Search NASA⌕ Search

SEARCH · Search NASA

Results for “Kernel Designs”

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.

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

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Code for the manuscript "Mori-Zwanzig Modal Decomposition"

We would like to create an open source repository in LANL's github on code written in Julia, in which we implement and extend the data-driven Mori-Zwanzig method for extracting large-scale spatio-temporal structures from data, which we call MZMD. This method is an extension of Dynamic Mode Decomposition (DMD) in which Mori-Zwanzig memory kernels are included into the associated companion matrix. In the code we would like to release, we apply MZMD to a flow over a cylinder with Reynolds number 100 rather than the much larger data set used in the associated manuscript. DMD is used extensively in the fluid dynamics community mainly for extracting large scale spatio-temporal structures (patters) from flow data. This is useful for understanding the key mechanisms that generate certain complex dynamical process relevant in engineering design. In MZMD, we improve upon DMD by adding the Mori-Zwanzig memory kernels, and show this improvement is especially important in strongly nonlinear regions of the flow.

Woodward, Michael↗
DOE OSTI2024

Multi-kernel Edge Attention Graph Autoencoder

MEAGraph (Multi-kernel Edge Attention Graph Autoencoder) is a graph-based autoencoder model designed for unsupervised data mining for datasets used in machine learning potentials. It provides accurate clustering for atomic environment identification, unsupervised and unlabeled data pruning for dataset construction.

Sun, Hong↗
DOE OSTI2023

Simulation and Analysis on Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS) under SBLOCA scenario by using Cardinal to support the fracture mechanics analyses

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended durations or under accident condition. As one of the most significant components of a Reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Ageing degradation mechanisms (e.g. thermos-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary. The multi-physics simulations are performed using Cardinal, a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and other multi-physics sub-modules within the MOOSE framework. Cardinal now fully supports MOOSE stochastic perturbations of NekRS models with varying boundary conditions, initial conditions, material properties, and any other quantity which is defined by a kernel (such as coefficients in a momentum source model). The implementation is designed in a flexible manner so that scalar values are sent from MOOSE into a user scratch space in NekRS, which can then be applied for any purpose within the NekRS case files (both on the host and device). When modeling PTS, several factors can impact the results significantly. In this report, the impacts of the geometry of the model, Reynolds number and buoyancy effect are investigated. Two geometry, i.e., a simplified model and a realistic RPV model, with both laminar and turbulent flow condition are adopted for the PTS simulation with and without buoyancy effect. The purpose of the investigation is to understand the impact of these factors on the prediction of temperature history of RPV. The accurate prediction on the temperature evolution, which will be exported to Grizzly code for further analyses on the progression of aging mechanisms and their effects on the integrity of RPV structures, is very crucial. Based on the understanding of these factors, a more sophisticated model is built to analysis the PTS under SBLOCA scenario. A literature survey is conducted to pick the SBLOCA scenario for the multi-physics simulation. The analysis helps to explain the form and the transformation of the cold plum when the ECC is activated under SBLOCA. This model can be can be applied to study the PTS effect for different RPV configurations. The results can help to assess structural component degradation for advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs [6, 7]. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN’s optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques [8]. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Comparison of structurally diverse simulation models for prediction of epidemic outcomes caused by a long-distance dispersed pathogen

Long-distance dispersal (LDD) pathogens pose substantial challenges for epidemic control due to their ability to generate new infection foci at great distances. While various modeling approaches have been developed to understand and manage such outbreaks, little work has compared how models of different structures behave under shared conditions. Here, in this study, we compare four structurally distinct epidemiological models — EPIMUL, GEMF, PoPS, and Warwick — each adapted to simulate the spread of wheat stripe rust (WSR), a wind-dispersed LDD pathogen, under identical epidemiological parameters and dispersal kernel. Using data from a controlled field experiment, we evaluate the ability of each model to replicate disease prevalence under nine intervention scenarios that vary in timing and culling area. While the models differ substantially in design — ranging from spatial grid-based to network-based and raster-based frameworks — the shared dispersal kernel allowed for close alignment in their predictions. All models accurately captured general epidemic trends, particularly the strong effect of early intervention on disease suppression. We qualitatively compared their behavioral responses across scenarios and also evaluated an ensemble prediction by averaging across model outputs. Our findings highlight how integrating shared epidemiological components into distinct modeling frameworks can improve consistency and accuracy, while reinforcing the importance of early culling in managing LDD pathogen outbreaks.

