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	Adaptive Mesh Refinement for Singular Current Sheets
		Since the singular structures like tubes and sheets are not space filling, adaptive mesh codes seem to be the right choice for studying these problems, as has been done by Pumir and Siggia[4,5].
		Finally, we conclude that adaptive mesh refinement is an ideal tool for studying singular structures and should be pursued further to study three dimensional problems as the finite time blow up in the incompressible Euler equations.
		Applying adaptive mesh refinement to the evolution of singular structures like current sheets in magnetohydrodynamics is motivated by the expected reduction of memory needed to resolve them.
	www.tp1.ruhr-uni-bochum.de /~grauer/amr2/amr.html (3032 words)

	COMPUTING SCIENCES: Zooming In On Data
		Using a technique called adaptive mesh refinement, researchers break their data down into cells, covering areas of particular interest with a mesh of thousands of segments, which then can be individually analyzed in detail.
		Adaptive mesh refinement allows scientists to focus on the details of the turbulent airflow around the wings without having to spend a large percentage of the available resources describing the relatively smooth flow in the much larger region of space away from the wings.
		Using this type of local mesh refinement, scientists are able to focus their existing computer power on a narrower part of the overall problem, so as to get the most information, given a limited amount of computer time and memory.
	www.lbl.gov /Science-Articles/Research-Review/Highlights/1998/v3/CS_zooming.html (976 words)

	ZIB: Visualization of Adaptive Mesh Refinement Data
		Adaptive Mesh Refinement (AMR) is a numerical multilevel technique, associated with a particular hierarchical data structure.
		Adaptive Mesh Refinement (AMR) schemes support both refinement in space that results in a time-dependent grid topology, as well as refinement in time that results in updates at higher rates for refined levels.
		AMR data results from simulations that are run on dedicated compute machines and is thus stored centrally, whereas the analysis of the data is performed on the local computers of the scientists.
	www.zib.de /visual/projects/amr/amrlong.en.html (1449 words)

	[No title]
		Refinement Using the carefully chosen error indicator, a mesh point that does not meet the error tolerance value can be flagged for further refinement at each iteration.
		Refinement of a mesh point is simply done by evenly dividing the point with a predefined constant, and updating the data structure appropriately.
		Adaptive mesh refinement is necessary to efficiently refine and compute the domain of interest.
	www.cs.uiuc.edu /homes/snir/PPP/patterns/AMR.doc (1844 words)

	New approach to software design for moving mesh method
		We must emphasize here that the grid generated by the moving mesh is totally non-uniform; thus legacy codes written for the uniform grid, if they want to employ the advantages of moving mesh, should be rewritten for a nonuniform grid.
		This is in contrast to the adaptive mesh refinement (AMR) method, in which the uniformity can be preserved during the refinement and hence the uniform legacy codes can be used without any difficulties.
		The regularization mesh function is only for a moving mesh to control the minimum spacing, which is most suitable for explicit moving mesh methods.
	www.cs.ucsb.edu /~shengtai/MM/html/node7.html (1090 words)

	A posteriori error estimation and adaptive mesh refinement for reliable finite element solutions
		It is, therefore, advantageous to vary the spatial mesh and time steps according to the behaviour of the solution, to ensure that the mesh and time step are sufficiently fine in those regions and stages of steep gradients and reasonably coarse in other regions and stages of less steep gradients.
		Adaptive improvement of FE solution aims at improving the quality of the solutions by enriching the approximation in some manner that will be enable one to achieve the ‘best’ solution for a given computational effort.
		In the case of static analysis, the adaptive strategy is concerned with refinement of stiffness representation while in free vibration and dynamic analysis, the adaptive strategy has to deal with refinement of stiffness as well as mass by modifying the FE mesh.
	www.ias.ac.in /currsci/nov25/articles21.htm (2839 words)

