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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.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Accelerating computational fluid dynamics simulation of post-combustion carbon capture modeling with MeshGraphNets

Packed columns are commonly used in post-combustion processes to capture CO 2 emissions by providing enhanced contact area between a CO 2 -laden gas and CO 2 -absorbing solvent. To study and optimize solvent-based post-combustion carbon capture systems (CCSs), computational fluid dynamics (CFD) can be used to model the liquid–gas countercurrent flow hydrodynamics in these columns and derive key determinants of CO 2 -capture efficiency. However, the large design space of these systems hinders the application of CFD for design optimization due to its high computational cost. In contrast, data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. We build our surrogates using MeshGraphNets (MGN), a graph neural network framework that efficiently learns and produces mesh-based simulations. We apply MGN to a random packed column modeled with over 160K graph nodes and a design space consisting of three key input parameters: solvent surface tension, inlet velocity, and contact angle. Our models can adapt to a wide range of these parameters and accurately predict the complex interactions within the system at rates over 1700 times faster than CFD, affirming its practicality in downstream design optimization tasks. This underscores the robustness and versatility of MGN in modeling complex fluid dynamics for large-scale CCS analyses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

SBML Level 3: an extensible format for the exchange and reuse of biological models

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a sampling-based approach that has widely used for quantification and propagation of uncertainties. However, the standard MC method is often time-consuming if the simulation-based model is computationally intensive. This article gives an overview of modern MC methods to address the existing challenges of the standard MC in the context of UQ. Specifically, multilevel Monte Carlo (MLMC) extending the concept of control variates achieves a significant reduction of the computational cost by performing most evaluations with low accuracy and corresponding low cost, and relatively few evaluations at high accuracy and corresponding high cost. Multifidelity Monte Carlo (MFMC) accelerates the convergence of standard Monte Carlo by generalizing the control variates with different models having varying fidelities and varying computational costs. Multimodel Monte Carlo method (MMMC), having a different setting of MLMC and MFMC, aims to address the issue of UQ and propagation when data for characterizing probability distributions are limited. Multimodel inference combined with importance sampling is proposed for quantifying and efficiently propagating the uncertainties resulting from small data sets. All of these three modern MC methods achieve a significant improvement of computational efficiency for probabilistic UQ, particularly uncertainty propagation. Finally, an algorithm summary and the corresponding code implementation are provided for each of the modern MC methods. The extension and application of these methods are discussed in detail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A thermodynamically consistent finite strain phase field approach to ductile fracture considering multi-axial stress states

Phase field models for ductile fracture have gained significant attention in the last two decades due to their ability in implicitly tracking the nucleation and propagation of cracks. However, most crack phase field formulations for elastoplastic solids focus only on the effects of plastic deformation, and do not consider the different multi-axial stress states that may arise in practical designs. In this work, a thermodynamically consistent phase field approach coupled with finite strain plasticity, considering multi-axial stress states is presented. In order to account for the coupling between plasticity and stress states, the Stress-Weighted Ductile Fracture Model (SWDFM) is utilized. The SWDFM represents a criterion for predicting ductile crack initiation under both monotonic and cyclic loadings based on histories of an internal plastic variable, stress triaxiality, and the Lode angle parameter. The excellent performance of the SWDFM for predicting ductile crack initiation motivates for its incorporation into a phase field approach for predicting both crack initiation and propagation through degradation of the fracture toughness. Moreover, based on the second law of thermodynamics, exact requirements are imposed on the rate at which the fracture toughness can evolve. Here, a novel function for degrading the plastic yield surface during the evolution of damage is introduced. This function, in line with experimental observations, leads to an accumulation of plastic deformation in damaged regions of a solid, and avoids numerical instabilities arising from concentrations of large plastic deformations in severely damaged regions. For validating the proposed model, results of computational simulations are compared to data from selected tests considering different multi-axial stress states. Comparisons of the numerical results with data from laboratory experiments demonstrate the capabilities of the proposed framework.