Dispersal kernel↗
DOE OSTI2023

Software-Hardware Co-design of Heterogeneous SmartNIC System for Recommendation Models Inference and Training

Deep Learning Recommendation Models (DLRMs) are critical applications in various domains and have evolved as one of the single largest machine learning applications. Trillions of DLRM parameters exceed the on-chip memory capacity of GPUs. Large-scale multi-node systems are required for distributed DLRM inference and training, which suffer from the all-to-all communication bottleneck, mainly limiting the scalability of ever-growing DLRMs. In recent years, SmartNICs have evolved with coupled computation and communication capabilities providing opportunities for a powerful heterogeneous device in the system. However, there isn't such a distributed system that fully leverages the abundant smartNIC resources that resolve the scalability issue of DLRMs. In this work, we proposed a software-hardware co-design of a heterogeneous smartNIC system that resolves the communication bottleneck of distributed DLRMs, mitigates the memory bandwidth pressure, and improves computation efficiency. We provide a set of smartNIC designs of cache systems (including local cache and remote cache) and smartNIC computation kernels which reduce data movement, relieve memory lookup intensity, and improve the GPU's computation efficiency. In addition, we propose a graph algorithm that improves the data locality of queries within batches which optimizes the overall system performance with higher data reuse. Our evaluation shows that our system achieves 2.1x latency speedup for inference and 1.6x throughput speedup for training.

Guo, Anqi↗
DOE OSTI2023

Simulation of Mechanical Fractionation of Chopped Whole-Plant Corn (WPC) Using Discrete Element Method (DEM)

Fractionating whole-plant corn (WPC) in a single-pass harvesting system requires studies on the WPC-to-equipment interaction for improved property control, as well as mechanical and air-driven separation processes compared to the traditional multi-pass grain and stover harvesting system. The discrete element method (DEM) technique has the potential to simulate WPC mechanical fractionation and support simulation-based design of WPC separation processes. In this study, methods to develop DEM particle models of WPC (kernel, cob, stalk, and husk) and their material properties for simulating mass fractionation using the ASABE standard mechanical shaker were proposed. Measurement was done on the axial dimensions (major, intermediate, and minor) and mass of each WPC type (mean sample size is 56), sampled from single-pass harvesting. Applying gaussian multivariate regression and bootstrapping re-sampling techniques, a DEM particle approximate to each WPC was developed. Sensitivity analysis of the DEM Young‘s modulus, Poisson‘s ratio, and interaction parameters of coefficient of restitution, coefficient of rolling friction, and coefficient of static friction on mass fraction was performed after 156 ASABE sieve-shaking DEM simulation runs, generated using Latin Hypercube Design (LHD) design of experiment (DOE) from 19 DEM material parameters. DEM simulation using Hertz-Mindlin with flexible bond contact laws and DOE optimized material properties successfully reproduced the mass fractions retained in ASABE sieves at 9.8% mean relative error and a coefficient of determination of R2 = 0.87. Here, the DEM methodology developed for mechanical WPC mass fractionation could be deployed to perform virtual design of feedstock handling equipment and performance analysis of mechanical fraction systems.

09 BIOMASS FUELS↗
DOE OSTI2022

A Framework for Error-Bounded Approximate Computing, with an Application to Dot Products

Approximate computing techniques, which trade off the computation accuracy of an algorithm for better performance and energy efficiency, have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing strategies that are not developed with guaranteed error bounds. While approximate computing techniques can be developed for individual high-performance computing applications by domain specialists, this often requires additional theoretical analysis and potentially extensive software modification. Hence, the development of low-level error-bounded approximate computing strategies that can be introduced into any high-performance computing application without requiring additional analysis or significant software alterations is desirable. In this paper, we provide a contribution in this direction by proposing a general framework for designing error-bounded approximate computing strategies and apply it to the dot product kernel to develop \bf qdot---an error-bounded approximate dot product kernel. Following the introduction of qdot, here we perform a theoretical analysis that yields a deterministic bound on the relative approximation error introduced by qdot. Empirical tests are performed to illustrate the tightness of the derived error bound and to demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks---the conjugate gradient (CG) and power methods. In some instances, using qdot for the dot products in CG can result in many components being quantized to half precision without increasing the iteration count required for convergence to the same solution as CG using a double precision dot product.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Temperature Inversions below 1 km from a V-Band Scanning Radiometer at the North Slope of Alaska

