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At least 181 records · Page 10

Parallel adaptive mesh refinement techniques for plasticity problems

The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.

Barry, W. J.↗

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗

Model Data Archive for Manuscript Titled "Evaluation of a Coupled Surface–Subsurface Hydrologic Model Using Dense Water‑Level Sensors in a Mixed Urban–Rural Watershed"

This archive provides scripts, input files, and datasets used for the implementation and evaluation of a fully coupled surface–subsurface hydrologic model in the Neches River Basin, southeast Texas. The study uses the Advanced Terrestrial Simulator (ATS) to simulate coupled surface–subsurface hydrologic processes over a mixed urban–rural watershed and evaluates model performance using a dense network of 136 in situ water-level sensors, nine U.S. Geological Survey (USGS) stream gauges, and SSEBop-derived evapotranspiration estimates during the period October 2014–June 2024. The workflow is implemented primarily in Python 3 using the Watershed Workflow package. The Jupyter notebooks can be executed using open-source software such as Anaconda JupyterLab or Visual Studio Code. Other data files include TXT, CSV, XML, SHP, TIF, NetCDF, HDF5, and ExodusII files, which can be processed using the provided Python scripts. ATS input files are provided in XML format and can be edited using any commonly used text editor. This archive contains: *Scripts and input files used to generate the ATS model setup, including watershed discretization, mesh generation, parameter mapping, and model configuration. *Jupyter notebooks used for preprocessing observational data, evaluating streamflow, water levels, and evapotranspiration, computing performance metrics, and generating the figures presented in the manuscript. *ATS simulation outputs and processed observational datasets, including OneRain and DD6 water-level sensors, USGS streamflow observations, GIS data, and supporting spatial datasets used throughout the study.

Dense water-level sensor network↗

Development of Physics-Based Transition Models for Unstructured-Mesh CFD Codes Using Deep Learning Models

Predicting transition locations over a vehicle surface is of fundamental importance for many engineering applications. With the transition information, the Reynolds-averaged Navier-Stokes (RANS) computations can turn on the turbulence model at the right locations so that drag, lift and other aerodynamic quantities can be accurately predicted. In contrast to the popularity of RANS-based transition modeling in which transition onset is governed by the turbulence equations, physics-based transition models that account for instability waves within the boundary layer, thus more compliant to flow physics, only gained more attention in recent years. This paper describes the development of a new physics-based transition model based on either the linear stability theory (LST) or parabolized stability equations (PSE). The model is designed to communicate with a structured or unstructured-mesh RANS solver back and forth in order to more accurately compute transition fronts over a three-dimensional body. In the developed model, the Python suite of interface codes in conjunction with the LASTRAC software can be executed autonomously to produce transition onset locations for a given laminar or RANS-computed transitional state. In addition, as a proof of concept, the tool set consists of a deep learning neural network model that has been designed and trained to predict instability wave evolutions inside the boundary layer for various instability wave mechanisms across a selected speed range. A machine-learned intelligent profile interpolation model has also been devised to enable reliable instability-wave spectra predictions with just a few points in the mean flow profiles.

Transition Modeling↗

Asynchronous-many-task systems: Challenges and opportunities - Scaling an AMR astrophysics code on exascale machines using Kokkos and HPX

Dynamic and adaptive mesh refinement is pivotal in high-resolution, multi-physics, multi-model simulations, necessitating precise physics resolution in localized areas across expansive domains. Today’s supercomputers’ extreme heterogeneity presents a significant challenge for dynamically adaptive codes, highlighting the importance of achieving performance portability at scale. Our research focuses on astrophysical simulations, particularly stellar mergers, to elucidate early universe dynamics. Here, we present Octo-Tiger, leveraging Kokkos, HPX, and SIMD for portable performance at scale in complex, massively parallel adaptive multi-physics simulations. Octo-Tiger supports diverse processors, accelerators, and network backends. Experiments demonstrate exceptional scalability across several heterogeneous supercomputers including Perlmutter, Frontier, and Fugaku, encompassing major GPU architectures and x86, ARM, and RISC-V CPUs. Parallel efficiency of 47.59% (110,080 cores and 6880 hybrid A100 GPUs) on a full-system run on Perlmutter (26% HPCG peak performance) and 51.37% (using 32,768 cores and 2048 MI250X) on Frontier are achieved.