42 ENGINEERING↗
DOE OSTI2025

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Assembly of short amphiphilic peptoids into nanohelices with controllable supramolecular chirality

Abstract A long-standing challenge in bioinspired materials is to design and synthesize synthetic materials that mimic the sophisticated structures and functions of natural biomaterials, such as helical protein assemblies that are important in biological systems. Herein, we report the formation of a series of nanohelices from a type of well-developed protein-mimetics called peptoids. We demonstrate that nanohelix structures and supramolecular chirality can be well-controlled through the side-chain chemistry. Specifically, the ionic effects on peptoids from varying the polar side-chain groups result in the formation of either single helical fiber or hierarchically stacked helical bundles. We also demonstrate that the supramolecular chirality of assembled peptoid helices can be controlled by modifying assembling peptoids with a single chiral amino acid side chain. Computational simulations and theoretical modeling predict that minimizing exposure of hydrophobic domains within a twisted helical form presents the most thermodynamically favorable packing of these amphiphilic peptoids and suggests a key role for both polar and hydrophobic domains on nanohelix formation. Our findings establish a platform to design and synthesize chiral functional materials using sequence-defined synthetic polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Interpreting dynamic-compression experiments to uncover the time dependence of freezing: Application to gallium

Using pulsed-power magnetic field sources to compress gallium to gigapascal pressures on nanosecond timescales, we report here experiments on shockless dynamic compression of a liquid metal. Time-resolved velocimetry data reveal signatures of rapid freezing from a metastable liquid state, and we demonstrate that the kinetics of this nonequilibrium solidification can be accurately simulated with a computational modeling framework we have developed in previous studies, where classical nucleation theory is coupled with hydrodynamics. Notably, velocity traces in some of our experiments show evidence of a phase transition, while others do not, even though other types of evidence suggest that solidification may be occurring in all of them. We explain how predictions made by our models regarding the presence or absence of these phase-transition signatures motivated additional experiments that later confirmed the theoretical predictions. Our analysis shows that due to the rapid, quasi-isentropic nature of the loading path, our experiments were able to compress liquid gallium to metastable states that are undercooled below the equilibrium melt temperature by more than 300 K and exhibit pressures that approach five times the equilibrium melt pressure. The understanding gained in this study should form the basis for future dynamic-compression experiments aimed at interrogating melt curves at high pressures.

gallium↗
DOE OSTI2022

Isolated Building Wake Experiment At Texas Tech University’s Wind Engineering Research Field Lab

Texas Tech University’s (TTU’s) Wind Engineering Research Field Lab (WERFL) building is an idealized rectangular building on the scale of a typical suburban house. It is surrounded almost entirely by unobstructed planes and is built on a turn table. WERFL is ideal for providing measurements of an idealized building under real-world conditions including atmospheric stability and variable relative wind angles. The intent of this data set is for verification and validation of computational fluid dynamics model simulations of flow around buildings. The primary focus of this dataset features 24 3D sonic anemometers (20 downwind and 4 upwind) and 10 2D sonic anemometers (9 downwind and 1 upwind) located in the immediate vicinity of the WERFL building. It also includes a variety of instruments intended to measure the ambient meteorological parameters and the undisturbed wind profile.

17 WIND ENERGY↗
DOE OSTI2026

Establishment of a Vertically Integrated Domestic Manufacturing Process for Production of Substrates Needed for Manufacture of Gas Diffusion Layers

In this project, AvCarb, LLC evaluated the baseline performance metrics of commercial carbon veils and their corresponding Gas Diffusion Layers (GDLs) with the goal of establishing an optimized, vertically integrated production system for wet-laid nonwoven substrates used in gas diffusion media for electrochemical energy storage and conversion devices. Mechanical testing and microstructural characterization were conducted and used to develop a multiscale computational model capable of simulating and predicting the performance of GDLs in fuel cells. Although the project successfully generated foundational transport and modeling data, it was terminated prior to identifying the critical GDL design parameters necessary for full optimization. The program aimed to improve carbon veil fabrication through enhanced fiber dispersion, fiber-fiber adhesion control, and improved web formation, enabling the production of high-quality, uniform substrates. Simulations were intended to guide mixing and solution delivery system design and process conditions, followed by production-scale trials to evaluate fiber dispersion, web uniformity, and mechanical robustness. At full deployment, the proposed production line would have been capable of producing approximately 650,000 m² of carbon veil annually. This capability remains strategically important, as the United States currently lacks a domestic source of wet-laid nonwoven carbon substrates that satisfy the stringent quality requirements for fuel-cell GDLs and electrolyzers representing an ongoing supply-chain vulnerability. Beyond supply-chain benefits, the project established a robust benchmarking dataset for existing commercial carbon veils while advancing next-generation material concepts targeting improved performance and manufacturing consistency.

