Relevant bibliographies by topics / Adaptive mesh method

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Academic literature on the topic 'Adaptive mesh method'

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Published: 22 June 2022

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Journal articles on the topic "Adaptive mesh method"

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Zhang, Jie, Abel Cherouat, and Houman Borouchaki. "Fast Point and Element Search Method in Adaptive Remeshing Procedure and Its Applications." ISRN Applied Mathematics 2011 (August 17, 2011): 1–13. http://dx.doi.org/10.5402/2011/509721.

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The FPES (fast point and element search) method is a useful and efficient strategy for node field transfer from old mesh to the new mesh in adaptive remeshing procedure. The FE mesh after adaptive remeshing with various error estimates will be refined at local region, and the mesh after adaptive remeshing has the heterogeneous density distribution. The FPES has the capacity to define the nearest search path adapting to the mesh with heterogeneous density distribution. It is a point location process which includes point searching, point location in element, and weight factor distribution. This strategy has been integrated to our finite element adaptive remeshing simulations, and it works well and rapidly. The three-dimension finite element numerical simulation of simply tensile test, orthogonal cutting, and metal milling process is given out to study its accuracy and efficiency.
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Guo, Zaoyang, Yujie Zhao, Zhaohui Chen, Minmao Liao, Zhengliang Li, and Bo Liu. "A Mesh Adaptive Procedure for Large Increment Method." International Journal of Applied Mechanics 07, no. 04 (August 2015): 1550061. http://dx.doi.org/10.1142/s1758825115500611.

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A posteriorih-version mesh adaptive procedure is presented in the framework of large increment method (LIM) for elastic problems. In this mesh adaptive strategy, the classical Zienkiewicz–Zhu (ZZ) error estimator is adopted and a first class h-adaptive mesh refinement procedure is implemented. A major advantage of the proposed mesh adaptive procedure is that the numerical results from the previous mesh can be utilized to obtain the initial solution for the new mesh. Two-dimensional (2D) examples show that this initial solution is much closer to the real solution than the minimum norm solution used in the original LIM and the revised method can converge faster than the original method.
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Azarenok, B. N. "Variational method for adaptive mesh generation." Computational Mathematics and Mathematical Physics 48, no. 5 (May 2008): 786–804. http://dx.doi.org/10.1134/s0965542508050084.

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Xu, Yan, Gao Feng Wei, and Hai Yan Chen. "Overview of High Precision Adaptive Numerical Manifold Method." Advanced Materials Research 962-965 (June 2014): 2988–91. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.2988.

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The core of the numerical manifold method (NMM) is a two-mesh problem description. Two meshes are employed in an analysis: the mathematical mesh provides the nodes for building a finite covering of the solution domain, while the physical mesh provides the domain of integration. The NMM can deal with the continuum and discontinuous problem, and has been applied to the rock mechanics and engineering widely. This paper introduces the research progress of the NMM in the basic theory and application aspects. The adaptive mesh generation of NMM is discussed. The adaptive finite cover mesh reconstruction technology is given.
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Koohi, Mahdi, and Abbas Shakery. "An Adaptive Mesh Method for Object Tracking." International Journal of Peer to Peer Networks 2, no. 2 (April 30, 2011): 1–10. http://dx.doi.org/10.5121/ijp2p.2011.2201.

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Fang, F., M. D. Piggott, C. C. Pain, G. J. Gorman, and A. J. H. Goddard. "An adaptive mesh adjoint data assimilation method." Ocean Modelling 15, no. 1-2 (January 2006): 39–55. http://dx.doi.org/10.1016/j.ocemod.2006.02.002.

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Kim, Jeong-Hun, Hyun-Gyu Kim, Byung-Chai Lee, and Seyoung Im. "Adaptive mesh generation by bubble packing method." Structural Engineering and Mechanics 15, no. 1 (January 25, 2003): 135–49. http://dx.doi.org/10.12989/sem.2003.15.1.135.

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Altas, Irfan, and John W. Stephenson. "A two-dimensional adaptive mesh generation method." Journal of Computational Physics 94, no. 1 (May 1991): 201–24. http://dx.doi.org/10.1016/0021-9991(91)90143-9.

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Lei, Humin, Tao Liu, Deng Li, Jikun Ye, and Lei Shao. "Adaptive Mesh Iteration Method for Trajectory Optimization Based on Hermite-Pseudospectral Direct Transcription." Mathematical Problems in Engineering 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/2184658.

