relationship. New results will be presented at the meeting.

Nishikawa, K.-I.↗
DOE OSTI2025

Parallel diffusion operator for magnetized plasmas with improved spectral fidelity

Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge for describing non-grid-aligned magnetic structures in Eulerian (grid-based) simulations. Here, the present paper describes and validates a new method for parallel diffusion in magnetized plasmas based on the anti-symmetry representation [Halpern and Waltz, Phys. Plasmas 25, 060703 (2018)]. In the anti-symmetry formalism, diffusion manifests as a flow operator involving the logarithmic derivative of the transported quantity. Qualitative plane wave analysis shows that the new operator naturally yields better discrete spectral resolution compared to its conventional counterpart. Numerical simulations comparing the new method against existing finite difference methods are carried out, showing significant improvement. In particular, we find that combining anti-symmetry with finite differences in diagonally staggered grids essentially eliminates the so-called “artificial numerical diffusion” that affects conventional finite difference and finite volume methods.

Anisotropic diffusion↗
DOE OSTI2021

MFIX DEM Enhancement for Industry-Relevant Flows (Final Report)

The overall goal of this two-phase project is to implement performance improvements of the Multiphase Flow with Interphase Exchanges (MFIX) Discrete Element Model (DEM) code that enable a transformative shift for industrial use. Prior to this effort, the largest simulations performed using MFIX are O(10 7 ) particles. This falls short of the O(10 9 ) particle simulations that must be completed on a timescale of days or weeks (vs. months or years) to enable simulations with physically-relevant domain sizes to be incorporated into industrial design cycles within five years. This was accomplished by tailoring best-in-class practices to bear on the unique challenges posed by the MFIX-DEM algorithm and code base. Scientific simulations (e.g., in cosmology, turbulent combustion) routinely use massively parallel computing to update far more particles in short wall clock times. Results from Phase 1 (1.5 years in duration) indicated significant gains in speed were possible for a wide range of benchmark cases. Moreover, a survey sent to >35 companies indicates that the timing is ideal for such an enhanced tool, with >80% of the respondents indicating that DEM is already value-added or will be within the next 5 years, and >70% of the respondents indicating that improved speed is the top computational priority. In Phase 2 (3.5 years in duration), the two major barriers that hinder industry from effectively using multiphase Computational Fluid Dynamics (CFD) to cut costs and improve performance, namely computational overhead and confidence in predictions, continued to be addressed. Regarding the former, the results from Phase 1 to guide the effort, with enhancements focused on an improved time-stepping algorithm and particle sorting. Four target problems of 1 billion particles each and increasing complexity were identified: homogeneous cooling, tumbler with continuous particle size distribution, discharge from a rectangular hopper and a cylindrical riser. Each of these were successfully simulated for relevant time scales (on order of seconds) using less than 24 hours of wall clock time. These represent the first 1-billion particle DEM simulations performed with MFIX, namely using the MFIX-Exa code. This code is currently under development at NETL in collaboration with Lawrence Berkeley National Laboratory. Regarding the second barrier on predictive uncertainty, experiments from Phase 1 (interacting nozzles - hydrodynamics only) and Phase 2 (very small-scale segregation experiments) were used to demonstrate the ability of two simplified approaches to uncertainty quantification (UQ). By limiting the number of particles, UQ based on the simplified treatment was compared to standard UQ, which was shown to have much higher computational demands. Experiments were also performed on a pilot-scale stripper unit to provide validation data for future CFD-DEM simulations and UQ.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2022

Cabana: A Performance Portable Library for Particle-Based Simulations

Particle-based simulations are ubiquitous throughout many fields of computational science and engineering, spanning the atomistic level with molecular dynamics (MD), to mesoscale particle-in-cell (PIC) simulations for solid mechanics, device-scale modeling with PIC methods for plasma physics, and massive N-body cosmology simulations of galaxy structures, with many other methods in between (Hockney & Eastwood, 1989). While these methods use particles to represent significantly different entities with completely different physical models, many low-level details are shared including performant algorithms for short- and/or long-range particle interactions, multi-node particle communication patterns, and other data management tasks such as particle sorting and neighbor list construction. Cabana is a performance portable library for particle-based simulations, developed as part of the Co-Design Center for Particle Applications (CoPA) within the Exascale Computing Project (ECP) (Alexander et al., 2020). The CoPA project and its full development scope, including ECP partner applications, algorithm development, and similar software libraries for quantum MD, is described in (Mniszewski et al., 2021). Cabana uses the Kokkos library for on-node parallelism (Edwards et al., 2014; Trott et al., 2022), enabling simulation on multi-core CPU and GPU architectures, and MPI for GPU-aware, multi-node communication. Cabana provides particle simulation capabilities on almost all current Kokkos backends, including serial execution, OpenMP (including OpenMP-Target for GPUs), CUDA (NVIDIA GPUs), HIP (AMD GPUs), and SYCL (Intel GPUs), providing a clear path for the coming generation of accelerator-based exascale hardware. Cabana builds on Kokkos by providing new particle data structures and particle algorithms resulting in a similar execution policy-based, node-level programming model that is intended to be used in addition to the core Kokkos library within an application. Cabana is designed as an application and physics agnostic, but particle-specific toolkit which can either be used to generate a new application, or to be used as needed in existing applications at various levels of invasiveness including through interfaces that wrap user memory in existing data structures.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2008

