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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Porous Nanomaterials for Ultrabroadband Omnidirectional Anti‐Reflection Surfaces with Applications in High Concentration Photovoltaics

Materials for nanoporous coatings that exploit optimized chemistries and self‐assembly processes offer capabilities to reach ≈98% transmission efficiency and negligible scattering losses over the broad wavelength range of the solar spectrum from 350 nm to 1.5 µm, on both flat and curved glass substrates. These nanomaterial anti‐reflection coatings also offer wide acceptance angles, up to ±40°, for both s‐ and p‐polarization states of incident light. Carefully controlled bilayer films have allowed for the fabrication of dual‐sided, gradient index profiles on plano‐convex lens elements. In concentration photovoltaics platforms, the resultant enhancements in the photovoltaics efficiencies are ≈8%, as defined by experimental measurements on systems that use microscale triple‐junction solar cells. These materials and their applications in technologies that require control over interface reflections have the potential for broad utility in imaging systems, photolithography, light‐emitting diodes, and display technologies.

Yao, Yuan↗
DOE OSTI2024

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

distribution system operator↗
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An improved current potential method for fast computation of stellarator coil shapes

Several fast methods for computing stellarator coil shapes are compared, including the classical NESCOIL procedure, its generalization using truncated singular value decomposition, and a Tikhonov regularization approach we call REGCOIL in which the squared current density is included in the objective function. Considering W7-X and NCSX geometries, and for any desired level of regularization, we find the REGCOIL approach simultaneously achieves lower surface-averaged and maximum values of both current density (on the coil winding surface) and normal magnetic field (on the desired plasma surface). This approach therefore can simultaneously improve the free-boundary reconstruction of the target plasma shape while substantially increasing the minimum distances between coils, preventing collisions between coils while improving access for ports and maintenance. The REGCOIL method also allows finer control over the level of regularization, it preserves convexity to ensure the local optimum found is the global optimum, and it eliminates two pathologies of NESCOIL: the resulting coil shapes become independent of the arbitrary choice of angles used to parameterize the coil surface, and the resulting coil shapes converge rather than diverge as Fourier resolution is increased. We therefore contend that REGCOIL should be used instead of NESCOIL for applications in which a fast and robust method for coil calculation is needed, such as when targeting coil complexity in fixed-boundary plasma optimization, or for scoping new stellarator geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. As a result, we use the convex ι 1 and the nonconvex ι 1 – ι 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Experiments and Analyses of Data Transfers Over Wide-Area Dedicated Connections

Dedicated wide-area network connections are increasingly employed in high-performance computing and big data scenarios. One might expect the performance and dynamics of data transfers over such connections to be easy to analyze due to the lack of competing traffic. However, non-linear transport dynamics and end-system complexities (e.g., multi-core hosts and distributed filesystems) can in fact make analysis surprisingly challenging. We present extensive measurements of memory-to-memory and disk-to-disk file transfers over 10 Gbps physical and emulated connections with 0–366 ms round trip times (RTTs). For memory-to-memory transfers, profiles of both TCP and UDT throughput as a function of RTT show concave and convex regions; large buffer sizes and more parallel flows lead to wider concave regions, which are highly desirable. TCP and UDT both also display complex throughput dynamics, as indicated by their Poincare maps and Lyapunov exponents. For disk-to-disk transfers, we determine that high throughput can be achieved via a combination of parallel I/O threads, parallel network threads, and direct I/O mode. Our measurements also show that Lustre filesystems can be mounted over long-haul connections using LNet routers, although challenges remain in jointly optimizing file I/O and transport method parameters to achieve peak throughput.

Rao, Nageswara S.↗
DOE OSTI2024

Spot size measurement of a deuterium–tritium dense plasma focus using neutron radiography

