Topic
Size function
About: Size function is a research topic. Over the lifetime, 75 publications have been published within this topic receiving 1413 citations.
Papers published on a yearly basis
Papers
Dissertation•
1 Jan 2005TL;DR: The iterative nature of the algorithm makes it particularly useful for moving meshes, and it is shown how to combine it with the level set method for applications in fluid dynamics, shape optimization, and structural deformations.
Abstract: We present new techniques for generation of unstructured meshes for geometries specified by implicit functions An initial mesh is iteratively improved by solving for a force equilibrium in the element edges, and the boundary nodes are projected using the implicit geometry definition Our algorithm generalizes to any dimension and it typically produces meshes of very high quality We show a simplified version of the method in just one page of MATLAB code, and we describe how to improve and extend our implementation
Prior to generating the mesh we compute a mesh size function to specify the desired size of the elements We have developed algorithms for automatic generation of size functions, adapted to the curvature and the feature size of the geometry We propose a new method for limiting the gradients in the size function by solving a non-linear partial differential equation We show that the solution to our gradient limiting equation is optimal for convex geometries, and we discuss efficient methods to solve it numerically
The iterative nature of the algorithm makes it particularly useful for moving meshes, and we show how to combine it with the level set method for applications in fluid dynamics, shape optimization, and structural deformations It is also appropriate for numerical adaptation; where the previous mesh is used to represent the size function and as the initial mesh for the refinements Finally, we show how to generate meshes for regions in images by using implicit representations (Copies available exclusively from MIT Libraries, Rm 14-0551, Cambridge, MA 02139-4307 Ph 617-253-5668; Fax 617-253-1690)
227 citations
1 Jan 1999
TL;DR: The usefulness of such a theory in comparing shapes is high lighted by showing some examples and the robustness of Size Theory with respect to noise and occlusions is pointed out.
Abstract: In this paper we give an outline of Size Theory and its main results The usefulness of such a theory in comparing shapes is high lighted by showing some examples The robustness of Size Theory with respect to noise and occlusions is pointed out In addition an algebraic approach to the theory is presented
181 citations
TL;DR: In this article, a sound approach to bandwidth selection in nonparametric kernel testing is proposed, where the main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions.
Abstract: We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed-form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions. For example, when a significance level is given, we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level. Both asymptotic theory and methodology are established. In addition, we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example.
157 citations
TL;DR: It is proved that every size function can be represented as a set of points and lines in the real plane, with multiplicities, which allows for an algebraic approach to size functions and the construction of new pseudo-distances between size functions for comparing shapes.
Abstract: In this paper we consider a mathematical tool for shape description called size function. We prove that every size function can be represented as a set of points and lines in the real plane, with multiplicities. This allows for an algebraic approach to size functions and the construction of new pseudo-distances between size functions for comparing shapes.
98 citations
1 Jan 2002
TL;DR: This paper describes a new technology of mesh size control using a background overlay grid size function, which is used as the base grid for determining the mesh size at each point during the meshing process.
Abstract: This paper describes a new technology of mesh size control using a background overlay grid size function. A background overlay grid is generated first according to the defined size functions and then is used as the base grid for determining the mesh size at each point during the meshing process. The definitions, classifications, implementations and control algorithms of three types of size functions including a fixed size function, a curvature size function and a proximity size function are presented in detail. Meshing results with controlled mesh sizes are given, and considerations for further improvement are listed.
56 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 1 |
| 2019 | 2 |
| 2018 | 2 |
| 2017 | 4 |
| 2015 | 3 |