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An adaptive mesh iteration method based on Hermite-Pseudospectral is described for trajectory optimization. The method uses the Legendre-Gauss-Lobatto points as interpolation points; then the state equations are approximated by Hermite interpolating polynomials. The method allows for changes in both number of mesh points and the number of mesh intervals and produces significantly smaller mesh sizes with a higher accuracy tolerance solution. The derived relative error estimate is then used to trade the number of mesh points with the number of mesh intervals. The adaptive mesh iteration method is applied successfully to the examples of trajectory optimization of Maneuverable Reentry Research Vehicle, and the simulation experiment results show that the adaptive mesh iteration method has many advantages.
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Tyranowski, Tomasz M., and Mathieu Desbrun. "R-Adaptive Multisymplectic and Variational Integrators." Mathematics 7, no. 7 (July 18, 2019): 642. http://dx.doi.org/10.3390/math7070642.

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Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation but redistribute them over time to follow the areas where a higher mesh point density is required. There are a very limited number of moving mesh methods designed for solving field-theoretic partial differential equations, and the numerical analysis of the resulting schemes is challenging. In this paper, we present two ways to construct r-adaptive variational and multisymplectic integrators for (1+1)-dimensional Lagrangian field theories. The first method uses a variational discretization of the physical equations, and the mesh equations are then coupled in a way typical of the existing r-adaptive schemes. The second method treats the mesh points as pseudo-particles and incorporates their dynamics directly into the variational principle. A user-specified adaptation strategy is then enforced through Lagrange multipliers as a constraint on the dynamics of both the physical field and the mesh points. We discuss the advantages and limitations of our methods. Numerical results for the Sine–Gordon equation are also presented.
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Dissertations / Theses on the topic "Adaptive mesh method"

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Antepara, Zambrano Oscar Luis. "Adaptive mesh refinement method for CFD applications." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/664931.

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The main objective of this thesis is the development of an adaptive mesh refinement (AMR) algorithm for computational fluid dynamics simulations using hexahedral and tetrahedral meshes. This numerical methodology is applied in the context of large-eddy simulations (LES) of turbulent flows and direct numerical simulations (DNS) of interfacial flows, to bring new numerical research and physical insight. For the fluid dynamics simulations, the governing equations, the spatial discretization on unstructured grids and the numerical schemes for solving Navier-Stokes equations are presented. The equations follow a discretization by conservative finite-volume on collocated meshes. For the turbulent flows formulation, the spatial discretization preserves symmetry properties of the continuous differential operators and the time integration follows a self-adaptive strategy, which has been well tested on unstructured grids. Moreover, LES model consisting of a wall adapting local-eddy-viscosity within a variational multi-scale formulation is used for the applications showed in this thesis. For the two-phase flow formulation, a conservative level-set method is applied for capturing the interface between two fluids and is implemented with a variable density projection scheme to simulate incompressible two-phase flows on unstructured meshes. The AMR algorithm developed in this thesis is based on a quad/octree data structure and keeps a relation of 1:2 between levels of refinement. In the case of tetrahedral meshes, a geometrical criterion is followed to keep the quality metric of the mesh on a reasonable basis. The parallelization strategy consists mainly in the creation of mesh elements in each sub-domain and establishes a unique global identification number, to avoid duplicate elements. Load balance is assured at each AMR iteration to keep the parallel performance of the CFD code. Moreover, a mesh multiplication algorithm (MM) is reported to create large meshes, with different kind of mesh elements, but preserving the topology from a coarser original mesh. This thesis focuses on the study of turbulent flows and two-phase flows using an AMR framework. The cases studied for LES of turbulent flows applications are the flow around one and two separated square cylinders, and the flow around a simplified car model. In this context, a physics-based refinement criterion is developed, consisting of the residual velocity calculated from a multi-scale decomposition of the instantaneous velocity. This criteria ensures grid adaptation following the main vortical structures and giving enough mesh resolution on the zones of interest, i.e., flow separation, turbulent wakes, and vortex shedding. The cases studied for the two-phase flows are the DNS of 2D and 3D gravity-driven bubble, with a particular focus on the wobbling regime. A study of rising bubbles in the wobbling regime and the effect of dimensionless numbers on the dynamic behavior of the bubbles are presented. Moreover, the use of tetrahedral AMR is applied for the numerical simulation of gravity-driven bubbles in complex domains. On this topic, the methodology is validated on bubbles rising in cylindrical channels with different topology, where the study of these cases contributed to having new numerical research and physical insight in the development of a rising bubble with wall effects.
El objetivo principal de esta tesis es el desarrollo de un algoritmo adaptativo de refinamiento de malla (AMR) para simulaciones de dinámica de fluidos computacional utilizando mallas hexaédricas y tetraédricas. Esta metodología numérica se aplica en el contexto de simulaciones Large-eddie (LES) de flujos turbulentos y simulaciones numéricas directas (DNS) de flujos interfaciales, para traer nuevas investigaciones numéricas y entendimiento físicas. Para las simulaciones de dinámica de fluidos, se presentan las ecuaciones governantes, la discretización espacial en mallas no estructuradas y los esquemas numéricos para resolver las ecuaciones de Navier-Stokes. Las ecuaciones siguen una discretización conservativa por volumenes finitos en mallas colocadas. Para la formulación de flujos turbulentos, la discretización espacial preserva las propiedades de simetría de los operadores diferenciales continuos y la integración de tiempo sigue una estrategia autoadaptativa, que ha sido bien probada en mallas no estructuradas. Además, para las aplicaciones que se muestran en esta tesis, se utiliza el modelo LES que consiste en una viscosidad local que se adapta a la pared dentro de una formulación multiescala variable. Para la formulación de flujo de dos fases, se aplica un método de conjunto de niveles conservador para capturar la interfaz entre dos fluidos y se implementa con un esquema de proyección de densidad variable para simular flujos de dos fases incompresibles en mallas no estructuradas. El algoritmo AMR desarrollado en esta tesis se basa en una estructura de datos de quad / octree y mantiene una relación de 1: 2 entre los niveles de refinamiento. En el caso de las mallas tetraédricas, se sigue un criterio geométrico para mantener la calidad de la malla en una base razonable. La estrategia de paralelización consiste principalmente en la creación de elementos de malla en cada subdominio y establece un número de identificación global único, para evitar elementos duplicados. El equilibrio de carga está asegurado en cada iteración de AMR para mantener el rendimiento paralelo del código CFD. Además, se ha desarrollado un algoritmo de multiplicación de malla (MM) para crear mallas grandes, con diferentes tipos de elementos de malla, pero preservando la topología de una malla original más pequeña. Esta tesis se centra en el estudio de flujos turbulentos y flujos de dos fases utilizando un marco AMR. Los casos estudiados para aplicaciones de LES de flujos turbulentos son el flujo alrededor de uno y dos cilindros separados de sección cuadrada, y el flujo alrededor de un modelo de automóvil simplificado. En este contexto, se desarrolla un criterio de refinamiento basado en la física, que consiste en la velocidad residual calculada a partir de una descomposición de escala múltiple de la velocidad instantánea. Este criterio garantiza la adaptación de la malla siguiendo las estructuras vorticales principales y proporcionando una resolución de malla suficiente en las zonas de interés, es decir, separación de flujo, estelas turbulentas y desprendimiento de vórtices. Los casos estudiados para los flujos de dos fases son el DNS de la burbuja impulsada por la gravedad en 2D y 3D, con un enfoque particular en el régimen de oscilación. Además, el uso de AMR tetraédrico se aplica para la simulación numérica de burbujas impulsadas por la gravedad en dominios complejos. En este tema, la metodología se valida en burbujas que ascienden en canales cilíndricos con topología diferente, donde el estudio de estos casos contribuyó a tener una nueva investigación numérica y una visión física en el desarrollo de una burbuja con efectos de pared.
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Offermans, Nicolas. "Towards adaptive mesh refinement in Nek5000." Licentiate thesis, KTH, Mekanik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-217501.