	LLNL Engineering Methods Development Group Projects Adaptivity
		Previous academic research in the field of adaptive mesh refinement has produced a voluminous literature focused on error estimators and demonstration problems; relatively little progress has been made on producing efficient implementations suitable for large-scale problem solving on state-of-the-art computer systems.
		The refinements were performed using a random selection of elements and random refinement directions.
		Localized mesh refinement near stress singularities and thermal point fluxes is evident, demonstrating the viability of the AMR scheme for a coupled mechanics problem.
	www-eng.llnl.gov /mdg/mdg_projects_adaptivity.html (261 words)

	Adaptive Mesh Refinement in Nonlinear Finite Element Analysis of Shell Structures - Okstad, Mathisen (ResearchIndex)
		Adaptive Mesh Refinement in Nonlinear Finite Element Analysis of Shell Structures (1993)
		Abstract: this paper is to present an adaptive strategy for general purpose geometrically nonlinear FE shell analysis.
		On h--Adaptive Mesh Refinement in Nonlinear Finite Element Analyses of Shell Structures.
	citeseer.ist.psu.edu /okstad93adaptive.html (439 words)

	Adaptive Mesh Refinement
		The adaptive mesh refinement (AMR) algorithm is used to numerically solve partial differential equations.
		The algorithm adaptively creates and destroys finer grids depending on where in the domain extra resolution is needed, according to user-defined error estimation criteria.
		AMR allows much larger problem sizes to be solved than static meshes, since only parts of the domain need to be resolved finely.
	www.cs.berkeley.edu /~ejr/GSI/cs267-s04/homework-0/results/kamil/hw0.html (607 words)

	Adaptive Finite Element Methods (Site not responding. Last check: 2007-10-10)
		The problems are to avoid increasing degeneration of the simplices during repeated refinement and the 'matching' between the coarse and fine zones.
		An adaptive finite-element-strategy for the three-dimensional time-dependent Navier-Stokes equations.
		Adaptive mesh refinement for single and two phase flow problems in porous media.
	www.mathematik.uni-freiburg.de /IAM/Research/projectskr/adaptivitaet (1334 words)

	Adaptive mesh refinement - Wikipedia, the free encyclopedia
		In numerical analysis, Adaptive mesh refinement is a method of adaptive meshing.
		As the calculation progresses, individual grid cells are tagged for refinement, using a criterion that can either be user-supplied (for example mass per cell remains constant, hence higher density regions are more highly resolved) or based on Richardson extrapolation.
		After refinement, individual grid patches on a single fixed level of refinement are passed off to an integrator which advances those cells in time.
	en.wikipedia.org /wiki/Adaptive_mesh_refinement (560 words)

	PPL: Adaptive Mesh Refinement Framework (AMR)
		Adaptive Mesh Refinement, AMR, is a technique used to solve partial differential equations and such applications efficiently for structured grids.
		Solutions without AMR are less efficient because all the mesh is evenly refined, rather than refining only the most interesting parts as in AMR, thus wasting a lot of computer resources in the process.
		The nature of the problems for which AMR is used is such that the mesh is required to adapt at the runtime in the areas where most of the small scale phenomenon occur.
	charm.cs.uiuc.edu /research/amr (361 words)

	Adaptive Blocks: A High Performance Data Structure
		Using this block data structure to support adaptive mesh refinement (AMR), we were able to sustain 17 GFLOPS in ideal magnetohydrodynamic (MHD) simulations of the solar wind emanating from the base of the solar corona, using a 512 processor Cray T3D at NASA Goddard.
		Note that the adaptive blocks for a decomposition of a two-dimensional domain are similar to the leaves of a quadtree decomposition, and in general the adaptive block decomposition of a d-dimensional domain are similar to the leaves of a d-dimensional generalized tree.
		Adaptive blocks amortize the costs of neighbor pointers (both time and space) over entire arrays, and their ghost cell to computational cell ratio is far superior to other data structures.
	www.eecs.umich.edu /~qstout/pap/SC97.html (2620 words)

