共查询到20条相似文献,搜索用时 0 毫秒
1.
Nazmiye Acikgoz Carlo L. Bottasso 《International journal for numerical methods in engineering》2007,71(2):201-223
We report on results obtained with a metric-driven mesh optimization procedure for simplicial meshes based on the simulated annealing (SA) method. The use of SA improves the chances of removing pathological clusters of bad elements, that have the tendency to lock into frozen configurations in difficult regions of the model such as corners and complex face intersections, prejudicing the overall quality of the final grid. A local version of the algorithm is developed that significantly lowers the computational cost. Numerical examples illustrate the effectiveness of the proposed methodology, which is compared to a classical greedy Gauss–Seidel optimization. Substantial improvement in the quality of the worst elements of the grid is observed for the local simulated annealing optimization. Furthermore, the method appears to be robust to the choice of the algorithmic parameters. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
2.
Gustavo C. Buscaglia Enzo A. Dari 《International journal for numerical methods in engineering》1997,40(22):4119-4136
The construction of solution-adapted meshes is addressed within an optimization framework. An approximation of the second spatial derivative of the solution is used to get a suitable metric in the computational domain. A mesh quality is proposed and optimized under this metric, accounting for both the shape and the size of the elements. For this purpose, a topological and geometrical mesh improvement method of high generality is introduced. It is shown that the adaptive algorithm that results recovers optimal convergence rates in singular problems, and that it captures boundary and internal layers in convection-dominated problems. Several important implementation issues are discussed. © 1997 John Wiley & Sons, Ltd. 相似文献
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Robert J. Renka 《International journal for numerical methods in engineering》2015,101(11):870-886
We describe a new mesh smoothing method that consists of minimizing the sum of squared element volumes over the free vertex positions. To the extent permitted by the fixed vertices and mesh topology, the resulting mesh elements have uniformly distributed volumes. In the case of a triangulation, uniform volume implies well‐shaped triangles. If a graded mesh is required, the element volumes may be weighted by centroidal values of a sizing function, resulting in a mesh that conforms to the required vertex density. The method has both a local and a global implementation. In addition to smoothing, the method serves as a simple parameter‐free means of untangling a mesh with inverted elements. It applies to all types of meshes, but we present test results here only for planar triangle meshes. Our test results show the new method to be fast, superior in uniformity or conformity to a sizing function, and among the best methods in terms of triangle shape quality. We also present a new angle‐based method that is simpler and more effective than alternatives. This method is directly aimed at producing well‐shaped triangles and is particularly effective when combined with the volume‐based method. It also generalizes to anisotropic mesh smoothing. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
5.
Alexander A. Shostko Rainald Lhner William C. Sandberg 《International journal for numerical methods in engineering》1999,44(9):1359-1376
A method for the rapid construction of meshes over intersecting triangulated shapes is described. The method is based on an algorithm that automatically generates a surface mesh from intersecting triangulated surfaces by means of Boolean intersection/union operations. After the intersection of individual components is obtained, the exposed surface parts are extracted. The algorithm is intended for rapid interactive construction of non‐trivial surfaces in engineering design, manufacturing, visualization and molecular modelling applications. Techniques to make the method fast and general are described. The proposed algorithm is demonstrated on a number of examples, including intersections of multiple spheres, planes and general engineering shapes, as well as generation of surface and volume meshes around clusters of intersecting components followed by the computation of flow field parameters. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
6.
Ko‐Foa Tchon Julien Dompierre Ricardo sCamarero 《International journal for numerical methods in engineering》2004,59(12):1539-1562
Conformal refinement using a shrink and connect strategy, known as pillowing or buffer insertion, contracts and reconnects contiguous elements of an all‐quadrilateral or an all‐hexahedral mesh in order to locally increase vertex density without introducing hanging nodes or non‐cubical elements. Using layers as shrink sets, the present method automates the anisotropic refinement of such meshes according to a prescribed size map expressed as a Riemannian metric field. An anisotropic smoother further enhances vertex clustering to capture the features of the metric. Both two‐ and three‐dimensional test cases with analytic control metrics confirm the feasibility of the present approach and explore strategies to minimize the trade‐off between element shape quality and size conformity. Additional examples using discrete metric maps illustrate possible practical applications. Although local vertex removal and reconnection capabilities have yet to be developed, the present refinement method is a step towards an automated tool for conformal adaptation of all‐quadrilateral and all‐hexahedral meshes. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
7.