Neutron radiography is a technique uniquely suited to applications in nuclear diagnostics, non-destructive testing, and subcritical experiments. The spatial resolution of neutron radiographs is degraded by optical blur in the imaging system and the neutron source size, where the ideal source is point-like to optimize the point-spread function. A potential neutron source for radiography is the dense plasma focus (DPF), a coaxial Z-pinch that produces thermonuclear and beam-target neutrons. To assess if the source size is suitable for radiography, a neutron imaging system was used to measure the source size of the 4 MA Sodium DPF at the Nevada National Security Site operating with deuterium–tritium gas-fill. The source size was measured using the edge-spread function of tungsten objects, each having a rolled (convex) edge. The spot size was found to be 7–12 mm full-width at half-max (FWHM) assuming a Gaussian source, though comparison is presented for Lorentzian and Bennett distributions. The average FWHM was found to be 8.6 ± 1.2 mm vertically and 10.8 ± 1.2 mm horizontally with respect to the image plane, averaging over varied edges and alignments. The results were sensitive to source alignment and edge metrology, which introduced notable uncertainties. These results are consistent with separate experimental measurements as well as magnetohydrodynamics simulations of this DPF, which suggest that neutron production can originate from pinches ∼5–7 mm off-axis. These results suggest that the DPF should be used for radiography at low magnification (M < 1) where spot size does not dominate spatial blur.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗
DOE OSTI2014

TU-C-17A-05: Dose Domain Optimization of MLC Leaf Patterns for Highly Complicated 4Ï€ IMRT Plans

Purpose: Highly conformal non-coplanar 4π radiotherapy plans typically require more than 20 intensity-modulated fields to deliver. A novel method to calculate multileaf collimator (MLC) leaf patterns is introduced to maximize delivery efficiency, accuracy and plan quality. Methods: 4 GBM patients, with a prescription dose of 59.4 Gy or 60 Gy, were evaluated using the 4π algorithm using 20 beams. The MLC calculation utilized a least square minimization of the dose distribution, with an anisotropic total variation regularization term to encourage piecewise continuity in the fluence maps. Transforming the fluence to the dose domain required multiplying the fluence with a sparse matrix. Exploiting this property made it feasible to solve the problem using CVX, a MATLAB-based convex modeling framework. The fluence was stratified into even step sizes, and the MLC segments, limited to 300, were calculated. The patients studied were replanned using Eclipse with the same beam angles. Results: Compared to the original 4π plan, the stratified 4π plan increased the maximum/mean dose for, in Gy, by 1.0/0.0 (brainstem), 0.5/0.2 (chiasm), 0.0/0.0 (spinal cord), 1.9/0.3 (L eye), 0.7/0.2 (R eye), 0.4/0.4 (L lens), 0.3/0.3 (R lens), 1.0/0.8 (L Optical Nerve), 0.5/0.3 (R Optical Nerve), 0.3/0.2 (L Cochlea), 0.1/0.1 (R Cochlea), 4.6/0.2 (brain), 2.4/0.1 (brain-PTV), 5.1/0.9 (PTV). Compared to Eclipse, which generated an average of 607 segments, the stratified plan reduced (−) or increased (+) the maximum/mean dose, in Gy, by −10.2/−4.1 (brainstem), −10.5/−8.9 (chiasm), +0.0/−0.1 (spinal cord), −4.9/−3.4 (L eye), −4.1/−2.5 (R eye), −2.8/−2.7 (L lens), −2.1/−1.9 (R lens), −7.6/−6.5 (L Optical Nerve), −8.9/−6.1 (R Optical Nerve), −1.3/−1.9 (L Cochlea), −1.8/−1.8 (R Cochlea), +1.7/−2.1 (brain), +3.2/−2.6 (brain-PTV), +1.8/+0.3 Gy (PTV. The stratified plan was also more homogeneous in the PTV. Conclusion: This novel solver can transform complicated fluence maps into significantly fewer deliverable MLC segments than the commercial system while achieving superior dosimetry. Funding support partially contributed by Varian.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ 2 ) in the L∞(Ω) norm, which is optimal considering the O(δ 2 ) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Finally, based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ 2 ) convergence.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Structural optimization of an alternate design for the space shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the shuttle solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in. diameter and 135 studs of 1 3/16 in. diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonliner displacement analysis. The minimum weight design has 135 studs of 1 3/16 in. diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, J.-F. M.↗
NASA NTRS1987

Structural optimization of an alternate design for the Space Shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the Shuttle's solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in diameter and 135 studs of 1 3/16 in diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonlinear displacement analysis. The minimum weight design has 135 studs of 1 3/16 in diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, Jean-Francois M.↗
DOE OSTI2016

Experimental evaluation of neural probe’s insertion induced injury based on digital image correlation method