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The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. While such techniques have been known for a long time, most simulations do not make use of them because of the lack of a robust implementation. In this work, we present recent progresses that have been made to develop adaptive mesh refinement features in Nek5000, a code based on the spectral element method. These developments are driven by the algorithmic challenges posed by future exascale supercomputers. First, we perform the study of the strong scaling of Nek5000 on three petascale machines in order to assess the scalability of the code and identify the current bottlenecks. It is found that strong scaling limit ranges between 5, 000 and 220, 000 degrees of freedom per core depending on the machine and the case. The need for synchronized and low latency communication for efficient computational fluid dynamics simulation is also confirmed. Additionally, we present how Hypre, a library for linear algebra, is used to develop a new and efficient code for performing the setup step required prior to the use of an algebraic multigrid solver for preconditioning the pressure equation in Nek5000. Finally, the main objective of this work is to develop new methods for estimating the error on a numerical solution of the Navier–Stokes equations via the resolution of an adjoint problem. These new estimators are compared to existing ones, which are based on the decay of the spectral coefficients. Then, the estimators are combined with newly implemented capabilities in Nek5000 for automatic grid refinement and adaptive mesh adaptation is carried out. The applications considered so far are steady and two-dimensional, namely the lid-driven cavity at Re = 7, 500 and the flow past a cylinder at Re = 40. The use of adaptive mesh refinement techniques makes mesh generation easier and it is shown that a similar accuracy as with a static mesh can be reached with a significant reduction in the number of degrees of freedom.

QC 20171114

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Morgenstern, Philipp [Verfasser]. "Mesh Refinement Strategies for the Adaptive Isogeometric Method / Philipp Morgenstern." Bonn : Universitäts- und Landesbibliothek Bonn, 2017. http://d-nb.info/1140525948/34.

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Pinchuk, Amy Ruth. "Automatic adaptive finite element mesh generation and error estimation." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63269.