Patrick M. Knupp 《International journal for numerical methods in engineering》2000,48(3):401-420
Structured mesh quality optimization methods are extended to optimization of unstructured triangular, quadrilateral, and mixed finite element meshes. New interpretations of well‐known nodally based objective functions are made possible using matrices and matrix norms. The matrix perspective also suggests several new objective functions. Particularly significant is the interpretation of the Oddy metric and the smoothness objective functions in terms of the condition number of the metric tensor and Jacobian matrix, respectively. Objective functions are grouped according to dimensionality to form weighted combinations. A simple unconstrained local optimum is computed using a modified Newton iteration. The optimization approach was implemented in the CUBIT mesh generation code and tested on several problems. Results were compared against several standard element‐based quality measures to demonstrate that good mesh quality can be achieved with nodally based objective functions. Published in 2000 by John Wiley & Sons, Ltd. 相似文献
8.
Juan R. Cebral Fernando E. Camelli Rainald Lhner 《International journal for numerical methods in engineering》2002,55(2):177-190
Several extensions and improvements to surface merging procedures based on the extraction of iso‐surfaces from a distance map defined on an adaptive background grid are presented. The main objective is to extend the application of these algorithms to surfaces with sharp edges and corners. In order to deal with objects of different length scales, the initial background grids are created using a Delaunay triangulation method and local voxelizations. A point enrichment technique that introduces points into the background grid along detected surface features such as ridges is used to ensure that these features are preserved in the final merged surface. The surface merging methodology is extended to include other Boolean operations between surface triangulations. The iso‐surface extraction algorithms are modified to obtain the correct iso‐surface for multi‐component objects. The procedures are demonstrated with various examples, ranging from simple geometrical entities to complex engineering applications. The present algorithms allow realistic modelling of a large number of complex engineering geometries using overlapping components defined discretely, i.e. via surface triangulations. This capability is very useful for grid generation starting from data originated in measurements or images. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
9.
O. Hassan E. J. Probert K. Morgan J. Peraire 《International journal for numerical methods in engineering》1995,38(7):1123-1148
An implicit–explicit procedure for the solution of the compressible Navier–Stokes equations on unstructured triangular and tetrahedral meshes is outlined. A procedure for constructing continuous lines, made up of edges in the mesh, is employed and the implicit equation system is solved via line relaxation. The problem of generating, and adapting, unstructured meshes for viscous flow simulations is addressed. A number of examples are included which demonstrate the numerical performance of the proposed procedures. 相似文献
10.
Patrick M. Knupp 《International journal for numerical methods in engineering》2000,48(8):1165-1185
Three‐dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid, high‐quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2×2 matrices do not hold for 3×3 matrices, significant differences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equality in two dimensions of the smoothness and condition number of the Jacobian matrix objective functions does not extend to three dimensions and further, that the equality of the Oddy and condition number of the metric tensor objective functions in two dimensions also fails to extend to three dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non‐dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all‐hexahedral ‘whisker‐weaved’ meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure. Published in 2000 by John Wiley & Sons, Ltd. 相似文献
11.
A. Rassineux 《International journal for numerical methods in engineering》1998,41(4):651-674
An algorithm for tetrahedron mesh generation and optimization with respect to a shape and a size criterion is presented. A well distributed set of nodes is first generated by an octree method, and the set is then triangulated. The advancing front technique is used to mesh the whole volume. Emphasis has been placed on management of the front. The method involves priority construction of enhanced quality tetrahedra. Each face is assigned to a front corresponding to the quality of the best tetrahedron which can be constructed. Elements are destroyed in the case of non-convergence. Optimization procedures make local use of the algorithm used to mesh the complete model. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method. © 1998 John Wiley & Sons, Ltd. 相似文献
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A. Gargallo‐Peiró X. Roca J. Peraire J. Sarrate 《International journal for numerical methods in engineering》2015,103(5):342-363
We present a robust method for generating high‐order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high‐order nodes, second, displacing the boundary nodes to ensure that they are on the computer‐aided design surface, and third, smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high‐order mesh. The smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh. This means that whenever possible, the resulting mesh preserves the geometrical features of the initial linear mesh such as shape, stretching, and size. We present several examples to illustrate the performance of the proposed algorithm. Furthermore, the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements. We consider cases with polynomial approximations up to degree ten, large deformations of the curved boundaries, concave boundaries, and highly stretched boundary layer elements. The meshes obtained are suitable for high‐order finite element analyses. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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A. KHAMAYSEH A. KUPRAT 《International journal for numerical methods in engineering》1996,39(18):3163-3174
An elliptic smoothing scheme for 2-D structured meshes is generalized to the case of 2-D unstructured meshes. The resulting scheme is similar to the familiar Laplacian smoothing scheme, but exhibits superior node diffusion in anisotropic domains. We then show further improvement of grid quality when smoothing is alternated with Lawson flipping (a technique commonly used to generate Delaunay triangulations). Two additional enhancements (‘controlled’ and ‘adaptive’ smoothing) allow us to create grids suitable for a realistic MOSFET semiconductor application. 相似文献
14.