Olson, Cynthia Lemay↗
DOE OSTI2020

Design and Development of a Robotic Exoskeleton Device for use in Glove Boxes - 20374

Glovebox operators in nuclear facilities often operate under radioactive environment and typically perform monotonous, dull and repetitive work. This can result in muscle fatigue leading to increased levels of accidents. Current research work aims in assisting the glovebox operators by designing a novel upper limb exoskeleton device to reduce injuries and increase worker efficiency. Almost none of the commercially available hand and upper body exoskeletons are directly suitable for use in gloveboxes. This explains the novelty of the present work in developing a wearable powered robotic exoskeleton device. The device consists of electronics, motors and spring systems mounted on adjustable plates and is supported by a stationary frame behind the worker. The device is intended to be portable and adjustable according to the operator height. The elbow has a flexion movement assisted with motor control by way of a Bowden cable system. The system is floated on a spring and pulley combination that allows for extra safety and smoothness of operation. The end points are fixed near the pivot points to help minimize unwanted movement/torque. The extension movement of the upper and lower arm are assisted by gravity and a counter spring. The shoulder and upper arm movement are held in a neutral position with a spring system for counter balance allowing small movements within the glovebox. This initial concept considers only the vertical movement of the arm. The abduction and adduction movement will not be assisted or impeded by the over shoulder plate or at the forearm plate allowing for full range of motion. Several glovebox aspects such as the level of task assistance, ergonomic design, minimum hindrance in dexterity/operator movements and tear resistance for hazardous safety reasons will be considered in the design of the exoskeleton. Computer models will be simulated to test the load levels and stress conditions on the exoskeleton to enhance the designs. The exoskeleton focusses on major muscular involvement reduction through weight offset and active assistance with minimal parts and hence the device is derived with several joint links and contains both passive and active joints. The paper details the various stages in the design development and prototype testing of the exoskeleton device. Upon successful prototype device development, human testing will be conducted in a replica of the SRS-235F hot cell facility constructed at FIU-ARC. The final stage of the project will be potential testing/deployment of the exoskeleton device in one of the glovebox facilities in Savannah River Nuclear Waste site. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Passive Energy-Saving Solutions for Clothes Dryers: A Modeling and Experimental Study for Improved Efficiency and Affordability

Dryers are integral appliances in modern households, yet their significant power consumption remains a critical challenge for reducing energy bills and upgrades. This work presents the outcomes of a comprehensive investigation aimed at lowering the operating energy costs of the dryer through modeling and experimental approaches. Specifically, the objectives of this research are twofold: (1) to reduce energy consumption without negatively impacting drying performance or time; and (2) to ensure affordability by developing retrofittable solutions characterized by low cost and a quick payback period. These strategies promise universal applicability to all dryer categories, encompassing both gas and electric models, by tackling core issues such as unnecessary heat loss and excess energy supply, both prevalent across dryer designs. Our methodology combines robust modeling frameworks and experimental validation to target energy efficiency improvements through three primary pathways: (1) effective heat loss management using ultralow-cost insulation materials tailored for dryer systems; (2) heat management across the drying cycle, facilitated by passive heat transfer mechanisms, and (3) optimization of heat supply to the load to ensure precise energy delivery, minimizing waste. These innovations are designed to seamlessly integrate with existing dryer configurations, providing a scalable and retrofittable solution that ensures affordability without requiring substantial redesigns or expensive components. Using these methods, the study demonstrates improvement opportunities in dryer energy consumption while maintaining the desired performance. The modeling component utilizes computational simulations to evaluate the thermal and energy performance of these innovations under varied operational conditions, providing foundational insights for experimental design. By addressing critical areas such as heat loss, energy recovery, and supply optimization, this work proposes impactful solutions for lowering the energy costs in domestic clothes dryers. The ultralow-cost, retrofittable nature of the proposed strategies ensures widespread adoption potential across diverse dryer categories, making significant strides toward affordable household energy practices.