Purpose: The application of neural probes in clinic has been challenged by probes’ short lifetime when implanted into brain tissue. The primary goal is to develop an evaluation system for testing brain tissue injury induced by neural probe’s insertion using microscope based digital image correlation method. Methods: A brain tissue phantom made of silicone rubber with speckle pattern on its surface was fabricated. To obtain the optimal speckle pattern, mean intensity gradient parameter was used for quality assessment. The designed testing system consists of three modules: (a) load module for simulating neural electrode implantation process; (b) data acquisition module to capture micrographs of speckle pattern and to obtain reactive forces during the insertion of the probe; (c) postprocessing module for extracting tissue deformation information from the captured speckle patterns. On the basis of the evaluation system, the effects of probe wedge angle, insertion speed, and probe streamline on insertion induced tissue injury were investigated. Results: The optimal quality speckle pattern can be attained by the following fabrication parameters: spin coating rate—1000 r/min, silicone rubber component A: silicone rubber component B: softener: graphite = 5 ml: 5 ml: 2 ml: 0.6 g. The probe wedge angle has a significant effect on tissue injury. Compared to wedge angle 40° and 20°, maximum principal strain of 60° wedge angle was increased by 40.3% and 87.5%, respectively; compared with a relatively higher speed (500 μm/s), the maximum principle strain within the tissue induced by slow insertion speed (100 μm/s) was increased by 14.3%; insertion force required by probe with convex streamline was smaller than the force of traditional probe. Based on the experimental results, a novel neural probe that has a rounded tip covered by a biodegradable silk protein coating with convex streamline was proposed, which has both lower insertion and micromotion induced tissue injury. Conclusions: The established evaluation system has provided a simulation environment for testing brain tissue injury produced by various insertion conditions. At the same time, it eliminates the adverse effect of biological factors on tissue deformation during the experiment, improving the repeatability of measurement results. As a result, the evaluation system will provide support on novel neural probe design that can reduce the acute tissue injury during the implantation of the probe.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS1993

Two generalizations of Kohonen clustering

The relationship between the sequential hard c-means (SHCM), learning vector quantization (LVQ), and fuzzy c-means (FCM) clustering algorithms is discussed. LVQ and SHCM suffer from several major problems. For example, they depend heavily on initialization. If the initial values of the cluster centers are outside the convex hull of the input data, such algorithms, even if they terminate, may not produce meaningful results in terms of prototypes for cluster representation. This is due in part to the fact that they update only the winning prototype for every input vector. The impact and interaction of these two families with Kohonen's self-organizing feature mapping (SOFM), which is not a clustering method, but which often leads ideas to clustering algorithms is discussed. Then two generalizations of LVQ that are explicitly designed as clustering algorithms are presented; these algorithms are referred to as generalized LVQ = GLVQ; and fuzzy LVQ = FLVQ. Learning rules are derived to optimize an objective function whose goal is to produce 'good clusters'. GLVQ/FLVQ (may) update every node in the clustering net for each input vector. Neither GLVQ nor FLVQ depends upon a choice for the update neighborhood or learning rate distribution - these are taken care of automatically. Segmentation of a gray tone image is used as a typical application of these algorithms to illustrate the performance of GLVQ/FLVQ.

Bezdek, James C.↗
DOE OSTI2022

Open-source Tools for Solving Grid Optimization Problems: ARPA-e Benchmark Algorithm Overview [Slides]

This document contains the official formulation that will be used for evaluation in Challenge 2 of the Grid Optimization (GO) Competition. Minor changes may occur within the formulation. Entrants will be notified when a new version is released. Changes are not expected to be of a significance that would cause a change in approach for the Entrants. This formulation builds upon the Challenge 1 formulation published in ARPA-E DE-FOA-0001952. Entrants will be judged based on the current official Challenge 2 formulation posted on the GO Competition website (this document, which is subject to change), not the formulation posted in DE-FOA-0001952. Entrants are permitted and encouraged to use any alternative problem formulation and modeling convention within their own software (such as convex relaxation, decoupled power flow formulations, current-voltage formulations, etc.) in an attempt to produce an exact or approximate solution to this particular mathematical program. However, the judging of all submitted approaches must conform to the official formulation presented here.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRSDate not supplied

Next Generation Exercise Device (NGED): Advancing Exercise Capabilities for Future Space Missions Through Biomechanical Modeling

