Download or read book Anisotropic Mesh Adaptation for Image Segmentation Based on Partial Differential Equations written by Karrar Kadhim Abbas and published by . This book was released on 2020 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the resolution of digital images increases significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this dissertation, we consider image segmentation by solving a partial differential equation (PDE) model based on the Mumford-Shah functional. We first, develop a new anisotropic mesh adaptation (AMA) framework to improve segmentation efficiency and accuracy. In the AMA framework, we incorporate an anisotropic mesh adaptation for image representation and a nite element method for solving the PDE model. Comparing to traditional algorithms solved by the finnite difference method, our AMA framework provides faster and better results without the need for re-sizing the images to lower quality. We also extend the algorithm to segment images with multiple regions. We also improve the well-known Chan-Vese model by developing a locally enhanced Chan-Vese (LECV) model. Our LECV model incorporates a newly define signed pressure force (SPF) function, which is built upon the local image information. The SPF function helps to attract the contour curve to the object boundaries for images with inhomogeneous intensities. The proposed LECV model, together with the AMA segmentation framework can successfully segment the image with or without inhomogeneous intensities. While most other segmentation methods only work on low-resolution images, our LECV model is successfully applied to high-resolution images, with improved efficiency and accuracy.
Download or read book Anisotropic hp Mesh Adaptation Methods written by Vít Dolejší and published by Springer Nature. This book was released on 2022-06-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.
Download or read book Two dimensional Three dimensional and Four dimensional Anisotropic Mesh Adaptation for the Time continuous Space time Finite Element Method with Applications to the Incompressible Navier Stokes Equations written by Pascal Tremblay and published by . This book was released on 2007 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Moving Mesh Methods written by Weizhang Huang and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.
Download or read book Four dimensional Anisotropic Mesh Adaptation for Spacetime Numerical Simulations written by Philip Claude Delhaye Caplan and published by . This book was released on 2019 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers and scientists are increasingly relying on high-fidelity numerical simulations. Within these simulations, mesh adaptation is useful for obtaining accurate predictions of an output of interest subject to a computational cost constraint. In the quest for accurately predicting outputs in problems with time-dependent solution features, a fully unstructured coupled spacetime approach has been shown to be useful in reducing the cost of the overall simulation. However, for the simulation of unsteady three-dimensional partial differential equations (PDEs), a four-dimensional mesh adaptation tool is needed. This work develops the first anisotropic metric-conforming four-dimensional mesh adaptation tool for performing adaptive numerical simulations of unsteady PDEs in three dimensions. The theory and implementation details behind our algorithm are first developed alongside an algorithm for constructing four-dimensional geometry representations. We then demonstrate our algorithm on three-dimensional benchmark cases and it appears to outperform existing implementations, both in metric-conformity and expected tetrahedra counts. We study the utility of the mesh adaptation components to justify the design of our algorithm. We then develop four-dimensional benchmark cases and demonstrate that metric-conformity and expected pentatope counts are also achieved. This is the first time anisotropic four-dimensional meshes have been presented in the literature. Next, the entire mesh adaptation framework, Mesh Optimization via Error Sampling and Synthesis (MOESS), is extended to the context of finding the optimal mesh to represent a function of four variables. The mesh size and aspect ratio distributions of the optimized meshes match the analytic ones, thus verifying our framework. Finally, we apply MOESS in conjunction with the mesh adaptation tool to perform the first four-dimensional anisotropic mesh adaptation for the solution of the advection-diffusion equation. The optimized meshes effectively refine the solution features corresponding to both a boundary layer solution as well as an expanding spherical wave.