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Prinja, Gaurav Kant. "Adaptive solvers for elliptic and parabolic partial differential equations." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/adaptive-solvers-for-elliptic-and-parabolic-partial-differential-equations(f0894eb2-9e06-41ff-82fd-a7bde36c816c).html.

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In this thesis our primary interest is in developing adaptive solution methods for parabolic and elliptic partial differential equations. The convection-diffusion equation is used as a representative test problem. Investigations are made into adaptive temporal solvers implementing only a few changes to existing software. This includes a comparison of commercial code against some more academic releases. A novel way to select step sizes for an adaptive BDF2 code is introduced. A chapter is included introducing some functional analysis that is required to understand aspects of the finite element method and error estimation. Two error estimators are derived and proofs of their error bounds are covered. A new finite element package is written, implementing a rather interesting error estimator in one dimension to drive a rather standard refinement/coarsening type of adaptivity. This is compared to a commercially available partial differential equation solver and an investigation into the properties of the two inspires the development of a new method designed to very quickly and directly equidistribute the errors between elements. This new method is not really a refinement technique but doesn't quite fit the traditional description of a moving mesh either. We show that this method is far more effective at equidistribution of errors than a simple moving mesh method and the original simple adaptive method. A simple extension of the new method is proposed that would be a mesh reconstruction method. Finally the new code is extended to solve steady-state problems in two dimensions. The mesh refinement method from one dimension does not offer a simple extension, so the error estimator is used to supply an impression of the local topology of the error on each element. This in turn allows us to develop a new anisotropic refinement algorithm, which is more in tune with the nature of the error on the parent element. Whilst the benefits observed in one dimension are not directly transferred into the two-dimensional case, the obtained meshes seem to better capture the topology of the solution.
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Sombra, Tiago GuimarÃes. "An adaptive parametric surface mesh generation parallel method guided by curvatures." Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=16628.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
This work describes a technique for generating parametric surfaces meshes using parallel computing, with distributed memory processors. The input for the algorithm is a set of parametric patches that model the surface of a given object. A structure for spatial partitioning is proposed to decompose the domain in as many subdomains as processes in the parallel system. Each subdomain consists of a set of patches and the division of its load is guided following an estimate. This decomposition attempts to balance the amount of work in all the subdomains. The amount of work, known as load, of any mesh generator is usually given as a function of its output size, i.e., the size of the generated mesh. Therefore, a technique to estimate the size of this mesh, the total load of the domain, is needed beforehand. This work makes use of an analytical average curvature calculated for each patch, which in turn is input data to estimate this load and the decomposition is made from this analytical mean curvature. Once the domain is decomposed, each process generates the mesh on that subdomain or set of patches by a quad tree technique for inner regions, advancing front technique for border regions and is finally applied an improvement to mesh generated. This technique presented good speed-up results, keeping the quality of the mesh comparable to the quality of the serially generated mesh.
Este trabalho descreve uma tÃcnica para gerar malhas de superfÃcies paramÃtricas utilizando computaÃÃo paralela, com processadores de memÃria compartilhada. A entrada para o algoritmo à um conjunto de patches paramÃtricos que modela a superfÃcie de um determinado objeto. Uma estrutura de partiÃÃo espacial à proposta para decompor o domÃnio em tantos subdomÃnios quantos forem os processos no sistema paralelo. Cada subdomÃnio à formado por um conjunto de patches e a divisÃo de sua carga à guiada seguindo uma estimativa de carga. Esta decomposiÃÃo tenta equilibrar a quantidade de trabalho em todos os subdomÃnios. A quantidade de trabalho, conhecida como carga, de qualquer gerador de malha à geralmente dada em funÃÃo do tamanho da saÃda do algoritmo, ou seja, do tamanho da malha gerada. Assim, faz-se necessÃria uma tÃcnica para estimar previamente o tamanho dessa malha, que à a carga total do domÃnio. Este trabalho utiliza-se de um cÃlculo de curvatura analÃtica mÃdia para cada patch, que por sua vez, à dado de entrada para estimar esta carga e a decomposiÃÃo à feita a partir dessa curvatura analÃtica mÃdia. Uma vez decomposto o domÃnio, cada processo gera a malha em seu subdomÃnio ou conjunto de patches pela tÃcnica de quadtree para regiÃes internas, avanÃo de fronteira para regiÃes de fronteira e por fim à aplicado um melhoramento na malha gerada. Esta tÃcnica apresentou bons resultados de speed-up, mantendo a qualidade da malha comparÃvel à qualidade da malha gerada de forma sequencial.
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Ferreira, Vitor Maciel Vilela. "A hybrid les / lagrangian fdf method on adaptive, block-structured mesh." Universidade Federal de Uberlândia, 2015. https://repositorio.ufu.br/handle/123456789/14982.

