Matrix-free voxel-based finite element method for materials with heterogeneous microstructures: Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur
Modern image detection techniques such as micro computer tomography (μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical m...
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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Weimar
Bauhaus-Universität
2018
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| Schriftenreihe: | ISM-Bericht
2018,7 |
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| Online-Zugang: | kostenfrei Inhaltsverzeichnis |
| Zusammenfassung: | Modern image detection techniques such as micro computer tomography (μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis. However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm. This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained |
| Beschreibung: | xviii, 95 Seiten Illustrationen, Diagramme |
| DOI: | /10.25643/bauhaus-universitaet.3844 |
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| 245 | 1 | 0 | |a Matrix-free voxel-based finite element method for materials with heterogeneous microstructures |b Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur |c von Andrea Keßler |
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| 520 | 3 | |a Modern image detection techniques such as micro computer tomography (μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis. However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm. This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained | |
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| spelling | Keßler, Andrea Verfasser aut Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur von Andrea Keßler Weimar Bauhaus-Universität 2018 xviii, 95 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier ISM-Bericht 2018,7 Dissertation Bauhaus-Universität Weimar 2018 Modern image detection techniques such as micro computer tomography (μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis. However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm. This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Konjugierte-Gradienten-Methode (DE-588)4255670-3 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s Mehrgitterverfahren (DE-588)4038376-3 s Konjugierte-Gradienten-Methode (DE-588)4255670-3 s DE-604 Erscheint auch als Online-Ausgabe 10.25643/bauhaus-universitaet.3844 ISM-Bericht 2018,7 (DE-604)BV035421217 2018,7 https://doi.org//10.25643/bauhaus-universitaet.3844 Resolving-System kostenfrei Volltext V:DE-601;B:DE-Wim2 application/pdf http://www.gbv.de/dms/weimar/toc/1046500287_toc.pdf Inhaltsverzeichnis |
| spellingShingle | Keßler, Andrea Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur ISM-Bericht Finite-Elemente-Methode (DE-588)4017233-8 gnd Konjugierte-Gradienten-Methode (DE-588)4255670-3 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4255670-3 (DE-588)4038376-3 (DE-588)4113937-9 |
| title | Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur |
| title_auth | Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur |
| title_exact_search | Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur |
| title_full | Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur von Andrea Keßler |
| title_fullStr | Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur von Andrea Keßler |
| title_full_unstemmed | Matrix-free voxel-based finite element method for materials with heterogeneous microstructures Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur von Andrea Keßler |
| title_short | Matrix-free voxel-based finite element method for materials with heterogeneous microstructures |
| title_sort | matrix free voxel based finite element method for materials with heterogeneous microstructures matrixfreie voxelbasierte finite elemente methode fur materialien mit komlizierter mikrostruktur |
| title_sub | Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komlizierter Mikrostruktur |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd Konjugierte-Gradienten-Methode (DE-588)4255670-3 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd |
| topic_facet | Finite-Elemente-Methode Konjugierte-Gradienten-Methode Mehrgitterverfahren Hochschulschrift |
| url | https://doi.org//10.25643/bauhaus-universitaet.3844 http://www.gbv.de/dms/weimar/toc/1046500287_toc.pdf |
| volume_link | (DE-604)BV035421217 |
| work_keys_str_mv | AT keßlerandrea matrixfreevoxelbasedfiniteelementmethodformaterialswithheterogeneousmicrostructuresmatrixfreievoxelbasiertefiniteelementemethodefurmaterialienmitkomliziertermikrostruktur |