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DTSTART:19700329T020000
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SUMMARY:The Finite Cell Method for Unstructured Meshes
DTSTART;TZID=Europe/Berlin:20160620T150000
DTEND;TZID=Europe/Berlin:20160620T163000
DTSTAMP:20160620T150000Z
LOCATION;ENCODING=QUOTED-PRINTABLE:Campus Campus Essen : V15 S04 C57
CONTACT:Prof. Dr. Carolin Birk (Statik und Dynamik der Flächentragwerke)
DESCRIPTION:Prof. Dr. Carolin Birk (Statik und Dynamik der Flächentragwerke)
The Finite Cell Method for Unstructured Meshes
Vortrag Dr. Sascha Duczek, Universität Magdeburg
Today, the Finite Element Method (FEM) is the dominant numerical tool for solving Partial Differential Equations (PDEs). The widespread use of this particular method is based on the flexibility to describe arbitrary geometries and on the ability to handle various constitutive laws. It suffers, however, from the need for body-fitted discretizations and therefore the mesh generation process is often regarded as the bottleneck in the simulation process, as it requires both a lot of manual input and is rather error-prone. One idea to circumvent or at least alleviate this drawback is to employ the Fictitious Domain Concept (FDC) which provides a simplified discretization strategy based on Cartesian meshes. In conjunction with higher order shape functions, known from the p-version of the FEM, the method is commonly referred to as the Finite Cell Method (FCM).
So far, the FCM has only been used in connection with structured quadrilateral (2D) and hexahedral (3D) meshes and therefore, it is the main goal of the current contribution to illustrate possibilities for an extension to unstructured grids. In two-dimensional cases, polygonal finite elements based on generalized barycentric coordinates are deployed, while in three-dimensional applications tetrahedral elements are preferred.
The main advantage of the proposed polygonal approach (2D) is that it inherits the ability of polygonal finite elements for local mesh refinements and for the construction of conforming quadtree meshes (without introducing hanging nodes). In the tetrahedral approach (3D) an important benefit is the possibility to re-use finite element grids from commercial FEM pre-processors. These meshes can be easily transferred to the FCM and only important micro-structural details, such as pores, need to be included by deploying the FDC. To this end, the geometry of the micro-structure is obtained by means of computed tomography (CT) where only the parts of interest are resolved with high resolution computer tomographs. The CT-scans can be included in the FCM model by using either the voxelized data or by using surface tessellation language (STL) files to describe the boundary of the micro-structure. The mentioned properties and the performance of both FCM-based methods are illustrated by means of several benchmark problems for static as well as dynamic applications.
Monday, 20. June 2016
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