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Fundação de Amparo a Pesquisa do Estado de Minas Gerais
Esta dissertação é parte de um amplo projeto de pesquisa, que visa ao desenvolvimento de uma plataforma computacional de dinâmica dos fluidos (CFD) capaz de simular a física de escoamentos que envolvem mistura de várias espécies químicas, com reação e combustão, utilizando um método hibrido Simulação de Grandes Escalas (LES) / Função Densidade Filtrada (FDF) Lagrangiana em malha adaptativa, bloco-estruturada. Uma vez que escoamentos com mistura proporcionam fenômenos que podem ser correlacionados com a combustão em escoamentos turbulentos, uma visão global da fenomenologia de mistura foi apresentada e escoamentos fechados, laminar e turbulento, que envolvem mistura de duas espécies químicas inicialmente segregadas foram simulados utilizando o código de desenvolvimento interno AMR3D e o código recentemente desenvolvido FDF Lagrangiana de composição. A primeira etapa deste trabalho consistiu na criação de um modelo computacional de partículas estocásticas em ambiente de processamento distribuído. Isto foi alcançado com a construção de um mapa Lagrangiano paralelo, que pode gerenciar diferentes tipos de elementos lagrangianos, incluindo partículas estocásticas, particulados, sensores e nós computacionais intrínsecos dos métodos Fronteira Imersa e Acompanhamento de Interface. O mapa conecta informações Lagrangianas com a plataforma Euleriana do código AMR3D, no qual equações de trans- porte são resolvidas. O método FDF Lagrangiana de composição realiza cálculos algébricos sobre partículas estocásticas e provê campos de composição estatisticamente equivalentes aos obtidos quando se utiliza o método de Diferenças Finitas para solução de equações diferenciais parciais; a técnica de Monte Carlo foi utilizada para resolver um sistema derivado de equações diferenciais estocásticas (SDE). Os resultados concordaram com os benchmarks, que são simulações baseadas em plataforma de Diferenças Finitas para solução de uma equação de transporte de composição filtrada.
This master thesis is part of a wide research project, which aims at developing a com- putational fluid dynamics (CFD) framework able to simulate the physics of multiple-species mixing flows, with chemical reaction and combustion, using a hybrid Large Eddy Simulation (LES) / Lagrangian Filtered Density Function (FDF) method on adaptive, block-structured mesh. Since mixing flows provide phenomena that may be correlated with combustion in turbulent flows, we expose an overview of mixing phenomenology and simulated enclosed, ini- tially segregated two-species mixing flows, at laminar and turbulent states, using the in-house built AMR3D and the developed Lagrangian composition FDF codes. The first step towards this objective consisted of building a computational model of notional particles transport on distributed processing environment. We achieved it constructing a parallel Lagrangian map, which can hold different types of Lagrangian elements, including notional particles, particu- lates, sensors and computational nodes intrinsic to Immersed Boundary and Front Tracking methods. The map connects Lagrangian information with the Eulerian framework of the AMR3D code, in which transport equations are solved. The Lagrangian composition FDF method performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by Finite Differences numerical solution of partially differential equations (PDE); we applied the Monte Carlo technique to solve a derived system of stochastic differential equations (SDE). The results agreed with the benchmarks, which are simulations based on Finite Differences framework to solve a filtered composition transport equation.
Mestre em Engenharia Mecânica
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Maddison, James R. "Adaptive mesh modelling of the thermally driven annulus." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:4b95031b-4517-4aaf-9bb2-4d6d4a145499.

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Numerical simulations of atmospheric and oceanic flows are fundamentally limited by a lack of model resolution. This thesis describes the application of unstructured mesh finite element methods to geophysical fluid dynamics simulations. These methods permit the mesh resolution to be concentrated in regions of relatively increased dynamical importance. Dynamic mesh adaptivity can further be used to maintain an optimised mesh even as the flow develops. Hence unstructured dynamic mesh adaptive methods have the potential to enable efficient simulations of high Reynolds number flows in complex geometries. In this thesis, the thermally driven rotating annulus is used to test these numerical methods. This system is a classic laboratory scale analogue for large scale geophysical flows. The thermally driven rotating annulus has a long history of experimental and numerical research, and hence it is ideally suited for the validation of new numerical methods. For geophysical systems there is a leading order balance between the Coriolis and buoyancy accelerations and the pressure gradient acceleration: geostrophic and hydrostatic balance. It is essential that any numerical model for these systems is able to represent these balances accurately. In this thesis a balanced pressure decomposition method is described, whereby the pressure is decomposed into a ``balanced'' component associated with the Coriolis and buoyancy accelerations, and a ``residual'' component associated with other forcings and that enforces incompressibility. It is demonstrated that this method can be used to enable a more accurate representation of geostrophic and hydrostatic balance in finite element modelling. Furthermore, when applying dynamic mesh adaptivity, there is a further potential for imbalance injection by the mesh optimisation procedure. This issue is tested in the context of shallow-water ocean modelling. For the linearised system on an $f$-plane, and with a steady balance permitting numerical discretisation, an interpolant is formulated that guarantees that a steady and balanced state remains steady and in balance after interpolation onto an arbitrary target mesh. The application of unstructured dynamic mesh adaptive methods to the thermally driven rotating annulus is presented. Fixed structured mesh finite element simulations are conducted, and compared against a finite difference model and against experiment. Further dynamic mesh adaptive simulations are then conducted, and compared against the structured mesh simulations. These tests are used to identify weaknesses in the application of dynamic mesh adaptivity to geophysical systems. The simulations are extended to a more challenging system: the thermally driven rotating annulus at high Taylor number and with sloping base and lid topography. Analysis of the high Taylor number simulations reveals a direct energy transfer from the eddies to the mean flow, confirming the results of previous experimental work.
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McDill, Jennifer Moyra Jeane Carleton University Dissertation Engineering Mechanical. "An adaptive mesh-management algorithm for three-dimensional finite element analysis." Ottawa, 1988.