Cheekatamarla, Praveen [ORNL] (ORCID:0000000248827↗
DOE OSTI2022

Exploring the Use of Novel Spatial Accelerators in Scientific Applications

Driven by the need to find alternative accelerators which can viably replace GPUs in next-generation Supercomputing systems, this paper proposes a methodology to enable agile application/hardware co-design. The application-first methodology provides the ability to come up with design of accelerators while working with real-world workloads, available accelerators, and system software. The iterative design process targets a set of kernels in a workload for performance estimates that can prune the design space for later phases of detailed architectural evaluations. To this effect, in this paper, a novel data-parallel device model is introduced that simulates the latency of performance-sensitive operations in an accelerator including data transfers and kernel computation using multi-core CPUs. The use of off-the-shelf simulators, such as pre-RTL simulator Aladdin or multiple tools available for exploring the design of deep neural network accelerators (e.g., Timeloop) is demonstrated for evaluation of various accelerator designs using applications with realistic inputs. Examples of multiple device configurations that are instantiable in a system are explored to evaluate the performance benefit of deploying novel accelerators. The proposed device is integrated with a programming model and system software to potentially explore the impacts of high-level programming languages/compilers and low-level effects such as task scheduling on multiple accelerators. We analyze our methodology for a set of applications that represent high-performance computing (HPC) and graph analytics. The applications include a computational chemistry kernel realized using tensor contractions, triangle counting, GraphSAGE and Breadth-first Search. These applications include kernels such as dense matrix-dense matrix multiplication, sparse matrix-spare matrix multiplication, and sparse matrix-dense vector multiplication. Our results indicate potential performance benefits and insights for system design by including accelerators that realize these kernels along-side general purpose accelerators.

AI, codesign, Accelerated Computing, Modeling and ↗
DOE OSTI2022

In Situ X-ray Radiography and Computational Modeling to Predict Grain Morphology in $\beta$-Titanium during Simulated Additive Manufacturing

The continued development of metal additive manufacturing (AM) has expanded the engineering metallic alloys for which these processes may be applied, including beta-titanium alloys with desirable strength-to-density ratios. To understand the response of beta-titanium alloys to AM processing, solidification and microstructure evolution needs to be investigated. In particular, thermal gradients (Gs) and solidification velocities (Vs) experienced during AM are needed to link processing to microstructure development, including the columnar-to-equiaxed transition (CET). In this work, in situ synchrotron X-ray radiography of the beta-titanium alloy Ti-10V-2Fe-3Al (wt.%) (Ti-1023) during simulated laser-powder bed fusion (L-PBF) was performed at the Advanced Photon Source at Argonne National Laboratory, allowing for direct determination of Vs. Two different computational modeling tools, SYSWELD and FLOW-3D, were utilized to investigate the solidification conditions of spot and raster melt scenarios. The predicted Vs obtained from both pieces of computational software exhibited good agreement with those obtained from in situ synchrotron X-ray radiography measurements. The model that accounted for fluid flow also showed the ability to predict trends unobservable in the in situ synchrotron X-ray radiography, but are known to occur during rapid solidification. A CET model for Ti-1023 was also developed using the Kurz–Giovanola–Trivedi model, which allowed modeled Gs and Vs to be compared in the context of predicted grain morphologies. Both pieces of software were in agreement for morphology predictions of spot-melts, but drastically differed for raster predictions. The discrepancy is attributable to the difference in accounting for fluid flow, resulting in magnitude-different values of Gs for similar Vs.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Learning compact physics‐aware delayed photocurrent models using dynamic mode decomposition

