Transformation invariant local element size specification

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• 作者：Florian Rudolf^a ; ^{rudolf@iue.tuwien.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Karl Rupp^a ; ^b ; ^{rupp@iue.tuwien.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Josef Weinbub^a ; ^{weinbub@iue.tuwien.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Andreas Morhammer^c ; ^{morhammer@iue.tuwien.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Siegfried Selberherr^a ; ^{selberherr@iue.tuwien.ac.at" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Mesh generation ; Element sizing ; Mesh refinement ; ViennaMesh
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：15 September 2015
• 年：2015
• 卷：267
• 期：Complete
• 页码：195-206
• 全文大小：3896 K

文摘

Quality and size of mesh elements are important for optimizing the accuracy and convergence of mesh-based simulation processes. Often, a priori information, like internal material properties, of regions of interest is available, which can be used to locally specify the mesh element size for finding a good balance between the mesh resolution on the one hand and the runtime and memory performance on the other. In many applications, like the optimization of geometric parameters, multiple meshes of similar objects are required. Typical mesh element size specification methods, like scalar fields, are inflexible because of their dependence on the geometry of the object. To avoid the creation of a mesh element size specifications for each object manually, a specification method based on the objects topology rather than on its geometry, is needed. We tackle this problem by extending our meshing software ViennaMesh with a dynamic framework for locally specifying the size of mesh elements. Our approach aims for convenient utilization by using a XML-based configuration with support for arithmetic expressions. To achieve a high level of flexibility and reusability, this configuration can be specified based on the object’s topology, for example interfaces between different material regions. Additionally, geometric parameters, like the radius of the circumsphere of the object, are provided and can be used to, e.g., scale the local mesh element size according to the total size of the object. As a result, our configuration method is invariant under large set transformations, especially deformations, of the object enabling a high level of geometry independence. We depict the practicability of our approach by providing examples for meshes generated with this element sizing framework and discussing a geometry optimization application.