Local optimization-based simplicial mesh untangling and improvement

Freitag, Lori A.; Plassmann, Paul E.

doi:10.1002/1097-0207(20000910/20)49:1/2<109::aid-nme925>3.0.co;2-u

Cited by 145 publications

(69 citation statements)

References 11 publications

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“…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. While gradient-based optimization methods are often preferred in general practice due to superior convergence rates, the mesh optimization problem is often non-smooth, implying that the gradients are not immediately available.…”

Section: Previous Workmentioning

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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Section: Previous Workmentioning

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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“…(5) Take their intersection R by plane sweep (typically in 0(n log n) time). (6) Otherwise, go back to step (4). Fig.…”

Section: Heuristic Algorithmmentioning

confidence: 99%

“…Mesh generation/improvement [5,6,10,12,13] is an important process for many purposes including Finite Element Method. In a simple setting, a given simple polygon is partitioned into many small triangles after inserting an appropriate number of points in its interior as vertices of triangular meshes.…”

Section: Introductionmentioning

confidence: 99%

Voronoi diagrams with respect to criteria on vision information

Asano

Katoh

Tamaki

et al. 2008

Japan J. Indust. Appl. Math.

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Voronoi diagrams for a set of geometric objects is a partition of the plane (or space in higher dimensions) into disjoint regions each dominated by some given object under a predetermined criterion. In this paper we are interested in various measures associated with criteria on goodness of an input line segment with respect to each point in the plane as the "point of view." These measures basically show how well a segment or information displayed on the segment can be seen from the point. Mathematically, the measures are defined in terms of the shapes of the triangle determined by the point and the line segment. We study the combinatorial and algorithmic complexities of those Voronoi diagrams We also study an associated optimization problem: find a point that maximizes the smallest measure value over the measures with respect to all the given line segments. We give sufficient conditions for an optimal point to lie on a Voronoi edge and present a heuristic optimization algorithm for those measures having this property.

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“…At each position, the quality of surrounding elements is updated and this process is iterated until the optimum is found. It has been demonstrated that the quality function has only one maximum inside the valid domain of the neighbour elements, so the algorithm is guaranteed to converge to the optimal solution [11].…”

Section: Tetrahedral Mesh Generationmentioning

confidence: 99%

Computational Mesh Generation for Vascular Structures with Deformable Surfaces

et al. 2006

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Computational blood flow and vessel wall mechanics simulations for vascular structures are becoming an important research tool for patient-specific surgical planning and intervention. An important step in the modelling process for patient-specific simulations is the creation of the computational mesh based on the segmented geometry. Most known solutions either require a large amount of manual processing or lead to a substantial difference between the segmented object and the actual computational domain. We have developed a chain of algorithms that lead to a closely related implementation of image segmentation with deformable models and 3D mesh generation. The resulting processing chain is very robust and leads both to an accurate geometrical representation of the vascular structure as well as high quality computational meshes. The chain of algorithms has been tested on a wide variety of shapes. A benchmark comparison of our mesh generation application with five other available meshing applications clearly indicates that the new approach outperforms the existing methods in the majority of cases.

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Local optimization-based simplicial mesh untangling and improvement

Cited by 145 publications

References 11 publications

Efficient parallel optimization of volume meshes on heterogeneous computing systems

Efficient parallel optimization of volume meshes on heterogeneous computing systems

Voronoi diagrams with respect to criteria on vision information

Computational Mesh Generation for Vascular Structures with Deformable Surfaces

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