Projekt

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Geometry-Aware FEM in Computational Mechanics

Gesuchsteller/in Hormann Kai
Nummer 140583
Förderungsinstrument Projektförderung (Abt. I-III)
Forschungseinrichtung Facoltà di scienze informatiche Università della Svizzera italiana
Hochschule Università della Svizzera italiana - USI
Hauptdisziplin Informatik
Beginn/Ende 01.09.2012 - 30.09.2014
Bewilligter Betrag 213'253.00
Alle Daten anzeigen

Alle Disziplinen (2)

Disziplin
Informatik
Mathematik

Keywords (4)

volumetric parameterizations, barycentric mappings, multilevel solvers, transfer operators

Lay Summary (Englisch)

Lead
Lay summary
The interdisciplinary research area of computational mechanics combines concepts from computer science, applied mathematics, and engineering for the efficient simulation of mechanical structures. Applications of such simulations can be found in a wide range of areas, including engineering, biomechanics, or life sciences. In the case of real-life-applications, particular emphasis has to be put on the discrete representation of the mechanical structures under consideration. On the one hand, the possibly highly complex surfaces have to be represented in a sufficiently accurate way; on the other hand, a volume mesh of high quality is required in order to ensure the quality of the finite element approximation and the good convergence of iterative solution methods.

Although state-of-the-art mesh generation methods and tools allow for a relatively comfortable generation of meshes, the creation of a high quality mesh for a complex structure still requires considerable effort and is a time-consuming task. Thus, it is desirable to make use of a created volume mesh as long as possible throughout the course of a simulation. However, this leads to two difficulties. The first is connected to surface representation and adaptivity. Using adaptive refinement strategies, a higher resolution at the boundary should be accompanied by a better approximation of the real surface of the structure under consideration. This requires changing the mesh along the boundary, which in turn may have a considerable influence on the quality of the volume mesh. The second is related to the degradation of mesh quality during time-dependent simulations which involve large deformations. Despite the fact that in case of a highly deformed mesh a complete remeshing will be necessary, the quality of the mesh might decrease gradually during the simulation process, thus affecting the quality of the simulation results and the speed of the simulation process significantly.

The main idea of this project is to overcome these difficulties by developing and implementing a geometry-aware simulation environment for computational mechanics, which combines in a modular and interactive fashion the handling of complex geometries and volume meshes with the discretization and solution process. Thus, instead of seeing geometry approximation as a burden which has to be taken into account when computing the finite element approximations, we aim at exploiting concepts and methods from the field of geometry processing in order to guarantee a constantly high quality of the boundary approximation and the volume mesh throughout the course of a transient simulation.
Direktlink auf Lay Summary Letzte Aktualisierung: 21.02.2013

Verantw. Gesuchsteller/in und weitere Gesuchstellende

Mitarbeitende

Publikationen

Publikation
Bijective Composite Mean Value Mappings
Schneider Teseo, Hormann Kai, Floater Michael S. (2013), Bijective Composite Mean Value Mappings, in COMPUTER GRAPHICS FORUM, 32(5), 137-146.
Curvature-based blending of closed planar curves
Saba Marianna, Schneider Teseo, Hormann Kai, Scateni Riccardo (2014), Curvature-based blending of closed planar curves, in GRAPHICAL MODELS, 76(5), 263-272.

Zusammenarbeit

Gruppe / Person Land
Felder der Zusammenarbeit
Michael S. Floater Norwegen (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
Stephen Nash Vereinigte Staaten von Amerika (Nordamerika)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten

Wissenschaftliche Veranstaltungen

Aktiver Beitrag

Titel Art des Beitrags Titel des Artikels oder Beitrages Datum Ort Beteiligte Personen
11th World Congress on Computational Mechanics Vortrag im Rahmen einer Tagung Stable mesh transfer for parallel multi-physics simulations 20.07.2014 Barcelona, Spanien Zulian Patrick; Krause Rolf
8th International Conference on Curves and Surfaces Vortrag im Rahmen einer Tagung Curvature-based blending of closed planar curves 12.06.2014 Paris, Frankreich Schneider Teseo; Hormann Kai
Workshop on Multivariate Approximation Vortrag im Rahmen einer Tagung Bijective composite mean value mappings 29.11.2013 Verona, Italien Hormann Kai
SIAM Conference on Geometric & Physical Modeling Vortrag im Rahmen einer Tagung Bijective composite mean value mappings 11.11.2013 Denver, Vereinigte Staaten von Amerika Schneider Teseo; Hormann Kai
CADMOS Day on Modeling and High-Performance Computing Vortrag im Rahmen einer Tagung Towards new directions of parallel computing: Multilevel and domain decomposition in space and time for large-scale nonlinear problems 01.11.2013 Geneva, Schweiz Krause Rolf
Multivariate Approximation and Interpolation with Applications Vortrag im Rahmen einer Tagung Bijective composite mean value mappings 25.09.2013 Erice, Italien Hormann Kai
12th U.S. National Congress on Computational Mechanics Vortrag im Rahmen einer Tagung A parallel approach to interface description and handling 22.07.2013 Raleigh, Vereinigte Staaten von Amerika Krause Rolf
Symposium on Geometry Processing Vortrag im Rahmen einer Tagung Bijective composite mean value mappings 03.07.2013 Genova, Italien Schneider Teseo; Hormann Kai
Frontiers in Finite-Deformation Electromechanics Vortrag im Rahmen einer Tagung Stable mesh transfer for multi-physics and large deformation simulations: Concepts and parallelization 22.05.2013 Dortmund, Deutschland Krause Rolf


