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At least 433 records · Page 24

Advancing Scientific Productivity through Better Scientific Software: Developer Productivity and Software Sustainability Report

The Exascale Computing Project (ECP) provides a unique opportunity to advance computational science and engineering (CSE) through an accelerated growth phase in extreme-scale computing. Central to the project is the development of next-generation applications and software technologies that can exploit emerging architectures for optimal performance and provide high-fidelity, multiphysics, multiscale capabilities. However, disruptive changes in computer architectures and the complexities of tackling new frontiers in extreme-scale modeling, simulation, and analysis present daunting challenges to the productivity of software developers and the sustainability of software artifacts. Members of the CSE community - especially at extreme scales but more broadly at all scales of computing - face an urgent need to improve developer productivity, positively impacting product quality, development time, and staffing resources, and software sustainability, reducing the cost of maintaining, sustaining, and evolving software capabilities.

97 MATHEMATICS AND COMPUTING↗

CFD simulations of Molten Salt Fast Reactor core cavity flows

Computational Fluid Dynamics (CFD) has become increasingly important in the research and development of advanced nuclear reactors. Here, in the current study, extensive CFD simulations were conducted for the coolant flow in Molten Salt Fast Reactor (MSFR) core models using the state-of-the-art spectral element flow solver Nek5000 and multiscale coarse-mesh thermal-hydraulic software Pronghorn. The underlying motivation is to seek an in-depth understanding of how the internal velocity distribution can be influenced by the MSFR core cavity shape, the Reynolds number, turbulence modeling options and the inlet boundary conditions. The CFD techniques involved in this investigation range from coarse-mesh CFD, RANS modeling, to the high-fidelity LES calculations. Specifically, a series of RANS simulations were performed for the 2-D axisymmetric core model and 3-D wedge domains to study the flow distribution inside the MSFR core. It is observed that a proper representation of the MSFR inlet channel duct is important for the prediction of internal flow distribution. It is also showcased here how researchers can leverage the Nek5000 CFD results to calibrate more efficient coarse-mesh CFD tools, like Pronghorn, for the actual MSFR design needs. Moreover, this paper highlights a 3-D LES model for an entire MSFR core using the spectral element method and demonstrates the feasibility of this modeling approach. The readiness and potential limitations of the RANS approach are examined with respect to the high-fidelity LES simulations. The present investigation lays a solid foundation as we are leveraging the high-fidelity CFD capabilities to inform MSFR design efforts.

97 MATHEMATICS AND COMPUTING↗

Modular Approach for the Synthesis of Bottlebrush Diblock Copolymers from Poly(Glycidyl Methacrylate)-block-Poly(Vinyldimethylazlactone) Backbones

A strategy that enables the facile synthesis of bottlebrush block copolymers with flexible backbones was developed. A demonstration of the strategy’s utility was carried out by grafting end-functionalized polymethylmethacrylate (PMMA) and polystyrene (PS) to the dually reactive block copolymer, poly(glycidyl methacrylate)-block-poly(vinyldimethylazlactone) (PGMA-b-PVDMA). Five different bottlebrush diblock copolymers were investigated by size-exclusion chromatography (SEC), 1H NMR, Fourier transform infrared (FT-IR), differential scanning calorimetry (DSC), X-ray scattering methods, atomic force microscopy (AFM), rheology and computational simulations using molecular dynamics (MD), and self-consistent field theory (SCFT). A relationship between the glass transition temperature and the fraction of chain ends was demonstrated by DSC and highlights the potential of this synthetic method to tailor polymer properties. All five samples were found to be in a disordered phase exhibiting multiscale structures revealed by two broad peaks in small-angle X-ray scattering (SAXS) that can be attributed to graft-to-graft and backbone-to-backbone density correlations using MD simulations. The SCFT-based simulations justify the observation of a disordered phase due to its stabilization by the grafts. Additionally, this modular approach can be easily extended to other grafts, including responsive, conducting, and charged polymers with the prerequisite end groups. The versatility and ease of assembling these functional bottlebrushes constitute a powerful “toolbox” method for the rapid and scalable synthesis of novel bottlebrush block copolymers with desired properties.