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Kunert, Gerd. "Anisotropic mesh construction and error estimation in the finite element method." Universitätsbibliothek Chemnitz, 2000. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200000033.

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In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh. However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators. Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error. The focus of this paper is on error estimation on anisotropic meshes. It is known that such error estimation is reliable and efficient only if the anisotropic mesh is aligned with the anisotropic solution. The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution. The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form. Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.
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Books on the topic "Adaptive mesh method"

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Mavriplis, Catherine. Adaptive mesh strategies for the spectral element method. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1992.

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Russell, R. D. (Robert D.), 1945-, ed. Adaptive moving mesh methods. New York, NY: Springer, 2011.

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Huang, Weizhang, and Robert D. Russell. Adaptive Moving Mesh Methods. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-7916-2.

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Baden, Scott B. Structured Adaptive Mesh Refinement (SAMR) Grid Methods. New York, NY: Springer New York, 2000.

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Baden, Scott B., Nikos P. Chrisochoides, Dennis B. Gannon, and Michael L. Norman, eds. Structured Adaptive Mesh Refinement (SAMR) Grid Methods. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1252-2.

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Zumbusch, Gerhard. Parallel Multilevel Methods: Adaptive Mesh Refinement and Loadbalancing. Wiesbaden: Vieweg+Teubner Verlag, 2003.

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Tomasz, Plewa, Linde Timur Jaan, and Weirs Vincent Gregory 1969-, eds. Adaptive mesh refinement, theory and applications: Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, Sept. 3-5, 2003. Berlin: Springer, 2005.

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Babuska, Ivo, William D. Henshaw, Joseph E. Oliger, Joseph E. Flaherty, John E. Hopcroft, and Tayfun Tezduyar, eds. Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4248-2.

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Adaptive mesh stategies for the spectral element method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1992.

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Center, Langley Research, ed. Adaptive mesh stategies for the spectral element method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1992.

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Book chapters on the topic "Adaptive mesh method"

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Appella, Simone, Chris Budd, and Tristan Pryer. "An Adaptive Conservative Moving Mesh Method." In Mesh Generation and Adaptation, 277–99. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-92540-6_13.

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Zheng, Guoxian, Jieqing Feng, Xiaogang Jin, and Qunsheng Peng. "Adaptive Level Set Method for Mesh Evolution." In Technologies for E-Learning and Digital Entertainment, 1094–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11736639_137.

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Paszyński, Maciej, Rafał Grzeszczuk, David Pardo, and Leszek Demkowicz. "Deep Learning Driven Self-adaptive Hp Finite Element Method." In Computational Science – ICCS 2021, 114–21. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77961-0_11.

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AbstractThe finite element method (FEM) is a popular tool for solving engineering problems governed by Partial Differential Equations (PDEs). The accuracy of the numerical solution depends on the quality of the computational mesh. We consider the self-adaptive hp-FEM, which generates optimal mesh refinements and delivers exponential convergence of the numerical error with respect to the mesh size. Thus, it enables solving difficult engineering problems with the highest possible numerical accuracy. We replace the computationally expensive kernel of the refinement algorithm with a deep neural network in this work. The network learns how to optimally refine the elements and modify the orders of the polynomials. In this way, the deterministic algorithm is replaced by a neural network that selects similar quality refinements in a fraction of the time needed by the original algorithm.
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Oñate, E., and J. Castro. "Adaptive Mesh Refinement Techniques for Structural Problems." In The finite element method in the 1990’s, 133–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-10326-5_14.

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Stürzlinger, W. "Adaptive Mesh Refinement with Discontinuities for the Radiosity Method." In Photorealistic Rendering Techniques, 244–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-87825-1_18.

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Selman, A., and E. Hinton. "One Dimensional Transient Dynamic Analysis with Adaptive Mesh Refinement." In The finite element method in the 1990’s, 234–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-10326-5_24.