Verbundene Projekte

Nummer Titel Start Förderungsinstrument
150053 Generalized Barycentric Interpolation 01.02.2014 Projektförderung (Abt. I-III)
156178 Geometry-Aware FEM in Computational Mechanics 01.10.2014 Projektförderung (Abt. I-III)

Abstract

The interdisciplinary research area of Computational Mechanics combines concepts from computer science, applied mathematics, and engineering for the efficient simulation of mechanical objects. Applications of such simulations can be found in a wide range of areas, including engineering, biomechanics, or life sciences. In the case of real-life-applications, particular emphasis has to be put on the discrete representation of the mechanical structures under consideration. On the one hand, the possibly highly complex surfaces have to be represented in a sufficiently accurate way; on the other hand, a volume mesh of high quality is required in order to ensure the quality of the finite element approximation and the good convergence of iterative solution methods. Although state-of-the-art mesh generation methods and tools allow for a relatively comfortable generation of meshes, the creation of a high quality mesh for a complex object still requires considerable effort and is a time-consuming task. This holds true for hexahedral meshes in particular, because they are much harder to generate but usually give rise to simulation results of higher quality in mechanics (better approximation of displacements and stresses, less stiff behaviour). Thus, it is desirable to make use of a created geometry representation (i.e., the volume mesh) as long as possible throughout the course of a simulation. At this point, however, several difficulties show up: the first difficulty is connected to surface representation and adaptivity: Using adaptive refinement strategies, a higher resolution (h-refinement) at the boundary should be accompanied by a better approximation of the real surface of the object under consideration. This requires changing the mesh along the boundary, which in turn may have a considerable influence on the quality of the volume mesh. The second difficulty is related to the degradation of mesh quality during time dependent simulations involving large deformations. Despite the fact that in case of a highly deformed mesh a complete remeshing will be necessary (with all the disadvantages listed above) the quality of the mesh might decrease gradually during the simulation process, thus affecting the quality of the simulation results (approximation error) and the speed of the simulation process (slowdown of iterative solvers) significantly. Most state-of-the-art simulation tools are based on a one-way connection between the geometry information and the simulation environment. Geometric information is taken into account during mesh generation, but not exploited any more afterwards. As a consequence, adaptive refinement is only seldom accompanied by an increase in geometry resolution, and for complex geometries, efficient solvers such as geometric multigrid methods are replaced by less efficient iterative methods. A notable exception from this one-way approach is isogeometric analysis (IGA), which allows for refining the used mesh and elevating the order of the used finite element basis without changing the geometry or its parameterization. This approach, however, is connected to a particular choice of basis functions for the finite element space. Moreover, in the case of sufficiently large deformations, the mesh quality tends to degrade. In this case, remeshing has to be employed in order to preserve the accuracy of the simulation results, thus posing the problem of mesh generation again. It is the main idea of this project to overcome these difficulties by developing and implementing a geometry-aware simulation environment for computational mechanics, which combines in a modular and interactive fashion the handling of complex geometries and volume meshes with the discretization and solution process. Thus, instead of seeing geometry approximation as a burden which has to be taken into account when computing the finite element approximations, we aim at exploiting concepts and methods from the field of Geometry Processing in order to guarantee a constantly high quality of the boundary approximation and the volume mesh throughout the course of a transient simulation. More precisely, we aim at the possibility of (i) improved geometry-adaptive boundary refinement; (ii) maintaining high mesh quality throughout transient simulations with large deformations; (iii) consistent handling of mesh transfer with different projection operators; (iv) construction of efficient and geometry-flexible multi-scale solvers. As a consequence, our approach turns the common one-way connection between geometry and simulation (geometry -> mesh -> simulation) into a two-way connection, as geometry-specific information is used within the adaptive simulation process, which in turn changes the mesh geometry under consideration.