	Adaptive Mesh Refinement (AdaptiveMeshRefinement)
		Its deformed mesh is shown in Figure "SPR Example" (b).
		The refined mesh is presented in Figure 6.59.
		The refined mesh captured the stress variation at the corner much better than the original mesh did, clearly showing the improvement in accuracy.
	www.ctcms.nist.gov /~langer/oof2man/RegisteredClass-AdaptiveMeshRefinement.html (327 words)

	Rolf Walder: AMRCART code
		We show the time-dependent construction of a hierarchical mesh with a total of 5 levels at the example of a 2D simulation of the interaction of a molecular, magnetic jet from a proto-star with the magnetic protostellar cloud.
		In the final constellation (29378 y), the fine mesh is covering the turbulent zone of the unstable jet as well as the bow shock formed where the jet interacts with the protostellar cloud (Fig.
		The mesh is Cartesian with a cell size of 1.25 x 10^(16) cm cubed on the coarsest level.
	www.astro.phys.ethz.ch /staff/walder/private/codes/A-MAZE/AMRCART/AMRCART.html (1128 words)

	CSE03 Short Course - Adaptive Methods for PDE-solution
		The use of adaptive methods is commonly recognized as a critical aspect in the numerical solution of large-scale PDE-based.
		Because this course is intended to be a survey of different adaptive techniques, we have invited three lecturers with expertise in different major categories of adaptivity.
		He is widely recognized for his contributions in high-resolution finite difference methods, adaptive mesh refinement, volume-of-fluid methods for fronts and irregular geometries, and multidimensional shock dynamics.
	www.siam.org /meetings/cs03/AMpdeshortcourse.htm (713 words)

	3.4 Using dynamic adaptive mesh refinement
		Instead we are going to use dynamic adaptive mesh refinement, where the quadtree structure of the discretisation is used to adaptively follow the small structures of the flow, thus concentrating the computational effort on the area where it is most needed.
		We see that the mesh is very refined around the solid and around the two vortices developing at the trailing edge and very coarse (one cell per box only) on the downstream part of the domain.
		The advantage of adaptive mesh refinement is even more obvious in situations where it is necessary to use very large domains to avoid any contamination of the solution by the boundary conditions.
	gfs.sourceforge.net /tutorial/tutorial/node13.html (821 words)

	IMA Special Workshop: Structured Adaptive Mesh Refinement Grid Methods, March 12-13, 1997
		Structured Adaptive Mesh Refinement (SAMR) methods are playing an increasing role in tackling difficult scientific applications, including compressible flows, cosmology, and electronic structures arising in local spin-density calculations.
		Adaptive Mesh Refinement for Sharp Fronts and Irregular Geometries
		The workshop papers will appear in conference proceedings to be published as a volume in the IMA Volumes in Mathematics and its Applications series (Springer-Verlag).
	www.ima.umn.edu /hpc/winter/hpc.wspec.html (304 words)

	CDIC - Abstract title1
		Adaptive mesh refinement (AMR) computations are complicated by their dynamic nature.
		AMR++ uses the Overture framework for the independent handling of the overlapping grid geometry.
		In the solution of complex problems in complex geometries reliably estimating regions of the computational domain where refinement is required during the AMR solution process is in itself an area of research.
	www.bnl.gov /csc/seminars/abstracts/a_philip.htm (432 words)

	The Finite Element Method (Partial Differential Equation Toolbox) (Site not responding. Last check: 2007-10-10)
		Then it is more economical to refine the mesh selectively, i.e., only where it is needed.
		The adaptive refinement generates a sequence of solutions on successively finer meshes, at each stage selecting and refining those elements that are judged to contribute most to the error.
		The three components of the algorithm are the error indicator function, which computes an estimate of the element error contribution, the mesh refiner, which selects and subdivides elements, and the termination criteria.
	www-rohan.sdsu.edu /doc/matlab/toolbox/pde/4fem8.html (275 words)