A single-channel (56.7 GHz) scanning radiometer was deployed in August 2022 at the Atmospheric Radiation Measurement (ARM) North Slope of Alaska site near Utqiaġvik. The radiometer is designed to provide temperature profiles between 0 and 1 km every 5 min. Averaging kernels show that this single-channel radiometer, taking observations at 10 discrete elevation angles, yields approximately the same information as a seven-channel V-band radiometer scanning three elevation angles. The instrument is able to reproduce the occurrence of temperature inversions between the surface and 1 km and their strength showing a correlation of 0.85, bias of −0.6 K, and slope of 1.04 with respect to radiosondes. Uncertainty in the inversion base height varies from 50 m near the surface to ∼300 m above 0.4 km when compared with radiosondes. Conversely, the inversion top height is overestimated and has higher uncertainty due to the degrading effects of the averaging kernels on the vertical resolution of the retrievals. Thanks to the high temporal resolution of the retrievals, the diurnal cycle of boundary layer temperature was evaluated showing that the radiometer can capture some aspects of the boundary layer thermal structure. The present analysis provides an overview of the capabilities of this simple observing configuration for selected applications.

Atmospheric profilers↗
DOE OSTI2020

A massively parallel and scalable multi-CPU material point method

Harnessing the power of modern multi-GPU architectures, we present a massively parallel simulation system based on the Material Point Method (MPM) for simulating physical behaviors of materials undergoing complex topological changes, self-collision, and large deformations. Our system makes three critical contributions. First, we introduce a new particle data structure that promotes coalesced memory access patterns on the GPU and eliminates the need for complex atomic operations on the memory hierarchy when writing particle data to the grid. Second, we propose a kernel fusion approach using a new Grid-to-Particles-to-Grid (G2P2G) scheme, which efficiently reduces GPU kernel launches, improves latency, and significantly reduces the amount of global memory needed to store particle data. Finally, we introduce optimized algorithmic designs that allow for efficient sparse grids in a shared memory context, enabling us to best utilize modern multi-GPU computational platforms for hybrid Lagrangian-Eulerian computational patterns. We demonstrate the effectiveness of our method with extensive benchmarks, evaluations, and dynamic simulations with elastoplasticity, granular media, and fluid dynamics. In comparisons against an open-source and heavily optimized CPU-based MPM codebase [Fang et al. 2019] on an elastic sphere colliding scene with particle counts ranging from 5 to 40 million, our GPU MPM achieves over 100x per-time-step speedup on a workstation with an Intel 8086K CPU and a single Quadro P6000 GPU, exposing exciting possibilities for future MPM simulations in computer graphics and computational science. Moreover, compared to the state-of-the-art GPU MPM method [Hu et al. 2019a], we not only achieve 2x acceleration on a single GPU but our kernel fusion strategy and Array-of-Structs-of-Array (AoSoA) data structure design also generalizes to multi-GPU systems. Our multi-GPU MPM exhibits near-perfect weak and strong scaling with 4 GPUs, enabling performant and large-scale simulations on a 10243 grid with close to 100 million particles with less than 4 minutes per frame on a single 4-GPU workstation and 134 million particles with less than 1 minute per frame on an 8-GPU workstation.

Wang, Xinlei↗
DOE OSTI2020

Scalability of high-performance PDE solvers

Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Performance Analysis and Optimal Node-aware Communication for Enlarged Conjugate Gradient Methods

Krylov methods are a key way of solving large sparse linear systems of equations but suffer from poor strong scalability on distributed memory machines. Furthermore, this is due to high synchronization costs from large numbers of collective communication calls alongside a low computational workload. Enlarged Krylov methods address this issue by decreasing the total iterations to convergence, an artifact of splitting the initial residual and resulting in operations on block vectors. In this article, we present a performance study of an enlarged Krylov method, Enlarged Conjugate Gradients (ECG), noting the impact of block vectors on parallel performance at scale. Most notably, we observe the increased overhead of point-to-point communication as a result of denser messages in the sparse matrix-block vector multiplication kernel. Additionally, we present models to analyze expected performance of ECG, as well as motivate design decisions. Most importantly, we introduce a new point-to-point communication approach based on node-aware communication techniques that increases efficiency of the method at scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Development of advanced machine learning models for analysis of plutonium surrogate optical emission spectra

