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search.filters.applied.f.access: openAccess × Author: Kamenski, Lennard × Has files: Yes × Subject: moving mesh × WGL Institute: WIAS ×

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Now showing 1 - 5 of 5
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    Tetrahedral Mesh Improvement Using Moving Mesh Smoothing and Lazy Searching Flips
    (Amsterdam [u.a.] : Elsevier, 2016) Dassi, Franco; Kamenski, Lennard; Si, Hang
    We combine the new moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the new lazy flip technique, a reversible edge removal algorithm for local mesh quality improvement. These strategies already provide good mesh improvement on themselves, but their combination achieves astonishing results not reported so far. Provided numerical comparison with some publicly available mesh improving software show that we can obtain final tetrahedral meshes with dihedral angles between 40° and 123°.
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    Tetrahedral mesh improvement using moving mesh smoothing and lazy searching flips
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dassi, Franco; Kamenski, Lennard; Si, Hang
    In this paper we combine two new smoothing and flipping techniques. The moving mesh smoothing is based on the integration of an ordinary differential coming from a given functional. The lazy flip technique is a reversible edge removal algorithm to automatically search flips for local quality improvement. On itself, these strategies already provide good mesh improvement, but their combination achieves astonishing results which have not been reported so far. Provided numerical examples show that we can obtain final tetrahedral meshes with dihedral angles between 40° and 123°. We compare the new method with other publicly available mesh improving codes.
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    A comparative numerical study of meshing functionals for variational mesh adaptation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Huang, Weizhang; Kamenski, Lennard; Russell, Robert D.
    We present a comparative numerical study for three functionals used for variational mesh adaptation. One of them is a generalization of Winslow's variable diffusion functional while the others are based on equidistribution and alignment. These functionals are known to have nice theoretical properties and work well for most mesh adaptation problems either as a stand-alone variational method or combined within the moving mesh framework. Their performance is investigated numerically in terms of equidistribution and alignment mesh quality measures. Numerical results in 2D and 3D are presented.
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    Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Dassi, Franco; Kamenski, Lennard; Farrell, Patricio; Si, Hang
    Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones.
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    A geometric discretization and a simple implementation for variational mesh generation and adaptation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Huang, Weizhang; Kamenski, Lennard
    We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation is approximated by the Jacobian matrices of affine mappings between elements. The advantage of this direct geometric discretization is that it preserves the basic geometric structure of the continuous functional, which is useful in preventing strong decoupling or loss of integral constraints satisfied by the functional. Moreover, the discretized functional is a function of the coordinates of mesh vertices and its derivatives have a simple analytical form, which allows a simple implementation of variational mesh generation and adaptation on computer. Since the variational mesh adaptation is the base for a number of adaptive moving mesh and mesh smoothing methods, the result in this work can be used to develop simple implementations of those methods. Numerical examples are given.