97 MATHEMATICS AND COMPUTING↗

Applications and development of communication models for the touchstone GAMMA and DELTA prototypes

The goal of this project was to develop models of the interconnection networks of the Intel iPSC/860 and DELTA multicomputers to guide the design of efficient algorithms for interprocessor communication in problems that commonly occur in CFD codes and other applications. Interprocessor communication costs of codes for message-passing architectures such as the iPSC/860 and DELTA significantly affect the level of performance that can be obtained from those machines. This project addressed several specific problems in the achievement of efficient communication on the Intel iPSC/860 hypercube and DELTA mesh. In particular, an efficient global processor synchronization algorithm was developed for the iPSC/860 and numerous broadcast algorithms were designed for the DELTA.

Seidel, Steven R.↗

CAVE3: A general transient heat transfer computer code utilizing eigenvectors and eigenvalues

The method of solution is a hybrid analytical numerical technique which utilizes eigenvalues and eigenvectors. The method is inherently stable, permitting large time steps even with the best of conductors with the finest of mesh sizes which can provide a factor of five reduction in machine time compared to conventional explicit finite difference methods when structures with small time constants are analyzed over long time periods. This code will find utility in analyzing hypersonic missile and aircraft structures which fall naturally into this class. The code is a completely general one in that problems involving any geometry, boundary conditions and materials can be analyzed. This is made possible by requiring the user to establish the thermal network conductances between nodes. Dynamic storage allocation is used to minimize core storage requirements. This report is primarily a user's manual for CAVE3 code. Input and output formats are presented and explained. Sample problems are included which illustrate the usage of the code as well as establish the validity and accuracy of the method.

Palmieri, J. V.↗

Spatial modeling algorithms for reactions and transport in biological cells

Biological cells rely on precise spatiotemporal coordination of biochemical reactions to control their functions. Such cell signaling networks have been a common focus for mathematical models, but they remain challenging to simulate, particularly in realistic cell geometries. Here we present Spatial Modeling Algorithms for Reactions and Transport (SMART), a software package that takes in high-level user specifications about cell signaling networks and then assembles and solves the associated mathematical systems. SMART uses state-of-the-art finite element analysis, via the FEniCS Project software, to efficiently and accurately resolve cell signaling events over discretized cellular and subcellular geometries. We demonstrate its application to several different biological systems, including yes-associated protein (YAP)/PDZ-binding motif (TAZ) mechanotransduction, calcium signaling in neurons and cardiomyocytes, and ATP generation in mitochondria. Throughout, we utilize experimentally derived realistic cellular geometries represented by well-conditioned tetrahedral meshes. These scenarios demonstrate the applicability, flexibility, accuracy and efficiency of SMART across a range of temporal and spatial scales.

59 BASIC BIOLOGICAL SCIENCES↗

A Comparative Study of Physics‐Informed and Data‐Driven Neural Networks for Compound Flood Simulation at River‐Ocean Interfaces: A Case Study of Hurricane Irene