Download or read book An Optimization Framework for Adaptive Higher order Discretizations of Partial Differential Equations on Anisotropic Simplex Meshes written by Masayuki Yano (Ph. D.) and published by . This book was released on 2012 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Improving the autonomy, efficiency, and reliability of partial differential equation (PDE) solvers has become increasingly important as powerful computers enable engineers to address modern computational challenges that require rapid characterization of the input-output relationship of complex PDE governed processes. This thesis presents work toward development of a versatile PDE solver that accurately predicts engineering quantities of interest to user-prescribed accuracy in a fully automated manner. We develop an anisotropic adaptation framework that works with any localizable error estimate, handles any discretization order, permits arbitrarily oriented anisotropic elements, robustly treats irregular features, and inherits the versatility of the underlying discretization and error estimate. Given a discretization and any localizable error estimate, the framework iterates toward a mesh that minimizes the error for a given number of degrees of freedom by considering a continuous optimization problem of the Riemannian metric field. The adaptation procedure consists of three key steps: sampling of the anisotropic error behavior using element-wise local solves; synthesis of the local errors to construct a surrogate error model based on an affine-invariant metric interpolation framework; and optimization of the surrogate model to drive the mesh toward optimality. The combination of the framework with a discontinuous Galerkin discretization and an a posteriori output error estimate results in a versatile PDE solver for reliable output prediction. The versatility and effectiveness of the adaptive framework are demonstrated in a number of applications. First, the optimality of the method is verified against anisotropic polynomial approximation theory in the context of L2 projection. Second, the behavior of the method is studied in the context of output-based adaptation using advection-diffusion problems with manufactured primal and dual solutions. Third, the framework is applied to the steady-state Euler and Reynolds-averaged Navier-Stokes equations. The results highlight the importance of adaptation for high-order discretizations and demonstrate the robustness and effectiveness of the proposed method in solving complex aerodynamic flows exhibiting a wide range of scales. Fourth, fully-unstructured space-time adaptivity is realized, and its competitiveness is assessed for wave propagation problems. Finally, the framework is applied to enable spatial error control of parametrized PDEs, producing universal optimal meshes applicable for a wide range of parameters.
Download or read book Mesh Adaptation for Computational Fluid Dynamics Volume 1 written by Alain Dervieux and published by John Wiley & Sons. This book was released on 2022-09-21 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation technology, and computational fluid dynamics (CFD) in particular, is essential in the search for solutions to the modern challenges faced by humanity. Revolutions in CFD over the last decade include the use of unstructured meshes, permitting the modeling of any 3D geometry. New frontiers point to mesh adaptation, allowing not only seamless meshing (for the engineer) but also simulation certification for safer products and risk prediction. Mesh Adaptation for Computational Dynamics 1 is the first of two volumes and introduces basic methods such as feature-based and multiscale adaptation for steady models. Also covered is the continuous Riemannian metrics formulation which models the optimally adapted mesh problem into a pure partial differential statement. A number of mesh adaptative methods are defined based on a particular feature of the simulation solution. This book will be useful to anybody interested in mesh adaptation pertaining to CFD, especially researchers, teachers and students.
Download or read book Geometric Modeling and Mesh Generation from Scanned Images written by Yongjie Jessica Zhang and published by CRC Press. This book was released on 2018-09-03 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cutting-Edge Techniques to Better Analyze and Predict Complex Physical Phenomena Geometric Modeling and Mesh Generation from Scanned Images shows how to integrate image processing, geometric modeling, and mesh generation with the finite element method (FEM) to solve problems in computational biology, medicine, materials science, and engineering. Based on the author’s recent research and course at Carnegie Mellon University, the text explains the fundamentals of medical imaging, image processing, computational geometry, mesh generation, visualization, and finite element analysis. It also explores novel and advanced applications in computational biology, medicine, materials science, and other engineering areas. One of the first to cover this emerging interdisciplinary field, the book addresses biomedical/material imaging, image processing, geometric modeling and visualization, FEM, and biomedical and engineering applications. It introduces image-mesh-simulation pipelines, reviews numerical methods used in various modules of the pipelines, and discusses several scanning techniques, including ones to probe polycrystalline materials. The book next presents the fundamentals of geometric modeling and computer graphics, geometric objects and transformations, and curves and surfaces as well as two isocontouring methods: marching cubes and dual contouring. It then describes various triangular/tetrahedral and quadrilateral/hexahedral mesh generation techniques. The book also discusses volumetric T-spline modeling for isogeometric analysis (IGA) and introduces some new developments of FEM in recent years with applications.
Download or read book Advanced Numerical Methods in Mesh Generation and Mesh Adaptation written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge-based error estimates. We conclude that the quasi-optimal mesh must be quasi-uniform in this metric. All numerical experiments are based on the publicly available Ani3D package, the collection of advanced numerical instruments.