This work investigates and applies machine learning paradigms seldom seen in analytical spectroscopy for quantification of gallium in cerium matrices via processing of laser-plasma spectra. Ensemble regressions, support vector machine regressions, Gaussian kernel regressions, and artificial neural network techniques are trained and tested on cerium-gallium pellet spectra. A thorough hyperparameter optimization experiment is conducted initially to determine the best design features for each model. The optimized models are evaluated for sensitivity and precision using the limit of detection (LoD) and root mean-squared error of prediction (RMSEP) metrics, respectively. Gaussian kernel regression yields the superlative predictive model with an RMSEP of 0.33% and an LoD of 0.015% for quantification of Ga in a Ce matrix. This study concludes that these machine learning methods could yield robust prediction models for rapid quality control analysis of plutonium alloys.

Rao, Ashwin P. (ORCID:0000000319312568)↗
DOE OSTI2023

AGR-5/6/7 Irradiation Disassembly and Metrology First Look

The Advanced Gas Reactor (AGR) Fuel Development and Qualification Program was established to perform research and development on tristructural isotropic (TRISO)-coated particle fuel to support deployment of high-temperature gas-cooled reactors (HTGRs), which are graphite-moderated nuclear reactors cooled with helium. This work continues as part of the Advanced Reactor Technologies (ART) TRISO Fuel Program. The overarching program goal is to provide a baseline fuel qualification data set to support licensing, deployment, and operation of HTGRs in the United States. To achieve these goals, the program includes fuel fabrication, irradiations of TRISO fuels and high-temperature materials (e.g., graphite), safety testing and post-irradiation examination (PIE), fuel performance modeling, and fission product transport and source term determination. The ART AGR program has conducted four distinct fuel irradiation experiments in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL). The first of these irradiation tests, designated AGR-1, began in ATR in December of 2006 and ended in November 2009. This experiment was primarily to act as a shakedown test of the multi-capsule test train design and to provide early data on fuel performance that would be used in fuel fabrication process development. AGR-1 fuel kernels were produced on an engineering scale, but the TRISO coatings and cylindrical fuel compacts were fabricated on a laboratory scale. The AGR-1 PIE was completed and the final report was published in 2015. The second irradiation test, AGR-2, started in ATR in June 2010 and ended in October 2013. The AGR-2 irradiation test was designed to provide fuel performance data for coated particles fabricated on an engineering-scale pilot line using a coater with an internal chamber diameter of 150 mm (6 in.). The final PIE report was published in 2021. AGR-3/4, a single irradiation that combined what were originally conceived as the third and fourth tests, was to support the refinement of fission product transport models and to assess the effects of sweep gas impurities on fuel performance and fission product transport. PIE of the AGR-3/4 experiment is still in progress as of this writing. The subject of this report is AGR-5/6/7, the final qualification test of AGR TRISO fuel made entirely at the engineering scale.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Post-irradiation examination of AGR-3/4 TRISO fuel compacts using three-dimensional X-ray computed tomography

The AGR-3/4 irradiation tests combined the third and fourth planned irradiation experiments in the US Department of Energy’s Advanced Gas Reactor (AGR) testing campaign of tri-structural isotropic (TRISO) fuel compacts. In this article, we present post-irradiation examination (PIE) using X-ray computed tomography (XCT) of two unirradiated and two irradiated compacts from the AGR-3/4 irradiation tests. The irradiated compacts studied (compact 7–1 and compact 12–4) represent the upper and lower limit of burnup within the AGR-3/4 irradiation experiment. This article presents a detailed quantitative analysis on the post-irradiation structure of TRISO fuel compacts. Various quantitative parameters including shape, size, and packing of kernels, and their spatial distribution, were utilized to gain insights into the structural changes caused by irradiation. The equivalent diameter and sphericity were found to increase and decrease, respectively, in irradiated compact 7–1 due to its higher burnup. Nearest neighbor distance between fuel kernels decreased after irradiation, suggesting irradiation-induced shrinkage of graphitic matrix. Furthermore, each compact in AGR-3/4 irradiation tests contained 20 designed-to-fail (DTF) fuel particles that were meant to act as a source of fission product release to the experiment test train. Furthermore, in the present work, all DTF fuel particles in the four compacts studied were identified, and it was found that they exhibited larger kernel swelling in compact 12–4 and smaller kernel swelling in compact 7–1, compared to the driver particles.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Sharp front tracking with geometric interface reconstruction

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

42 ENGINEERING↗