Aeroacoustic Simulations of Tandem Cylinders with Subcritical Spacing

Tandem cylinders are being studied because they model a variety of component level interactions of landing gear. The present effort is directed at the case of two identical cylinders with their centroids separated in the streamwise direction by 1.435 diameters. Experiments in the Basic Aerodynamic Research Tunnel and Quiet Flow Facility at NASA Langley Research Center have provided an extensive experimental database of the nearfield flow and radiated noise. The measurements were conducted at a Mach number of 0.1285 and Reynolds number of 1.66x10(exp 5) based on the cylinder diameter. A trip was used on the upstream cylinder to insure a fully turbulent flow separation and, hence, to simulate a major aspect of high Reynolds number flow. The parallel computational effort uses the three-dimensional Navier-Stokes solver CFL3D with a hybrid, zonal turbulence model that turns off the turbulence production term everywhere except in a narrow ring surrounding solid surfaces. The experiments exhibited an asymmetry in the surface pressure that was persistent despite attempts to eliminate it through small changes in the configuration. To model the asymmetry, the simulations were run with the cylinder configuration at a nonzero but small angle of attack. The computed results and experiments are in general agreement that vortex shedding for the spacing studied herein is weak relative to that observed at supercritical spacings. Although the shedding was subdued in the simulations, it was still more prominent than in the experiments. Overall, the simulation comparisons with measured near-field data and the radiated acoustics are reasonable, especially if one is concerned with capturing the trends relative to larger cylinder spacings. However, the flow details of the 1.435 diameter spacing have not been captured in full even though very fine grid computations have been performed. Some of the discrepancy may be associated with the simulation s inexact representation of the experimental configuration, but numerical and flow modeling errors are also likely contributors to the observed differences.

Lockard, David P.↗
NASA NTRS1997

CFD Analysis and Design Optimization Using Parallel Computers

A versatile and efficient multi-block method is presented for the simulation of both steady and unsteady flow, as well as aerodynamic design optimization of complete aircraft configurations. The compressible Euler and Reynolds Averaged Navier-Stokes (RANS) equations are discretized using a high resolution scheme on body-fitted structured meshes. An efficient multigrid implicit scheme is implemented for time-accurate flow calculations. Optimum aerodynamic shape design is achieved at very low cost using an adjoint formulation. The method is implemented on parallel computing systems using the MPI message passing interface standard to ensure portability. The results demonstrate that, by combining highly efficient algorithms with parallel computing, it is possible to perform detailed steady and unsteady analysis as well as automatic design for complex configurations using the present generation of parallel computers.

Martinelli, Luigi↗
NASA NTRS1993

Real-time dynamics simulation of the Cassini spacecraft using DARTS. Part 1: Functional capabilities and the spatial algebra algorithm

This paper describes the Dynamics Algorithms for Real-Time Simulation (DARTS) real-time hardware-in-the-loop dynamics simulator for the National Aeronautics and Space Administration's Cassini spacecraft. The spacecraft model consists of a central flexible body with a number of articulated rigid-body appendages. The demanding performance requirements from the spacecraft control system require the use of a high fidelity simulator for control system design and testing. The DARTS algorithm provides a new algorithmic and hardware approach to the solution of this hardware-in-the-loop simulation problem. It is based upon the efficient spatial algebra dynamics for flexible multibody systems. A parallel and vectorized version of this algorithm is implemented on a low-cost, multiprocessor computer to meet the simulation timing requirements.

Jain, A.↗
NASA NTRS1999

Adaptive Mesh Refinement for Microelectronic Device Design

Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of the spectrum as well as active device simulations that model charge transport and Maxwell's equations will be presented.

Cwik, Tom↗
DOE OSTI2024

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Many time-dependent problems and simulations are often modeled using Partial Differential Equations. Traditional modeling approaches that use sequential time-stepping are reaching a bottleneck in optimizing efficiency. The Center of Applied Science and Computing at Lawrence Livermore National Laboratory extensively works on parallelizing these algorithms to leverage the increasing computational power from the growing number of processors in computer hardware. In particular, they aim to design non-intrusive algorithms that can generalize to a variety of problems and sizes without requiring additional information from or modifications on the original problems. Multigrid Reduction in Time (MGRIT) is a parallel-in-time algorithm that is designed to be non-intrusive. This project focuses on increasing the efficiency of MGRIT by approximating the coarse-grid operator using machine learning approaches as a means to find the most non-intrusive, or general, solution.

97 MATHEMATICS AND COMPUTING↗