Simulating compound flooding (CF) at the river-ocean interface within large-scale Earth System Models (ESMs) presents significant challenges due to complex interactions between river discharge, storm surge, and tides. This study assesses the comparative advantages of physics-informed and data-driven machine learning (ML) approaches for enhancing local ESM performance. We systematically compare data-driven neural network models (i.e., CNNs, U-Net, Long Short-Term Memory (LSTM), Gated Recurrent Unit), and physics-informed neural network (PINN) models, including vanilla PINN and a finite-difference-based PINN (FD-PINN). Specifically, FD-PINN is introduced to enhance computational efficiency, accelerating vanilla PINNs by ∼6.5 times while improving accuracy. To enhance data-driven model training, a new data-generation approach is developed to sample historical fluvial and coastal flood events, which ensures a robust data set for extreme event prediction. The models are evaluated using a realistic one-dimensional river domain extracted from an ESM's river mesh and the Hurricane Irene event as an independent test case. Results show that FD-PINN achieves accurate predictions with significantly reduced computational costs relative to vanilla PINNs. Among data-driven models, the best overall performance is achieved by a CNN-LSTM hybrid, which balances accuracy and efficiency. While a fully connected CNN (CNN-FC) provides the best accuracy, it incurs high computational cost. Architectures lacking strong temporal modeling tend to underperform on unseen events. These findings highlight the importance of sequence-aware designs for robust generalization. This study reveals the trade-offs between physics-informed and data-driven models and proposes an adaptive hybrid framework for integrating ML into ESMs to enhance local flood simulations.

Earth Systems Modeling↗

NASA Tech Briefs, January 2013

Topics include: Single-Photon-Sensitive HgCdTe Avalanche Photodiode Detector; Surface-Enhanced Raman Scattering Using Silica Whispering-Gallery Mode Resonators; 3D Hail Size Distribution Interpolation/Extrapolation Algorithm; Color-Changing Sensors for Detecting the Presence of Hypergolic Fuels; Artificial Intelligence Software for Assessing Postural Stability; Transformers: Shape-Changing Space Systems Built with Robotic Textiles; Fibrillar Adhesive for Climbing Robots; Using Pre-Melted Phase Change Material to Keep Payloads in Space Warm for Hours without Power; Development of a Centrifugal Technique for the Microbial Bioburden Analysis of Freon (CFC-11); Microwave Sinterator Freeform Additive Construction System (MS-FACS); DSP/FPGA Design for a High-Speed Programmable S-Band Space Transceiver; On-Chip Power-Combining for High-Power Schottky Diode-Based Frequency Multipliers; FPGA Vision Data Architecture; Memory Circuit Fault Simulator; Ultra-Compact Transputer-Based Controller for High-Level, Multi-Axis Coordination; Regolith Advanced Surface Systems Operations Robot Excavator; Magnetically Actuated Seal; Hybrid Electrostatic/Flextensional Mirror for Lightweight, Large-Aperture, and Cryogenic Space Telescopes; System for Contributing and Discovering Derived Mission and Science Data; Remote Viewer for Maritime Robotics Software; Stackfile Database; Reachability Maps for In Situ Operations; JPL Space Telecommunications Radio System Operating Environment; RFI-SIM: RFI Simulation Package; ION Configuration Editor; Dtest Testing Software; IMPaCT - Integration of Missions, Programs, and Core Technologies; Integrated Systems Health Management (ISHM) Toolkit; Wind-Driven Wireless Networked System of Mobile Sensors for Mars Exploration; In Situ Solid Particle Generator; Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature; Rad-Tolerant, Thermally Stable, High-Speed Fiber-Optic Network for Harsh Environments; Towed Subsurface Optical Communications Buoy; High-Collection-Efficiency Fluorescence Detection Cell; Ultra-Compact, Superconducting Spectrometer-on-a-Chip at Submillimeter Wavelengths; UV Resonant Raman Spectrometer with Multi-Line Laser Excitation; Medicine Delivery Device with Integrated Sterilization and Detection; Ionospheric Simulation System for Satellite Observations and Global Assimilative Model Experiments - ISOGAME; Airborne Tomographic Swath Ice Sounding Processing System; flexplan: Mission Planning System for the Lunar Reconnaissance Orbiter; Estimating Torque Imparted on Spacecraft Using Telemetry; PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils; Multiple-Frame Detection of Subpixel Targets in Thermal Image Sequences; Metric Learning to Enhance Hyperspectral Image Segmentation; Basic Operational Robotics Instructional System; Sheet Membrane Spacesuit Water Membrane Evaporator; Advanced Materials and Manufacturing for Low-Cost, High-Performance Liquid Rocket Combustion Chambers; Motor Qualification for Long-Duration Mars Missions.