Download or read book Adaptive Mesh Methods and Software for Time dependent Partial Differential Equations written by Shengtai Li and published by . This book was released on 1998 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Residual based Isotropic and Anisotropic Mesh Adaptation for Computational Fluid Dynamics written by Amir R. Baserinia and published by . This book was released on 2008 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The accuracy of a fluid flow simulation depends not only on the numerical method used for discretizing the governing equations, but also on the distribution and topology of the mesh elements. Mesh adaptation is a technique for automatically modifying the mesh in order to improve the simulation accuracy in an attempt to reduce the manual work required for mesh generation. The conventional approach to mesh adaptation is based on a feature-based criterion that identifies the distinctive features in the flow field such as shock waves and boundary layers. Although this approach has proved to be simple and effective in many CFD applications, its implementation may require a lot of trial and error for determining the appropriate criterion in certain applications. An alternative approach to mesh adaptation is the residual-based approach in which the discretization error of the fluid flow quantities across the mesh faces is used to construct an adaptation criterion. Although this approach provides a general framework for developing robust mesh adaptation criteria, its incorporation leads to significant computational overhead. The main objective of the thesis is to present a methodology for developing an appropriate mesh adaptation criterion for fluid flow problems that offers the simplicity of a feature-based criterion and the robustness of a residual-based criterion. This methodology is demonstrated in the context of a second-order accurate cell-centred finite volume method for simulating laminar steady incompressible flows of constant property fluids. In this methodology, the error of mass and momentum flows across the faces of each control volume are estimated with a Taylor series analysis. Then these face flow errors are used to construct the desired adaptation criteria for triangular isotropic meshes and quadrilateral anisotropic meshes. The adaptation results for the lid-driven cavity flow show that the solution error on the resulting adapted meshes is 80 to 90 percent lower than that of a uniform mesh with the same number of control volumes. The advantage of the proposed mesh adaptation method is the capability to produce meshes that lead to more accurate solutions compared to those of the conventional methods with approximately the same amount of computational effort.
Download or read book Rapport written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Anisotropic Mesh Adaptation Based on Hessian Recovery and A Posteriori Error Estimates written by Lennard Kamenski and published by . This book was released on 2009 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Adaptive Mesh Moving and Local Refinement Method for Time Dependent Partial Differential Equations written by and published by . This book was released on 1990 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss mesh-moving, static mesh regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse based mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes to distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.
Download or read book Time accurate Anisotropic Mesh Adaptation for Three dimensional Moving Mesh Problems written by Nicolas Barral and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time dependent simulations are still a challenge for industry, notably due to problems raised by moving boundaries, both in terms of CPU cost and accuracy. This thesis presents contributions to several aspects of simulations with moving meshes. A moving-mesh algorithm based on a large deformation time step and connectivity changes (swaps) is studied. An elasticity method and an Inverse Distance Weighted interpolation method are compared on many 3D examples, demonstrating the efficiency of the algorithm in handling large geometry displacement without remeshing. This algorithm is coupled with an Arbitrary-Lagrangian-Eulerian (ALE) solver, whose schemes and implementation in 3D are described in details. A linear interpolation scheme is used to handle swaps. Validation test cases showed that the use of swaps does not impact notably the accuracy of the solution, while several other complex 3D examples demonstrate the capabilities of the approach both with imposed motion and Fluid-Structure Interaction problems. Metric-based mesh adaptation has proved its efficiency in improving the accuracy of steady simulation at a reasonable cost. We consider the extension of these methods to unsteady problems, updating the previous fixed-point algorithm thanks to a new space-time error analysis based on the continuous mesh model. An efficient p-thread parallelization enables running 3D unsteady adaptative simulations with a new level of accuracy. This algorithm is extended to moving mesh problems, notably by correcting the optimal unsteady metric. Finally several 3D examples of adaptative moving mesh simulations are exhibited, that prove our concept by improving notably the accuracy of the solution for a reasonable time cost.
Download or read book Anisotropic Mesh Adaptation for Solution of Finite Element Problems Using Hierarchical Edge based Error Estimates written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}−1 and the gradient of error is proportional to N{sub h}−12 which are optimal asymptotics. The methodology is verified with numerical experiments.
Download or read book An Adaptive Method with Mesh Moving and Local Mesh Refinement for Time Dependent Partial Differential Equations written by David C. Arney and published by . This book was released on 1988 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors discuss mesh moving, static mesh regeneration, and local mesh refinement algorithms that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time-dependent partial differential equations in two-space dimensions and time. A coarse base mesh of quadrilateral cells is moved by an algebraic mesh movement function so that it may follow and isolate spatially distinct phenomena. The local mesh refinement method recursively divides the time step and spatial cells of the moving base mesh in regions were error indicators are high until a prescribed tolerance is satisfied. The static mesh regeneration procedure is used to create a new base mesh when the existing ones become too distorted. In order to test our adaptive algorithms, the authors implemented them in a system code with an initial mesh generator, a MacCormack finite difference scheme for hyperbolic systems, and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples. (kr).