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de Siqueira, Daniel M. B., Markos O. Freitas, Joaquim B. Cavalcante-Neto, Creto A. Vidal, and Romildo J. da Silva. "An Adaptive Parametric Surface Mesh Generation Method Guided by Curvatures." In Proceedings of the 22nd International Meshing Roundtable, 425–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02335-9_24.

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Furuyama, Sho-ichi, and Teruo Matsuzawa. "A suitable domain decomposition for the adaptive mesh refinement method." In Lecture Notes in Computer Science, 363–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0094938.

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Kopyssov, Sergey, and Alexander Novikov. "Parallel Adaptive Mesh Refinement with Load Balancing for Finite Element Method." In Lecture Notes in Computer Science, 266–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44743-1_26.

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Fish, Jacob, and Vladimir Belsky. "Adaptive Multi-Grid Method for a Periodic Heterogeneous Medium in 1 − D." In Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, 243–65. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4248-2_13.

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Conference papers on the topic "Adaptive mesh method"

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Haber, E., E. Holtham, J. Granek, D. Marchant, D. Oldenburg, C. Schwarzbach, and R. Shekhtman. "An adaptive mesh method for electromagnetic inverse problems." In SEG Technical Program Expanded Abstracts 2012. Society of Exploration Geophysicists, 2012. http://dx.doi.org/10.1190/segam2012-0828.1.

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Avdeev, E. V., V. A. Fursov, and V. A. Ovchinnikov. "An adaptive mesh refinement in the finite volume method." In Information Technology and Nanotechnology-2015. Image Processing Systems Institute, Russian Academy of Sciences, Samara, Russia, Samara State Aerospace University, Samara, Russia, 2015. http://dx.doi.org/10.18287/1613-0073-2015-1490-234-241.

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Higgins, John C., Oliver M. Browne, and Christoph Brehm. "Adaptive Mesh Refinement for a Sharp Immersed Boundary Method." In AIAA Scitech 2021 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-0747.

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ARNEY, DAVID. "An adaptive method with mesh moving and mesh refinement for solving the Euler equations." In 1st National Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1988. http://dx.doi.org/10.2514/6.1988-3567.

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Liang, Ruquan, and Satoru Komori. "Computation of a Propagating Interface in Multiphase Flows Using an Adaptive Coupled Level Set Method." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39044.

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We present a numerical strategy for a propagating interface in multiphase flows using a level set method combined with a local mesh adaptative technique. We use the level set method to move the propagating interface in multiphase flows. We also use the local mesh adaptative technique to increase the grid resolution at regions near the propagating interface and additionally at the regions near points of high curvature with a minimum of additional expense. For illustration, we apply the adaptive coupled level set method to a collection of bubbles moving under passive transport. Good agreement has been obtained in the comparision of the numerical results for the collection of bubbles using an adaptative grid with those using a single grid. We also apply the adaptive coupled level set method to a droplet falling on a step where it is important to accurately model the effect of surface tension force and the motion of the free-surface, and the numerical results agree very closely with available data.
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Zhou, Mingdong, Michael Yu Wang, and Li Li. "Structural Optimization Using Adaptive Level Set Method." In ASME/ISCIE 2012 International Symposium on Flexible Automation. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/isfa2012-7110.

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A novel structural optimization method that utilizes both explicit and implicit geometric representations is presented. In this method, an octree grid is adopted to accommodate the free structural interface of an implicit level set model and a corresponding 2-manifold triangle mesh model. Within each iteration of optimization, the interface is evolved implicitly by using a semi-Lagrange level set method, during which the signed distance field is evaluated directly and accurately from the current surface model other than interpolation. After that, another mesh model is extracted from the updated field and serves as the input of subsequent design process. This hybrid and adaptive representation scheme not only achieves “narrow band computation”, but also facilitates the structural analysis by using a geometry-aware mesh-free approach. Moreover, a feature preserving and topological errorless mesh simplification algorithm can also be leveraged to enhance the computational efficiency. A three dimensional benchmark example is provided to demonstrate the capability and potential of this method.
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"An Adaptive Mesh Refinement Method, Based on Gershgorin Circle Theorem." In 2015 The 5th International Workshop on Computer Science and Engineering-Information Processing and Control Engineering. WCSE, 2015. http://dx.doi.org/10.18178/wcse.2015.04.028.

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Adams, Michael D. "An improved content-adaptive mesh-generation method for image representation." In 2010 17th IEEE International Conference on Image Processing (ICIP 2010). IEEE, 2010. http://dx.doi.org/10.1109/icip.2010.5650466.

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Liu, Dengxue, Youliang Zhang, Shuling Huang, Xiuli Ding, Yuting Zhang, and Jun He. "An adaptive local mesh refinement strategy in numerical manifold method." In 2021 7th International Conference on Hydraulic and Civil Engineering & Smart Water Conservancy and Intelligent Disaster Reduction Forum (ICHCE & SWIDR). IEEE, 2021. http://dx.doi.org/10.1109/ichceswidr54323.2021.9656277.