Source record↗

Airline flight planning - The weather connection

The history of airline flight planning is briefly reviewed. Over half a century ago, when scheduled airline services began, weather data were almost nonexistent. By the early 1950's a reliable synoptic network provided upper air reports. The next 15 years saw a rapid growth in commercial aviation, and airlines introduced computer techniques to flight planning. The 1970's saw the development of weather satellites. The current state of flight planning activities is analyzed. It is found that accurate flight planning will require meteorological information on a finer scale than can be provided by a synoptic forecast. Opportunities for a new approach are examined, giving attention to the available options, a mesoscale numerical weather prediction model, limited area fine mesh models, man-computer interactive display systems, the use of interactive techniques with the present upper air data base, and the implementation of interactive techniques.

Steinberg, R.↗

Portable Parallel Programming for the Dynamic Load Balancing of Unstructured Grid Applications

The ability to dynamically adapt an unstructured -rid (or mesh) is a powerful tool for solving computational problems with evolving physical features; however, an efficient parallel implementation is rather difficult, particularly from the view point of portability on various multiprocessor platforms We address this problem by developing PLUM, tin automatic anti architecture-independent framework for adaptive numerical computations in a message-passing environment. Portability is demonstrated by comparing performance on an SP2, an Origin2000, and a T3E, without any code modifications. We also present a general-purpose load balancer that utilizes symmetric broadcast networks (SBN) as the underlying communication pattern, with a goal to providing a global view of system loads across processors. Experiments on, an SP2 and an Origin2000 demonstrate the portability of our approach which achieves superb load balance at the cost of minimal extra overhead.

Biswas, Rupak↗

Reactive Transport Modeling with Physics-Informed Machine Learning for Critical Minerals Applications

This study presents a physics-informed neural network (PINN) framework for reactive transport modeling for simulating fast bimolecular reactions in porous media. Accurate characterization of cAhemical interactions and product formation in surface and subsurface environments is essential for advancing critical mineral extraction and related geoscience applications. The proposed methodology sequentially addresses the flow and diffusion–reaction subproblems. The flow field is computed using a mixed formulation, while the diffusion–reaction system is modeled via two uncoupled tensorial diffusion equations reformulated in terms of chemical invariants. PINNs are employed to solve the governing equations, enabling data-efficient, mesh-free prediction of chemical concentration fields. The framework is validated through a series of benchmark problems involving flow in heterogeneous porous media. Initial verification is conducted using patch tests for the flow field, followed by validation of the transport problem with emphasis on preserving non-negativity of concentrations. The complete fast bimolecular reaction scenario is then solved, yielding spatial distributions of reactants and product species. Results demonstrate that the PINNs-based approach effectively captures sharp, mixing-limited reaction fronts and dispersive mixing behavior, offering reliable predictions of reactive plume evolution. These capabilities are crucial for evaluating long-term subsurface behavior in applications such as fluid storage, energy extraction, and efficient extraction of critical minerals.

42 ENGINEERING↗

Measuring pH Changes Inside a Bipolar Membrane Junction

Here, the local pH environment within bipolar membrane (BPM) junctions is complex and not well understood, yet it is important to control for advancing the performance of BPM-based electrochemical systems. We report a voltammetric strategy using an ultrathin Ni mesh pH probe to spatially resolve pH changes in the BPM junction during model BPM electrolyzer operation. Under reverse bias, we observe depletion of OH – at the anion-exchange layer (AEL) interface, with a degree diminishing with increasing distance from the AEL. These gradients correlate with current-dependent water dissociation (WD) and are modulated by the electric field and the surface charge state of the catalyst. By correlating spatial pH profiles with the surface-charging behavior of WD catalysts, we explore a mechanism of catalyst-mediated H + and OH – transfer facilitated by hydrogen-bonding networks. These findings highlight the role of local chemistry and electrostatics in BPM performance and offer new methods to probe and engineer catalytic junctions in electrochemical energy devices.

