A new adaptive mesh refinement data structure with an application. Adaptive mesh refinement solution techniques for the multigroup s n transport equation using a higherorder discontinuous finite element method a dissertation by yaqi wang submitted to the o. We consider a finiteelement formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. Despite these interesting properties, from the fixed mesh ale point of view the adaptive refinement algorithm acts as a black box that allows to modify the mesh during runtime, with two particularities. Soft tissue and organ modeling is the most critical function of any virtual surgical system. This frame work, using libraries from the sumaa3d project, allows a user to build a parallel finiteelement. About this book advanced numerical simulations that use adaptive mesh refinement amr methods have now become routine in engineering and science. Ale adaptive meshing and remapping in abaqusexplicit. Pdf we present scalable algorithms for parallel adaptive mesh refinement and coarsening amr, partitioning, and 2.
The methods for describing damage evolution can be mainly classified into two. Automatic thresholding based on a distribution function. Time adaptive mesh refinement of a model of a rising bubble solved with a twophase flow model. Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Adaptive mesh refinement amr has been recognized as one of the most. Parallel algorithms for adaptive mesh refinement siam. Jim ruppert, a delaunay refinement algorithm for quality 2dimensional mesh generation, journal of algorithms 183. Berger courant institute, new york university, neh york, new york 10012 and joseph iger computer science department, stanford university, stanford, california 94305 received march 8, 1983, revised august 24, 1983 an adaptive method based on the idea of multiple.
Adaptive mesh refinement using wavepropagation algorithms. Simple algorithm for adaptive refinement of threedimensional finite element tetrahedral meshes. Oliger 1 that has been proposed by marsha berger and phil collela in 2. Adaptive mesh refinement in 2d an efficient implementation. Adaptive meshing technique applied to an orthopaedic. This allows its use on a variety of new problems, including hyperbolic equations not in conservation form, problems with source terms or capacity functions. We present a framework for the parallel implementation of such complex algorithms. Adaptive mesh refinement amr algorithms the basic adaptive refinment strategy used in amrclaw description and detailed contents is to refine on logically rectangular patches. An adaptive fixedmesh ale method for free surface flows. Parallel adaptive mesh refinement for highorder finite. The finite element mesh is finer around the phase boundary. A data structure based on adaptive mesh refinement for efficient storage and visualization of volumetric datasets.
This special algorithm is designed especially as a general framework for the adaptive solution of hyperbolic partial differential equations. As the image shows, the algorithm uses high resolution grids only. The first one is an algorithm for increasingdecreasing the richness of the interpolation in. Using adaptive meshing for local solution improvement. Blockstructured adaptive mesh refinement algorithms for. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Abstractthis paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in matlab. Adaptive and quality quadrilateralhexahedral meshing from. The first is the subdivision of the target triangles and the second is the refinement propagation to assure mesh conformity. Adaptive mesh refinement an overview sciencedirect topics.
Automatic adaptive grid refinement for the euler equations. First, mesh refinement criterion needs to be provided so that the algorithm can decide which areas of the mesh need to be refined. Visualization tools for adaptive mesh refinement data. In this paper we present a novel algorithm for adaptive mesh refinement in computational physics meshes in a distributed memory parallel setting. We assume the existence of an oracle that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Over recent years, adaptive mesh refinement amr algorithms which dynamically match the local resolution of the computational grid to the numerical solution.
Adaptive mesh refinement and cutcell algorithms for dsmc. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most. However, the refinement of the pressure element mesh also implies an increase. Dec 27, 20 the adaptive mesh refinement algorithm will globally adjust the mesh to better resolve the local stresses, and these stresses depend on the solution everywhere else in the model. Specifically, algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail. Adaptive mesh refinement amr and cutcell algorithms were developed for a 3level cartesian mesh based direct simulation monte carlo dsmc implementation. Furthermore, we have implemented the adaptive mesh refine. Usually the cells partition the geometric input domain. Several researchers are devoted to the development of adaptive refinement strategies for effective finite element analyses. We use the phrase autonomous meshing to encompass converges entire set of robust and innovative gridrelated capabilities. Cunningham 1, adam frank 1, peggy varniere 1,2, sorin mitran 3, and thomas w.