针对传统有限元法求解Oldroyd-B本构方程时需加入稳定化方案的缺点,本文基于非结构网格给出了统一间断有限元求解框架.该框架包含采用IPDG(interior penalty discontinuous Galerkin)求解质量方程和动量方程,与采用RKDG(Runge-Kutta discontinuous Galerkin)求解本构方程这两个核心.数值结果表明:该方法在求解Oldroyd-B本构方程时无需加入稳定化方案,实施比有限元法简便,且具有较高的计算精度,可有效地模拟包含应力奇异点的复杂粘弹流动问题,进而揭示非牛顿粘弹流动的基本特征. 相似文献
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P. BATTEN C. LAMBERT D. M. CAUSON 《International journal for numerical methods in engineering》1996,39(11):1821-1838
Despite their geometric flexibility, unstructured mesh schemes for compressible gas dynamics do not usually resolve captured shocks and contact discontinuities as well as corresponding structured mesh schemes. The main reason for this appears to be the difficulty in constructing analogous extensions to higher-order accuracy. This issue is addressed in some detail and a new, compact stencil, Maximum Limited Gradient (MLG) reconstruction technique is presented for unstructured elements. The MLG reconstruction turns out to be a multidimensional analogue of the one-dimensional Superbee slope. We then describe a simple and robust extension to systems of equations, which does not require any diagonalization of flux Jacobian matrices. An application to a blast wave hazard prediction problem is presented using the wave-by-wave extension of the MLG limiter to the Euler equations. 相似文献
16.
Houman Borouchaki Frdric Hecht Pascal J. Frey 《International journal for numerical methods in engineering》1998,43(6):1143-1165
This paper gives a procedure to control the size variation in a mesh adaption scheme where the size specification (the so-called control space) is used to govern the mesh generation stage. The method consists in replacing the initial control space by a reduced one by means of size or metric. It allows to improve, a priori, the quality of the adapted mesh and to speed up the adaption procedure. Several numerical examples show the efficiency of the reduction scheme. © 1998 John Wiley & Sons, Ltd. 相似文献
17.
A framework for the construction of node-centred schemes to solve the compressible Euler and Navier–Stokes equations is presented. The metric quantities are derived by exploiting some properties of C0 finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated. 相似文献
18.
Harm Askes Antonio Rodríguez‐Ferran 《International journal for numerical methods in engineering》2001,51(3):253-273
An adaptive scheme is proposed in which the domain is split into two subdomains. One subdomain consists of regions where the discretization is refined with an h‐adaptive approach, whereas in the other subdomain node relocation or r‐adaptivity is used. Through this subdivision the advantageous properties of both remeshing strategies (accuracy and low computer costs, respectively) can be exploited in greater depth. The subdivision of the domain is based on the formulation of a desired element size, which renders the approach suitable for coupling with various error assessment tools. Two‐dimensional linear examples where the analytical solution is known illustrate the approach. It is shown that the combined rh‐adaptive approach is superior to its components r‐ and h‐adaptivity, in that higher accuracies can be obtained compared to a purely r‐adaptive approach, while the computational costs are lower than that of a purely h‐adaptive approach. As such, a more flexible formulation of adaptive strategies is given, in which the relative importance of attaining a pre‐set accuracy and speeding‐up the computational process can be set by the user. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
19.
P. D. ZAVATTIERI E. A. DARI G. C. BUSCAGLIA 《International journal for numerical methods in engineering》1996,39(12):2055-2071
We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer. 相似文献
20.
D. Guégan O. Allain A. Dervieux F. Alauzet 《International journal for numerical methods in engineering》2010,84(11):1376-1406
This paper discusses the contribution of mesh adaptation to high‐order convergence of unsteady multi‐fluid flow simulations on complex geometries. The mesh adaptation relies on a metric‐based method controlling the L p‐norm of the interpolation error and on a mesh generation algorithm based on an anisotropic Delaunay kernel. The mesh‐adaptive time advancing is achieved, thanks to a transient fixed‐point algorithm to predict the solution evolution coupled with a metric intersection in the time procedure. In the time direction, we enforce the equidistribution of the error, i.e. the error minimization in L ∞ norm. This adaptive approach is applied to an incompressible Navier–Stokes model combined with a level set formulation discretized on triangular and tetrahedral meshes. Applications to interface flows under gravity are performed to evaluate the performance of this method for this class of discontinuous flows. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献