Hou, Shujin [University of California, Berkeley, C↗

Microstrip Antenna for Remote Sensing of Soil Moisture and Sea Surface Salinity

This compact, lightweight, dual-frequency antenna feed developed for future soil moisture and sea surface salinity (SSS) missions can benefit future soil and ocean studies by lowering mass, volume, and cost of the antenna system. It also allows for airborne soil moisture and salinity remote sensors operating on small aircraft. While microstrip antenna technology has been developed for radio communications, it has yet to be applied to combined radar and radiometer for Earth remote sensing. The antenna feed provides a key instrument element enabling high-resolution radiometric observations with large, deployable antennas. The design is based on the microstrip stacked-patch array (MSPA) used to feed a large, lightweight, deployable, rotating mesh antenna for spaceborne L-band (approximately equal to 1 GHz) passive and active sensing systems. The array consists of stacked patches to provide dual-frequency capability and suitable radiation patterns. The stacked-patch microstrip element was designed to cover the required L-band center frequencies at 1.26 GHz (lower patch) and 1.413 GHz (upper patch), with dual-linear polarization capabilities. The dimension of patches produces the required frequencies. To achieve excellent polarization isolation and control of antenna sidelobes for the MSPA, the orientation of each stacked-patch element within the array is optimized to reduce the cross-polarization. A specialized feed-distribution network was designed to achieve the required excitation amplitude and phase for each stacked-patch element.

Ramhat-Samii, Yahya↗

Deciphering supramolecular and polymer-like behavior in metallogels: real-time insights into temperature-modulated gelation and rapid self-assembly dynamics

Bis(pyridyl) urea-based gelators, namely L2 and its isomeric mixture ( L1 + L2 ), are known to self-assemble into 1D architectures capable of inducing supramolecular gelation. Coordination with metal ions such as Ag( I ), Cu( II ), and Fe( III ) introduces structural reinforcement, enabling the formation of distinct 3D networks governed by metal-specific coordination geometries. Here, we present a comprehensive investigation into the temperature-responsive behavior (20–60 °C) of L2 and L1 + L2 , both in the absence and presence of Ag( I ), Dy( III ), Fe( III ), Cu( II ), and Ho( III ), using real-time small-angle neutron scattering (SANS). To probe long-term structural evolution/kinetics of self-assembly, real-time small-angle X-ray scattering (SAXS) was employed on L2 + Ag gels, complemented by differential scanning calorimetry (DSC) to evaluate thermal transitions. Our results reveal strikingly divergent gelation behaviors: L2 forms a highly rigid, covalent polymer-like network, while L1 + L2 exhibits remarkable thermal adaptability. Upon metal coordination, the assemblies exhibit pronounced crystallinity and exceptional thermal stability, as evidenced by persistent Bragg reflections and invariant d-spacings. Intriguingly, L2 : Fe (2 : 1) and L1 : L2 : Fe (0.5 : 0.5 : 1) in acetonitrile-d 3 (ACN-d 3 ) deviate from this trend, forming thermally labile amorphous gels. These systems show a complete loss of crystalline order, reduced Porod exponents—indicative of collapsed or branched fiber morphologies—and prominent melting and glass transition events in DSC. Fitting SANS and SAXS data to the correlation length model unveiled insightful nanostructural features. While most systems displayed minimal temperature-induced variation in mesh size or surface morphology, L2 : Ag in dimethyl sulfoxide-d 6 (DMSO-d 6 )/D 2 O and L2 : Fe (1 : 1) in ACN-d 3 exhibited a rare combination of thermally stable correlation lengths and increasing high- q exponents—strongly suggesting progressive fiber densification or surface smoothing within a robust gel framework. These findings highlight the tunability and structural resilience of supramolecular gels through precise control of ligand architecture, metal coordination, and temperature, offering valuable design principles for functional soft materials.