Block structured adaptive mesh refinement for simulations on. We can also see that using manual mesh refinement to predict the peak stress may be very difficult, because we usually cannot easily determine what other parts of the. The local refinement of triangle meshes involves two main tasks. The proposed algorithm employs both the finite element method and the finite difference method to integrate the equations of motion of a linear elastic material with simple isotropic microcracking. We present scalable algorithms for parallel adaptive mesh refinement and coarsening amr, partitioning, and 2. Department of mechanical engineering, seoul national university of science and technology, 232 gongneung. Fully threaded tree algorithms for adaptive mesh fluid dynamics simulations. Colella, local adaptive mesh refinement for shock hydrodynamics, j. Scalable algorithms for parallel adaptive mesh refinement. The basic adaptive refinment strategy used in amrclaw description and detailed contents is to refine on logically rectangular patches. Numerical results for a pillbox cavity and a discloaded structure are shown. Parallelization of structured, hierarchical adaptive mesh.
Adaptive mesh refinement and adaptive time integration for. Adaptivity in finite element computations requires three main ingredients. Moreover, all stages of the amr algorithm only use distributed. Frequently, important finescale features in phase space, which could substantially benefit from higher resolution, only occupy limited regions in phase space. When modeling in the frequency domain, both the range of excitation frequencies and the material properties are known ahead of time. Opus fau blockstructured adaptive mesh refinement for. An adaptive hrefinement algorithm for local damage models. Oliger, adaptive mesh refinement for hyperbolic partial differential equations, j.
Adaptive mesh refinement ieee conferences, publications. Advanced numerical simulations that use adaptive mesh refinement amr methods have now become routine in engineering and science. Ale adaptive meshing consists of two fundamental tasks. Adaptive mesh refinement strategy for the semianalytical solution. This study proposes a softnessbased adaptive mesh refine. The simple and efficient amr algorithm adapts the cell size to the local mean free path of the flow field. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. Adaptive mesh refinement fem for damage evolution of. The success of the adaptive meshing technique depends on the choice of the methods used for each of these tasks. Blockstructured adaptive mesh refinement, is a natural fit for certain vlasovmaxwell problems. In addition, modifications to the basic amr algorithm that enable the use of highorder spatial and temporal discretizations are discussed. Feng developed an adaptive mesh refinement fem algorithm to demonstrate the damage evolution of brittle materials 9. Blockstructured adaptive mesh refinement algorithms for vlasov.
Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Evolving concerns for parallel algorithms, a talk about the evolution of goalsconcerns of parallel models and algorithms, including cellular automata, mesh connected computers, reconfigurable meshes, and powerconstrained algorithms for mesh connected computers. Some rectangular portions of this grid are covered by level 2 grids refined by some refinement factor r in each direction anisotropic refinement is now allowed. Mar 14, 2015 in this video, i make a transition from modeling and simulation technology to the adaptive mesh refinement techniques. The new refinement algorithm satisfies important topological mesh properties, e. Algorithms and data structures for massively parallel. An advanced data structure for large medical datasets. Adaptive mesh refinement theory and applications springerlink. Furthermore, all local topological modifications of the triangle mesh are based on stellar operators implemented on.
Amr is applied to problems which have features developing on di. The book presents a collection of papers by experts in the field of amr who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing. When solutions are calculated numerically, they are often limited to predetermined quantified grids as in the cartesian plane which constitute the computational. This objective is recommended only for adaptive mesh domains with. Structured adaptive mesh refinement samr grid methods the. Thanks for contributing an answer to computational science stack exchange. Fourtriangles adaptive algorithms for rtin terrain meshes. The specific techniques presented in this book are characterized by stability and robustness. Specifically, converge automatically creates the mesh at runtime, dynamically adapts the mesh throughout the simulation, and invokes adaptive mesh refinement to maximize both accuracy and computational efficiency. Quentin stout publications electrical engineering and. We say that a mesh is conforming if any adjacent elements share an entire edge or a common vertex. It is an overview of amr that makes beguinner familiar with new terms and. Structured adaptive mesh refinement samr grid methods.