BACKGROUND As space exploration extends to long-duration missions on the Moon and Mars, maintaining astronaut health and fitness becomes increasingly critical. The Next Generation Exercise Device (NGED), developed and tested by the HumanWorks Lab in NASA Johnson Space Center's (JSC) Software, Robotics, and Simulation Division, aims to address this challenge through innovative approaches. This study presents the development and evaluation of an NGED system, focusing on its adaptability to various mission scenarios, including prospective use in a Lunar Pressurized Rover (LPR). Central to this project is the application of biomechanical modeling to optimize exercise efficacy and safety in microgravity and partial gravity environments. The project is a collaborative effort with the Human Health and Performance group at Johnson Space Center, ensuring a comprehensive approach to astronaut well-being that integrates biomechanical principles with practical exercise solutions. The NGED represents the next generation of exercise capabilities for missions in space, on the Moon and Mars, with a specific focus on applications such as the LPR. METHODS AND RESULTS Data collection for NGED development was conducted with two motor-driven Beyond Power Voltra I [1] systems and a custom test structure to allow placement of the cable-based devices on the ground, at shoulder height, and overhead. The collection was performed in JSC’s Prototype Immersive Technology (PIT) Lab, utilizing an OptiTrack motion capture system and AMTI force platform, to enable detailed biomechanical analysis via OpenSim [2,3]. Motion capture data were collected for three subjects representing different body types and statures. The marker set used was an enhanced version of the full-body Plug-in Gait marker set [4], with additional markers strategically placed for the primary objective of informing exercise volume requirements. Subjects performed a series of 17 exercises, carefully selected to engage various muscle groups, including novel spaceflight exercises such as skiing (ergometer style), lateral pulldowns, wood chops, triceps extensions, and flies, with load variations ranging from 10 to 90 pounds to maintain kinematic form. This comprehensive approach allowed for a thorough evaluation of the NGED's performance across a wide range of motions and loads. The biomechanical modeling and analysis were conducted using a modified OpenSim Full Body Rajagopal Model [4,5] and also scaled to the maximum and minimum anthropometry provided in NASA-STD-3001 [6]. Volumetric convex hulls were generated based on model marker trajectories and aggregated into geometric assemblies. These can be placed in models of vehicle designs to assess fit to protect for exercise as well as to adapt NGED exercise to fit available space. Preliminary findings from the collection indicate that the NGED prototype demonstrates significant adaptability across varying user anthropometrics and exercise types. The device showed consistent performance in load-bearing exercises, with subjects able to perform exercises effectively while maintaining proper biomechanical form. CONCLUSION NGED represents a forward-looking advancement in exercise capabilities for future space missions. In the future, this system can be used to capture valuable metrics (e.g., isometric mid-thigh pull for force output measurements, assessments of postural muscle strength, overall isometric strength). Its versatility in accommodating various exercises and user physiques, coupled with the ability to provide targeted biomechanical loading, makes it a promising approach for maintaining astronaut health during long-duration missions to the Moon and Mars. Future work will focus on refining the NGED based on initial biomechanical findings, leveraging the detailed insights provided by motion capture and analysis techniques. Particular emphasis will be placed on optimizing its use within the confined spaces of a LPR and other space habitats. This work contributes significantly to NASA's goals of supporting human health and performance in deep space exploration, paving the way for sustainable long-term presence beyond Low Earth Orbit through advanced, biomechanically-informed exercise solutions.

C Wang↗
DOE OSTI2020

Metric Type in the Target-matrix Mesh Optimization Paradigm

The Target Matrix Optimization Paradigm (TMOP) is a method for improving the accuracy, efficiency, and robustness of numerical solutions to partial differential equations by improving the geometric quality of the computational mesh, primarily through node movement. TMOP has been successfully applied to a number applications even though the paradigm was not fully understood at the time. With this work, TMOP can be seen to be a tightly woven fabric of interconnecting ideas and concepts that provides a powerful approach to mesh optimization. The central unifying concepts in TMOP are the concept of a Target Matrix and the concept of Metric Type. Target matrices are motivated by the desire to make mesh quality improvement application-specific and, when needed, solution-adaptive. Metric type plays an essential role because it provides, through the use of typed metrics, the bridge between application-specific quality and target construction. It is shown that there are eight theoretical metric types, including the shape and shape+size types used informally in the past. It is shown further that there exist well-posed metrics corresponding to six of the eight metric types. A well-posed metric is a metric that is typed and convex, polyconvex, or invex, and further, it is a metric that simplifies target construction.

97 MATHEMATICS AND COMPUTING↗