36 MATERIALS SCIENCE↗

A multiscale recurrent neural network model for predicting energy production from geothermal reservoirs

Optimization of energy production from geothermal reservoirs requires reliable prediction of energy production performance under alternative operation and development scenarios. Traditionally, reservoir simulation models are used for the evaluation and screening of alternative production and development plans. However, simulation models require extensive data collection and modeling efforts and are time-consuming to build, run, and update. Data-driven predictive models, on the other hand, can serve as efficient prediction tools that can be used for decision support and management of daily operations and surveillance activities. Data-driven models become particularly attractive when a reservoir simulation model for a field does not exist and/or is difficult to build. Machine learning (ML)-based data-driven models that have recently become popular in several fields exploit statistical patterns and relations in training data to generate predictions. As such, they tend to perform better in interpolation problems (that is, prediction within the training data range) than when they are used to extrapolate beyond the training data. Production data from geothermal reservoirs tend to exhibit short-term variabilities as well as long-term trends, such as monotonically declining production temperatures. Capturing both short-term features and long-term trends with ML-based models is not trivial. We evaluate the use of recurrent neural networks (RNN) for the prediction of energy production from geothermal reservoirs. RNN is a class of ML architectures that are used to represent and predict sequential/dynamic data. Thus, it can be challenging to apply RNN to problems where long-term trends must be captured and extrapolation beyond the training data range is needed. We introduce the multiscale RNN architecture to extend the application of RNN to detect and predict both short-term variabilities and long-term trends in geothermal data. The developed architecture consists of a long-term component to only capture low-frequency data patterns, and a short-term component to detect features with higher frequency and more nonlinearity. The final prediction is obtained by combining the long-term and short-term predictions. Both synthetic and field data are used to evaluate the presented multiscale RNN model. The prediction performance of the multiscale RNN is compared against those obtained from the regular RNN and the autoregressive (AR) model. The results suggest that the multiscale architecture improves the long-term prediction performance of the regular RNN and enhances its robustness against noise.

15 GEOTHERMAL ENERGY↗

Role of chemical production and depositional losses on formaldehyde in the Community Regional Atmospheric Chemistry Multiphase Mechanism (CRACMM)

Abstract. Formaldehyde (HCHO) is an important air pollutant with direct cancer risk and ozone-forming potential. HCHO sources are complex because HCHO is both directly emitted and produced from oxidation of most gas-phase reactive organic carbon. We update the secondary production of HCHO in the Community Regional Atmospheric Chemistry Multiphase Mechanism (CRACMM) in the Community Multiscale Air Quality (CMAQ) model. Production of HCHO from isoprene and monoterpenes is increased, correcting an underestimate in the current version. Simulated June–August surface HCHO during peak photochemical production (11:00–15:00 LT, local time) increased by 0.6 ppb (32 %) over the southeastern USA and by 0.2 ppb (13 %) over the contiguous USA. The increased HCHO compares more favorably with satellite-based observations from the TROPOspheric Monitoring Instrument (TROPOMI) and from aircraft-based observations. Evaluation against hourly surface observations indicates a missing nighttime sink that can be improved by increased nighttime deposition, which reduces June–August nocturnal (20:00–04:00 LT) surface HCHO by 1.1 ppb (36 %) over the southeastern USA and 0.5 ppb (29 %) over the contiguous USA. The ability of CRACMM to capture peak levels of HCHO at midday is improved, particularly at sites in the northeastern USA, while peak levels at sites in the southeastern USA are improved, although still lower than observed. Using established risk assessment methods, lifetime exposure of the population in the contiguous USA (∼ 320 million) to ambient HCHO levels predicted here may result in 6200 lifetime cancer cases, with 40 % from controllable anthropogenic emissions of nitrogen oxides and reactive organic compounds. Chemistry updates will be available in CRACMM version 2 (CRACMM2) in CMAQv5.5.

Skipper, T. Nash↗

Modeling and Simulation of Advanced Manufacturing Techniques using MOOSE and MALAMUTE

Advanced manufacturing techniques offer increased geometry complexity, energy and material usage efficiency improvements, and an expanded palette of materials as compared to conventional manufacturing approaches. Advanced-manufacturing-produced parts can experience wide variations in the final microstructure, and these microstructure variations significantly impact the parts’ performance. In this chapter, we present recent code developments within Multiphysics Object-Oriented Simulation Environment (MOOSE) and in the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE). Here we demonstrate applying these modeling and simulation codes to two advanced manufacturing process types: advanced sintering techniques and laser-based additive manufacturing techniques. The multiphysics and multiscale capabilities of these codes enable prediction of the microstructure evolution resulting from variations in the Advanced manufacturing process parameters.