	Hugues Hoppe's home page
		The irregular meshes reduce the number of triangles for a given level of approximation accuracy, and allow large regions of the terrain to be pre-simplified.
		Indeed, the sequence of refinement transformations encodes both the geometry and the topology of the model in a unified multiresolution framework.
		We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).
	research.microsoft.com /~hoppe (10139 words)

	Lecture 8, 1/31/02: Structured Adaptive Mesh Refinement
		Refinement structures may not generally be represented as a tree, e.g.
		Refinements must be properly nested, that is, there must be some padding around each refinements such that it doesn't abut the edge of the coarse mesh.
		Adaptive mesh refinement structures tend to be fragmented to avoid unnecessary over-refinement.
	www-cse.ucsd.edu /~baden/classes/cse262_wi02/lectures/Lec08/Lec08.html (3125 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		Adaptive mesh refinement is a technique of numerical analysis which may be used to deal effectively with these difficulties.
		In order to use the same library of adaptive mesh refinement routines to deal with a wide variety of hyperbolic conservation laws, John Trangenstein has developed such a library in the object oriented language C++.
		Whether one uses adaptive mesh refinement or not, a great deal of computational power is often necessary to resolve problems in the aforementioned fields, particulary when the number of space dimensions is three.
	www.math.duke.edu /faculty/bertozzi/AMRpar.html (215 words)

	Adaptive Mesh Refinement for Poisson's Equation
		However, there are often also large portions of the domain where high levels of refinement are not needed; using a highly refined mesh in these regions represents a waste of computational effort.
		By locally refining the mesh only where needed, Adaptive Mesh Refinement (AMR) allows concentration of effort where it is needed, allowing better resolution of the problem.
		If adaptive grid generation is desired, the code can locate places where the error in a coarse solution is high based on either Richardson extrapolation or on a user supplied criterion.
	seesar.lbl.gov /anag/staff/martin/AMRPoisson.html (637 words)

	PARS -- Adaptive Mesh Refinement
		In order to efficiently solve these problems, adaptive mesh strategies are used to concentrate grid points in regions where the error contribution is large.
		To refine triangles in parallel, we use independent sets of elements as determined by the dual graph of the mesh.
		The adaptive mesh generated by the strategy described above must be repartitioned after each modification to achieve good load balancing on parallel computers.
	www.mcs.anl.gov /sumaa3d/PARS/refinement.html (356 words)

	PARALLEL ADAPTIVE MESH REFINEMENT
		Adaptive computations accelerate the convergence process by dynamically adding and removing local refinements in the lattice as needed.
		Adaptive computations may converge more quickly with fewer lattice points but the cost on parallel machinery is possible nonuniformity in both computation and communication stemming from interpolation and data management.
		To make adaptive methods useful on parallel machines, this group has developed an algorithm using fixed- sized patches and nonstandard data layouts.
	www.crpc.rice.edu /newsletters/jan94/wip.mesh.html (312 words)

	CT Project: Adaptive Mesh Refinement
		Adaptive mesh refinement (AMR) automatically produces smaller grids within the overall grid to follow structures as they form in a simulation.
		Computational Technologies Project inhouse computational scientists are developing two AMR software packages for use with a variety of Earth and space sciences applications on scalable parallel architectures.
		One package will provide AMR capability for structured grids, the other for unstructured grids.
	ct.gsfc.nasa.gov /amr.html (77 words)

	Berkeley Astrophysical Fluid Dynamics Group: Adaptive Mesh Refinement
		Central to any direct computational method is the manner in which it discretizes the continuous domain of interest into a grid of many individual elements.
		The image to the left shows the grid structure of an AMR calculation of a shock impacting an inclined slope.
		This lets us solve problems that are completely intractable on a uniform grid; for example,we have used the code to model the filamentary nature of isothermal collapse down to an effective resolution of 131,072 cells per initial cloud radius, corresponding to a resolution of 10^15 cells on a uniform grid.
	astro.berkeley.edu /~cmckee/bafd/amr.html (463 words)

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