Jan 18, 2018 this work presents a new efficient arraybased algorithm for adaptive mesh refinement capable of interactively generating millions of triangles. An adaptive mesh refinement strategy is proposed for local damage models that often arise from internal state variable based continuum damage models. Pdf adjointbased adaptive mesh refinement for complex. The aim is to achieve the best mesh possible within certain constraints for each load level. The main algorithm of the approach to solve contact problems using adaptive. The adaptive mesh refinement amr algorithm applied for this study discretizes the fiber network into a hierarchy of dynamically, locally, and adaptively refined grids. Set smoothing objective graded default if the adaptive mesh domain has one or more eulerian boundary regions in explicit dynamic analysis to perform adaptive meshing that attempts to preserve initial mesh gradation while reducing distortions as the analysis evolves. Adaptive mesh refinement on graphics processing units for. Finite element mesh generation provides a concise and comprehensive guide to the application of finite element mesh generation over 2d domains, curved surfaces, and 3d space. Oliger that has been proposed by marsha berger and phil collela in. Softnessbased adaptive mesh refinement algorithm for soft. In order to improve the computational accuracy, an adaptive mesh refinement has been. Visualization tools for adaptive mesh refinement data gunther h.
Adaptive mesh refinement amr is a common technique for dealing with the problem of widely varying spatial scales in the numerical solution of pdes. Highlights the progression of meshing technologies and their applications. Numerical experiments on the 2011 japan tsunami and a local tsunami triggered by a hypothetical m w 7. What are the strategies for local adaptive mesh refinement local amr on unstructured meshes. It is shown that the approach reduces the communication costs and simplifies the implementation. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. Adaptive mesh refinementtheory and applications lecture notes. Jul 25, 2019 the use of adaptive mesh refinement and spherical coordinates allows modeling transoceanic tsunami simulation. Parallel clustering algorithms for structured amr journal. Accelerating an adaptive mesh refinement code for depth. Simulation of isothermal random spherical crystal nucleation and growth in 2 and 3 dimensions utilizing adaptive mesh refinement amr and cuda. Adaptive mesh refinement theory and applications proceedings.
Wes bethel1 1lawrence berkeley national laboratory 2lawrence livermore national laboratory. Structured adaptive mesh refinement samr grid methods the ima volumes in mathematics and its applications. Therefore, they are excellent computer analysis and design cad tools. In numerical analysis, adaptive mesh refinement amr is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. A new cellbased structured adaptive mesh refinement csamr data structure. See figure 2 for a few composite grids, each of which consists of five locally refined grids, at different times. Adaptive mesh refinement algorithms and the difference between amr and moving mesh. Over recent years, adaptive mesh refinement amr algorithms which dynamically match the local resolution of the computational grid to the numerical solution being sought have emerged as powerful tools for solving problems that contain disparate length and time scales.
The strategy of the adaptive mesh refinement method applied to the eigenvalue problem is studied to improve the accuracy of the eigenvector. Structured adaptive mesh refinement samr grid methods the ima volumes in mathematics and its applications 117 softcover reprint of the original 1st ed. A single level 1 grid covers the entire domain usually if it is too large it may be split into multiple level 1 grids. Building on first principles of timedomain electromagnetic simulations, this book presents advanced concepts and cuttingedge modeling techniques in an intuitive way for programmers, engineers, and graduate students. We have developed a moving window full maxwell solver algorithm with perfectly matched absorbing layer pml boundary conditions in order to accurately simulate the propagation of localized waves over a very long distance millions of wavelength in complex media. An adaptive mesh refinement algorithm developed for the euler equations of gas dynamics has been extended to employ highresolution wavepropagation algorithms in a more general framework. The proposed method is developed for nodally based parallel domain partitions where the nodes of the mesh belong to a single processor, whereas the elements can belong to multiple processors. The development of efficient and accurate numerical algorithms for astrophysical. Adaptive mesh refinement amr algorithms clawpack 5. Paul chew and jim ruppert, improves the algorithms in several minor ways, and most importantly, helps to solve the dif.
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