36 MATERIALS SCIENCE↗

Theory, observations, and simulations of kinetic entropy in a magnetotail electron diffusion region

In this work, we examine velocity-space kinetic entropy, a spatially local measure of entropy for systems out of thermal equilibrium, during an encounter of an electron diffusion region at a magnetic reconnection site in Earth’s magnetotail by the Magnetospheric Multiscale (MMS) mission. We start by generalizing the theory of kinetic entropy to the case of non-uniform velocity space grids and transforming the equations into spheri- cal energy coordinates useful to experimental plasma detectors. The theory is then applied to MMS data and compared to particle-in-cell simulations of reconnection. We demonstrate that the entropy-based non-Maxwellianity measure from the MMS data is of sufficiently high precision to reliably identify non-Maxwellian distributions and therefore the measurements when kinetic effects are most significant. By comparing two different non-Maxwellian measures, we show that total entropy density suffers from “information loss” because it lacks a dependence on the velocity space grid, and so has lost information about how well a distribution function is resolved. Local velocity-space kinetic entropy density recovers this information. We quantify information loss and argue that the considerations needed to minimize it are crucial for instruments designed to measure distribution functions in situ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Novel fractal-textured solar absorber surfaces for concentrated solar power

The solar absorptance of a thermal receiver surface significantly affects the photothermal conversion efficiency of concentrated solar power (CSP) plants. The development of low-cost Gen3 CSP systems calls for increasing the solar absorptance of the thermal receivers at operating temperatures above 750 °C. This study presents an innovative approach to the fractal, multiscale texturing of absorber surfaces to significantly enhance solar energy absorption for Gen3 CSP applications. The absorber surface is described in terms of its fractal parameters that are uniquely determined from surface profile measurements. The interaction of solar radiation with the fractal surface is numerically simulated by solving the governing Maxwell’s equations for electromagnetic wave propagation to investigate the effect of texturing on the absorptance of the surfaces. It is shown that absorption of the solar spectrum increases with an increase in the fractal dimension and the multiscale asperity height of the surface texturing. Here, the theoretical model is demonstrated to be in close agreement with experimental measurements of spectral absorptance of electrodeposited copper (Cu), copper mono-oxide (CuO), and copper-manganese oxide (CuMnO) surfaces that are textured to produce a range of fractal parameters by tailoring the deposition parameters. Fractal surface texturing is shown to reduce reflectance by over one order of magnitude, yielding an absorptance of greater than 0.985 for CuMnO. For the first time, the study presents a significant effective means of increasing solar absorptance and a fundamental theoretical description of the underlying physics.

14 SOLAR ENERGY↗

Impact of the Earthquake Rupture on Ground-Motion Variability of the 24 August 2016 M w 6.2 Amatrice, Italy, Earthquake

Here, the devastating 24 August 2016 M w 6.2 earthquake that struck Amatrice, Italy, marked the beginning of a prolonged seismic sequence dominated by three subsequent M w ≥6.0 events in the central Apennines region. The earthquake destroyed Amatrice’s historic center, claiming the lives of 299 individuals and causing widespread damage in the neighboring villages. The severity of the ground shaking, with a recorded maximum acceleration of 850 cm/s 2 on the east–west component at the Amatrice station, was far greater than the predicted acceleration based on the Italian ground-motion model (GMM). As pointed out by several investigations, the observed ground-motion amplitude and its spatial variability during the earthquake can be linked to specific rupture characteristics, including slip distribution and rupture directivity effects revealed by the observed data (Tinti et al., 2016; Pischiutta et al., 2021). In this study, we conducted physics-based 3D numerical simulations of ground motion for the Amatrice earthquake for frequencies up to 3 Hz. We employed a series of kinematic rupture models and a well-constrained local 3D velocity model incorporating surface topography. The kinematic rupture realizations were generated using multiscale hybrid and fully stochastic models, following the technique proposed by Graves and Pitarka (2016). We focused on assessing the sensitivity of near-fault ground-motion amplitudes to earthquake rupture characteristics, in particular, the spatial slip pattern. To evaluate the quality of our simulations, we employed goodness-of-fit measurements performed in comparisons of simulated and recorded ground motions. The simulated ground motions compare well with the recorded data and predictions from GMMs for Italy, ITA18 (Lanzano et al., 2019). However, we found that the simulated interevent ground-motion variability (randomness in the source process) of peak ground velocity, σ (PGV) is higher than the constant σ (PGV) predicted by conventional GMMs. Our simulations using several rupture scenarios demonstrate that the near-fault ground-motion amplification pattern is directly related to the slip distribution pattern.