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Ma, Yu, Yahui Wang, Kuilong Song, and Qian Sun. "Adaptive Mesh Refinement for Neutron Transfer With Lattice Boltzmann Scheme." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66093.

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This paper presents a novel lattice Boltzmann (LB) model for neutron transfer and a block-structured adaptive-mesh-refinement (SAMR) technique for proposed LB model. By discretizing the general Boltzmann equation, the LB model for neutron transfer is established and the corresponding parameters are obtained. The SAMR technique removes the requirement of tree-type data structure in traditional adaptive-mesh-refinement technique and adjusts the time step adaptively and identically in all blocks. By applying the node-type distribution function, the needs for rescaling the distribution functions is eliminated. To solve the discontinuities of scalar flux at fine-coarse blocks interface, a novel technique is presented which treats the inner boundary condition by streaming process of LB method. Simulation results show good accuracy and efficiency of the proposed neutron LB model with SAMR technique. This paper may provide a powerful technique for large engineering calculation.
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Reports on the topic "Adaptive mesh method"

1

Guzik, S., and X. Gao. Adaptive Mesh Refinement for Parallel in Time Methods. Office of Scientific and Technical Information (OSTI), May 2021. http://dx.doi.org/10.2172/1784604.

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Martín, A., L. Cirrottola, A. Froehly, R. Rossi, and C. Soriano. D2.2 First release of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.010.

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This document presents a description of the octree mesh-generation capabilities and of the parallel mesh adaptation kernel. As it is discussed in Section 1.3.2 of part B of the project proposal there are two parallel research lines aimed at developing scalable adaptive mesh refinement (AMR) algorithms and implementations. The first one is based on using octree-based mesh generation and adaptation for the whole simulation in combination with unfitted finite element methods (FEMs) and the use of algebraic constraints to deal with non-conformity of spaces. On the other hand the second strategy is based on the use of an initial octree mesh that, after make it conforming through the addition of templatebased tetrahedral refinements, is adapted anisotropically during the calculation. Regarding the first strategy the following items are included:
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Hindman, Richard G. Computational Fluid Dynamics Research On Dynamically Adaptive Mesh Methods For Transonic Flows. Fort Belvoir, VA: Defense Technical Information Center, November 1992. http://dx.doi.org/10.21236/ada264833.

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Saltzman, J. Patched based methods for adaptive mesh refinement solutions of partial differential equations. Office of Scientific and Technical Information (OSTI), September 1997. http://dx.doi.org/10.2172/584924.

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Ayoul-Guilmard, Q., S. Ganesh, M. Nuñez, R. Tosi, F. Nobile, R. Rossi, and C. Soriano. D5.3 Report on theoretical work to allow the use of MLMC with adaptive mesh refinement. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.002.

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This documents describes several studies undertaken to assess the applicability of MultiLevel Monte Carlo (MLMC) methods to problems of interest; namely in turbulent fluid flow over civil engineering structures. Several numerical experiments are presented wherein the convergence of quantities of interest with mesh parameters are studied at different Reynolds’ numbers and geometries. It was found that MLMC methods could be used successfully for low Reynolds’ number flows when combined with appropriate Adaptive Mesh Refinement (AMR) strategies. However, the hypotheses for optimal MLMC performance were found to not be satisfied at higher turbulent Reynolds’ numbers despite the use of AMR strategies. Recommendations are made for future research directions based on these studies. A tentative outline for an MLMC algorithm with adapted meshes is made, as well as recommendations for alternatives to MLMC methods for cases where the underlying assumptions for optimal MLMC performance are not satisfied.
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Keith, B., A. Apostolatos, A. Kodakkal, R. Rossi, R. Tosi, B. Wohlmuth, and C. Soriano. D2.3. Adjoint-based error estimation routines. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.022.

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This document presents a simple and ecient strategy for adaptive mesh renement (AMR) and a posteriori error estimation for the transient incompressible Navier{Stokes equations. This strategy is informed by the work of Prudhomme and Oden [22, 23] as well as modern goal-oriented methods such as [5]. The methods described in this document have been implemented in the Kratos Multiphysics software and uploaded to https://zenodo.org [27].1 This document includes: A review of the state-of-the-art in solution-oriented and goal-oriented AMR. The description of a 2D benchmark model problem of immediate relevance to the objectives of the ExaQUte project. The denition and a brief mathematical summary of the error estimator(s). The results obtained. A description of the API.
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Friedman, A., and W. Jr Miller. Modeling, mesh generation and adaptive numerical methods for partial differential equations: IMA summer program. Final report, April 1, 1993--March 31, 1994. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/71368.

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