Pajoubpong, Jinnipha [Univ. of Cincinnati, OH (Uni↗

The Mars 2020 Ground Data System Architecture

The Mars 2020 Mission’s primary objective is to collect 20 geographically unique samples during its prime mission of one and a quarter Martian years, or just over 2 Earth years. Mission planners determined the project needed to develop a system that would enable the operations team to analyze engineering and science data, make science decisions, select viable rover targets at a millimeter resolution and validate an uplink bundle for a car sized rover with more complex science instruments than any previous Mars surface mission. All this had to be done within a five hour time frame. Doing this with a small team would be a challenge, but this had to be accomplished by a large team of engineers and scientists located across North America and Europe. Achieving this level of operational efficiency was unheard of in the prime mission. In addition, the mission had another set of requirements that had nothing to do with surface operations; the Mars 2020 Ground Data System (GDS) was also expected to comply with a new set of security requirements to keep up with the ever changing cybersecurity landscape. The Mars 2020 Ground Data System (GDS) is a re-architected version of the Mars Science Laboratory GDS. The primary goal was to integrate the lessons learned from previous Mars surface missions, accommodate a set of new requirements and capabilities required to ensure mission success, and comply with a new set of cybersecurity controls. The new architecture includes several unique qualities including a data lake, language-agnostic system-wide event-based operations, containerization, automated deployment, network segmentation, infrastructure-as-code, API-driven interfaces, and the first Mars surface GDS to operate primarily in the cloud. The new architecture enabled greater access to the system’s data, tighter integration with the operations team, and a higher level of traceability. The availability of the data also enabled a new set of capabilities previously not possible on surface missions. These new capabilities include an autonomous data to information, pipeline for downlink analysis, horizontal scaling of science data processing capabilities, autonomous round trip data tracking of science and engineering data, integration of flight system state into the tactical planning cycle, high fidelity targeting utilizing kinematic data, and hierarchical image and 3d meshes data representations. This paper will introduce the requirements for the Mars 2020 Mission, the heritage architecture, and the rationale for the changes to achieve the new architecture. The paper will continue to describe the fundamental changes made to the GDS architecture, how these changes enabled a more tightly integrated GDS, and the new capabilities that were enabled by the new architecture. The paper will conclude with the lessons learned from the process of rearchitecting a heritage GDS system and from the first 200 days of operations supporting over 800 users from around the world.

Lopez-Roig, Reynaldo↗

Use of a Hybrid Edge Node-Centroid Node Approach to Thermal Modeling

A recent proposal submitted for an ESA mission required that models be delivered in ESARAD/ESATAN formats. ThermalDesktop was the preferable analysis code to be used for model development with a conversion done as the final step before delivery. However, due to some differences between the capabilities of the two codes, a unique approach was developed to take advantage of the edge node capability of ThermalDesktop while maintaining the centroid node approach used by ESARAD. In essence, two separate meshes were used: one for conduction and one for radiation. The conduction calculations were eliminated from the radiation surfaces and the capacitance and radiative calculations were eliminated from the conduction surfaces. The resulting conduction surface nodes were coincident with all nodes of the radiation surface and were subsequently merged, while the nodes along the edges remained free. Merging of nodes on the edges of adjacent surfaces provided the conductive links between surfaces. Lastly, all nodes along edges were placed into the subnetwork and the resulting supernetwork included only the nodes associated with radiation surfaces. This approach had both benefits and disadvantages. The use of centroid, surface based radiation reduces the overall size of the radiation network, which is often the most computationally intensive part of the modeling process. Furthermore, using the conduction surfaces and allowing ThermalDesktop to calculate the conduction network can save significant time by not having to manually generate the couplings. Lastly, the resulting GMM/TMM models can be exported to formats which do not support edge nodes. One drawback, however, is the necessity to maintain two sets of surfaces. This requires additional care on the part of the analyst to ensure communication between the conductive and radiative surfaces in the resulting overall network. However, with more frequent use of this technique, the benefits of this approach can far outweigh the additional effort.

Peabody, Hume L.↗