3D Ground Motions Simulations↗

Assessing Two Approaches for Enhancing the Range of Simulated Scales in the E3SMv1 and the Impact on the Character of Hourly US Precipitation

Abstract Improving the representation of precipitation in Earth system models is essential for understanding and projecting water cycle changes across scales. Progress has been hampered by persistent deficiencies in representing precipitation frequency, intensity, and timing in current models. Here, we analyze simulated US precipitation in the low‐resolution (LR) configuration of the Energy Exascale Earth System Model (E3SMv1) and assess the effect of two approaches to enhance the range of explicitly resolved scales: high‐resolution (HR) and multiscale modeling framework (MMF), which incur similar computational expense. Both E3SMv1‐MMF and E3SMv1‐HR capture more intense and less frequent precipitation on hourly and daily timescales relative to E3SMv1‐LR. E3SMv1‐HR improves the intensity over the Eastern and Northwestern US during winter, while E3SMv1‐MMF improves the intensity over the Eastern US and summer diurnal timing over the Central US. These results indicate that both methods may be needed to improve simulations of different storm types, seasons, and regions.

58 GEOSCIENCES↗

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (↗

Evaluation of present-day extreme precipitation over the United States: an inter-comparison of convection and dynamic permitting configurations of E3SMv1

Abstract Accurate simulation of the present-day characteristics of mean and extreme precipitation at regional scales remains a challenge for Earth system models, which is due in part to deficiencies in model physics such as convective parameterization (CP), and coarse resolution. High horizontal resolution (HR, ∼25 km) and multiscale modeling framework (MMF, i.e. replacing conventional CP with embedded km-scale cloud-resolving models) are two promising directions that could help improve the interaction between subgrid-scale physical processes and large-scale climate. Here, we evaluate simulated extreme precipitation over the United States (US) across three configurations (i.e. low-resolution [LR], HR, and MMF) of the Energy Exascale Earth System Model (E3SMv1) and intercompare them against two gridded observation datasets (climate prediction center daily US precipitation and integrated multi-satellite retrievals for global precipitation measurement). We assess the model’s ability to simulate very heavy seasonal precipitation (illustrated by the difference between the 99th and 90th percentile values) as well as the spatial distributions of several extreme precipitation indices defined by the expert team on climate change detection and indices. Our results show that both the dry (i.e. consecutive dry days (CDD)) and wet (i.e. consecutive wet days, maximum 5 day precipitation, and very wet days) extremes evaluated herein show some improvement as well as degradation with MMF and HR relative to LR. These results vary across seasons and US subregions. For instance, only the very heavy precipitation of winter is improved with MMF and HR. Both configurations alleviate the well-known drizzling bias evident in LR across both winter and summer in many parts of the US, largely due to the overall improvement in intensity and frequency of precipitation. Additionally, our results suggest that while E3SMv1-MMF has higher intensity rates when it does rain, it has too many CDD during the summer, contributing to a low mean precipitation bias.

54 ENVIRONMENTAL SCIENCES↗

Multiscale and Machine Learning Modeling for Process-informed Microstructure Prediction in Additively Manufactured Materials using MALAMUTE

The Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy aims to develop and qualify additively manufactured materials for nuclear applications. One key challenge to this is the microstructural variability observed in the additively manufactured products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-throughput experimental and modeling techniques to accelerate qualification. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the additive manufacturing process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture microstructural variability is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning models to develop a digital twin for additive manufacturing that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation. The melting and subsequent solidification that occurs during the additive process is a complex phenomenon that requires multiscale multiphysics analysis. This work package focuses on understanding the role of process variabilities on the unique microstructural characteristics of additively manufactured materials. Microstructural features at the subgrain level, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. Idaho National Laboratory’s Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for additively manufactured materials in an efficient, reliable, and cost-effective way. This work focuses on capturing the microstructural variabilities at the subgrain level that are often missing in the part-scale models. In fiscal year 2025, we significantly advanced upon our work in the last fiscal year, in terms of the predictive capabilities of the physics-based and ML models, by adding the capabilities to capture subgrain-level micro-segregation during solidification using phase-field model and to predict the time-dependent dynamics of the AM process through the MOGPAR model. The alloy solidification model in MOOSE incorporates the thermodynamic properties and free energy relevant to 316 stainless steel. The model demonstrates the Cr and Ni segregation that occurs during solidification, including that the rate of solidification. The microstructural evolution model is connected to the process conditions via the surrogate model developed in this work. This enables predictions of the final microstructure in conjunctions with the manufacturing process. This work supports AMMT's rapid qualification goals by laying the foundation for an efficient and cost-effective model establishing the PSPP correlation for AM. The generated microstructures and predicted micro-segregation can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work helps to identify the key microstructural features at the subgrain level that are significant in property and performance predictions of additively manufactured components. This work will also provide inputs to the large-scale process variability models to reevaluate and validate assumptions and simplifications made in the part-scale models. Furthermore, through active learning this work can help identify the data need from both modeling and experimental sides for development of a robust digital twin for additive manufacturing and accelerate the AMMT's qualification efforts.

36 - MATERIALS SCIENCE↗

Multiscale and multidimensional modeling of particle acceleration and transport in solar flares

Multi-messenger, multi-viewpoint, and time-resolved observations of solar flares are now providing unprecedented constraints on particle acceleration sites, energy conversion, and energy transport. The interpretation of current observations, including microwave imaging spectroscopy from EOVSA, hard x-ray (HXR) imaging from Solar Orbiter/STIX, gamma-ray diagnostics from Fermi, and in situ measurements from Parker Solar Probe and Solar Orbiter, collectively demands modeling frameworks that go beyond traditional spatially unresolved, one-zone models or single-mechanism descriptions. This review surveys multiscale and multidimensional modeling approaches, including kinetic, magnetohydrodynamic (MHD), and macroscopic particle models, that are being developed to meet the need. Kinetic simulations reveal that three-dimensional (3D) effects, including field-line chaos and self-generated turbulence, are essential for sustained power-law particle acceleration. MHD simulations now capture flux-rope eruptions, plasmoid-unstable current sheets, and turbulent flare regions in realistic magnetic topologies. Macroscopic models coupling MHD with energetic-particle models produce spatially resolved electron distributions and synthetic HXR and microwave emissions for direct comparison with observations. Despite these advances, outstanding challenges remain in bridging kinetic and global scales, improving MHD simulations and macroscopic particle models, and achieving quantitative model-observation closure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigating the Unique Ability of Trichodesmium To Fix Carbon and Nitrogen Simultaneously Using MiMoSA

The open ocean is an extremely competitive environment, partially due to the dearth of nutrients. Trichodesmium erythraeum, a marine diazotrophic cyanobacterium, is a keystone species in the ocean due to its ability to fix nitrogen and leak 30 to 50% into the surrounding environment, providing a valuable source of a necessary macronutrient to other species. While there are other diazotrophic cyanobacteria that play an important role in the marine nitrogen cycle, Trichodesmium is unique in its ability to fix both carbon and nitrogen simultaneously during the day without the use of specialized cells called heterocysts to protect nitrogenase from oxygen. Here, we use the advanced modeling framework called multiscale multiobjective systems analysis (MiMoSA) to investigate how Trichodesmium erythraeum can reduce dimolecular nitrogen to ammonium in the presence of oxygen. Our simulations indicate that nitrogenase inhibition is best modeled as Michealis-Menten competitive inhibition and that cells along the filament maintain microaerobia using high flux through Mehler reactions in order to protect nitrogenase from oxygen. We also examined the effect of location on metabolic flux and found that cells at the end of filaments operate in distinctly different metabolic modes than internal cells despite both operating in a photoautotrophic mode. These results give us important insight into how this species is able to operate photosynthesis and nitrogen fixation simultaneously, giving it a distinct advantage over other diazotrophic cyanobacteria because they can harvest light directly to fuel the energy demand of nitrogen fixation.

09 BIOMASS FUELS↗

iMMD

Iterative Multiscale Molecular Dynamics in OpenMM: Accelerating Conformational Sampling of Biomolecular Systems by Iterating All-Atom and Coarse-Grained Molecular Dynamics Simulations

Do, Hung Nguyen [Los Alamos National Laboratory]↗

A multiresolution adaptive wavelet method for nonlinear partial differential equations

We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

97 MATHEMATICS AND COMPUTING↗