Abstract Radiation‐induced photocurrent in semiconductor devices can be simulated using complex physics‐based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high‐level circuit simulations where it is computationally infeasible to evaluate detailed models for multiple individual circuit elements. In this work we demonstrate a procedure for learning compact delayed photocurrent models that are efficient enough to implement in large‐scale circuit simulations, but remain faithful to the underlying physics. Our approach utilizes dynamic mode decomposition (DMD), a system identification technique for learning reduced‐order discrete‐time dynamical systems from time series data based on singular value decomposition. To obtain physics‐aware device models, we simulate the excess carrier density induced by radiation pulses by solving numerically the ambipolar diffusion equation, then use the simulated internal state as training data for the DMD algorithm. Our results show that the significantly reduced‐order delayed photocurrent models obtained via this method accurately approximate the dynamics of the internal excess carrier density—which can be used to calculate the induced current at the device boundaries—while remaining compact enough to incorporate into larger circuit simulations.

Hanson, Joshua↗
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↗
DOE OSTI2022

An Efficient Time-Domain Model to Simulate Parametric Resonances in a Floating Body Free to Move in Six Degrees of Freedom: Preprint

We present a computationally efficient time-domain model capable of simulating parametric resonances in a floating body in waves. The model assumes all wave forces to be linear, but the inertia and restoring forces acting on the body are expanded to second order in body motions. The simulation speed on a standard computer is approximately 40 times faster than real time. The model is applied to a soft-moored floating axisymmetric body which absorbs energy through heave, but is otherwise free to move in six degrees of freedom. Under certain conditions, we show that the body responds parametrically with large amplitudes not only in surge and pitch, but also in sway, roll, and yaw, provided it is given some small initial displacement in one of these out-of-plane modes. The predictions are confirmed by simulations using state-of-the-art nonlinear Froude-Krylov and computational fluid dynamics models.

parametric resonance↗
DOE OSTI2022

Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers

We reformulate the continuous-space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. A binary encoding of position produces a spin-1/2 Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code (BRGC), and a Hamming-distance-2 Gray code (H2GC) reduces the model complexity down to the 𝑋⁢𝑍 and transverse Ising model, respectively. For 𝐴 qubits BRGC yields 2 𝐴 positions and is reduced to its 2-local form with O⁡(𝐴) ancillary qubits. H2GC yields 2 𝐴/2+1 positions with O⁡(𝐴 2 ) three-local penalty terms. We also identify the bijective mapping between diagonal unitaries and the Walsh series, producing the mapping of any real potential to a series of 𝑘 -local Ising models through the fast Walsh transform. Finally, in a finite volume, we provide some numerical evidence to support the claim that the total time needed for adiabatic evolution is protected by the infrared cutoff of the system. As a result, initial state preparation from a free-field wave function to an interacting system is expected to exhibit polynomial time complexity with volume and constant scaling with respect to lattice discretization for all encodings. For H2GC, if the evolution starts with the transverse Hamiltonian due to hardware restrictions, then penalties are dynamically introduced such that the low-lying spectrum reproduces the energy levels of the Laplacian. The adiabatic evolution of the penalty Hamiltonian is therefore sensitive to the ultraviolet scale. It is expected to exhibit polynomial time complexity with lattice discretization, or exponential time complexity with respect to the number of qubits given a fixed volume.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Race conditions and data partitioning: risks posed by common errors to reproducible parallel simulations

When parallel algorithms for simulation were introduced in the 1970s, their development and use interested only experts in parallel computation. This circumstance changed as multi-core processors became commonplace, putting a parallel computer into the hands of every modeler. A natural outcome is growing interest in parallel simulation among persons not intimately familiar with parallel computing. At the same time, parallel simulation tools continue to be developed with the implicit assumption that the modeler is knowledgeable about parallel programming. The unintended consequence is a rapidly growing number of users of parallel simulation tools that are unlikely to recognize when the interaction of race conditions, partitioning strategies, and simultaneous action in their simulation models make results non-reproducible, thereby calling into question the validity of conclusions drawn from the simulation data. Here, we illustrate the potential dangers of exposing parallel algorithms to users who are not experts in parallel computation with example models constructed using existing parallel simulation tools. By doing so, we hope to refocus tool developers on usability, even if this new focus incurs loss of some performance.

97 MATHEMATICS AND COMPUTING↗