Identification of and discontinuities for surface meshes in CAD

Jiao, Xiangmin; Bayyana, Narasimha R.

doi:10.1016/j.cad.2007.10.005

Cited by 26 publications

(12 citation statements)

References 20 publications

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“…In this manner the requirements of preserving smoothness, stretching and singular features are fully satisfied. The block division process can be made fully automatic as in the literature there are already several reliable methods to detect the geometrical singularities (Jiao, 2008). The block-division process consumes negligible CPU time and the cost overhead is less than 0.1%, according to our tests.…”

Section: Accurate and Robust Curvilinear Mesh Refinementmentioning

confidence: 69%

Extending the Building Cube Method to Curvilinear Mesh with Adaptive Mesh Refinement

Chen

Yamamoto

Nakahashi

2014

JFST

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Building Cube Method (BCM) adopts block-structured Cartesian mesh and finer resolution can be used where the flow contains detailed flow structures. This paper reports the recent progress in extending BCM to curvilinear body-fitted mesh with Adaptive Mesh Refinement (AMR). Compared to Cartesian mesh based AMR, body-fitted AMR strategy is more complicated and less studied. In this paper the key components of body-fitted curvilinear mesh based AMR are introduced. A pressure based refinement criterion is used to detect both shock wave and strong vortex. Cubic interpolation is used to preserve the quality of the refined mesh. A sub-block based refinement strategy is also developed for the treatment of singular geometry features. Combined with the high order scheme, an accurate and robust curvilinear mesh based AMR tool is developed with which the flow details can be automatically captured. Numerical examples are given to validate the numerical properties of current AMR tool and to demonstrate the benefits of current body-fitted AMR strategy.

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Section: Accurate and Robust Curvilinear Mesh Refinementmentioning

confidence: 69%

Extending the Building Cube Method to Curvilinear Mesh with Adaptive Mesh Refinement

Chen

Yamamoto

Nakahashi

2014

JFST

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“…For the latter case, additional preprocessing of the linear surface mesh is required to detect discontinuities. 23 Additionally, a method to automatically estimate good support radius for the RBF procedure is being developed. This would lead to a fully automated procedure for interior mesh regularization.…”

Section: Discussionmentioning

confidence: 99%

Curved mesh generation using radial basis functions

Kashi

Luo

2016

46th AIAA Fluid Dynamics Conference

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A method for generating curved meshes from linear meshes is presented in this work. The method is designed to generate a curved mesh for any type of grid in a computationally inexpensive and numerically robust manner. In this method, high-order nodes are first placed in the linear mesh, the high-order boundary nodes are then relocated to the true boundary, and finally, the high-order interior nodes are moved using radial basis function (RBF) interpolation based on the motion of the high-order boundary nodes. The developed method is used to generate curved meshes for two-and three-dimensional geometries. The numerical experiments indicate that the RBF-interpolation method is much better than the prevalent linear-elasticity methods for generating high-order curved meshes judging by curved-mesh quality, computing cost, and ease of implementation.

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“…Typically, mesh improvement is accomplished by targeting the worst element, as determined by a quality metric which is related in some way to the impact the element has on the convergence of a numerical simulation that employs the mesh as a domain. Excellent references on the surprisingly large array of quality metrics employed in practice include [12] and [24]. Some of the worst-element improvement techniques most relevant to the work presented in this paper include [7] which was one of the first to use numerical optimization techniques.…”

Section: Previous Workmentioning

confidence: 99%

“…We detect mesh features by making use of the technique called the medial quadric [12], which analyzes the eigenvalue decomposition of the normal tensor of a vertex. faces surrounding the vertex v are smooth.…”

Section: Feature Preservationmentioning

confidence: 99%

Efficient parallel optimization of volume meshes on heterogeneous computing systems

Cheng

Shaffer

Yeh

et al. 2015

Engineering with Computers

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being very popular. The shape of mesh elements significantly impacts the efficiency and accuracy of simulation codes. The problem of improving element quality in unstructured tetrahedral meshes and triangular surface meshes is classically framed as an optimization problem. In this framework, the positions of the mesh vertices are adjusted to optimize element quality. In this paper, we explore how modern computer hardware, meaning heterogeneous many-core systems, accelerates these optimization computations. The reward for optimizing meshes faster is significant in practical terms, with fewer simulations failing due to poor mesh quality and a faster engineering design cycle.The wide availability of massively multi-threaded graphics processing units (GPUs) and multi-core CPUs offers a new direction for the acceleration of mesh optimization algorithms. Our work shows how optimization is effectively accomplished on a per-vertex basis on heterogeneous systems, exposing fine-grained parallelism in the same manner as Freitag et al.[4] did for more traditional parallel architectures. Our algorithm specifically seeks to reduce the maximum and average inverse mean ratio, which detects irregular and inverted simplex elements [5,6,15,18]. The framework of the algorithm is very flexible and accommodates essentially any underlying quality metric and core numerical optimization method.The main contribution of this paper is an examination of the effectiveness of a hybrid parallel optimization scheme as opposed to GPU-only parallelism for mesh optimization. In addition, we compare the performance of three different core numerical optimization techniques on a Kepler-class GPU. We describe in detail the use of the derivative-free Nelder-Mead simplex method, which in a previous work was seen to converge faster than several peer optimization methods for this application [22]. In our new results, Nelder-Mead continues to demonstrate superiority Abstract We describe a parallel algorithmic framework for optimizing the shape of elements in a simplicial volume mesh. Using fine-grained parallelism and asymmetric multiprocessing on multi-core CPU and modern graphics processing unit hardware simultaneously, we achieve speedups of more than tenfold over current state-of-the-art serial methods. In addition, improved mesh quality is obtained by optimizing both the surface and the interior vertex positions in a single pass, using feature preservation to maintain fidelity to the original mesh geometry. The framework is flexible in terms of the core numerical optimization method employed, and we provide performance results for both gradient-based and derivative-free optimization methods.

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Identification of and discontinuities for surface meshes in CAD

Cited by 26 publications

References 20 publications

Extending the Building Cube Method to Curvilinear Mesh with Adaptive Mesh Refinement

Extending the Building Cube Method to Curvilinear Mesh with Adaptive Mesh Refinement

Curved mesh generation using radial basis functions

Efficient parallel optimization of volume meshes on heterogeneous computing systems

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