Müller, Joel (2015)
A Subdivision-Based Approach to the Heat Equation for Simulation-Based Modeling.
Technische Universität Darmstadt
Bachelorarbeit, Bibliographie
Kurzbeschreibung (Abstract)
In this thesis a subdivision-based method is presented for calculating numerical solutions to differential equations on the basis of a geometric representation that is also well suited for modeling. While modern CAD programs mainly use continuous representations, like B-splines or NURBS, numerical methods like FEM require a discrete mesh to perform the calculation on. The conversion between these two representations can become a hugely time consuming process. Utilizing the same representation for modeling and simulating objects speeds up the whole engineering process, as the need for mesh generation is eliminated. This also reduces the error made by approximating the geometry. As subdivision schemes are intuitive and efficient to use for modeling and visualizing complex geometries, they serve well as a basis for this method. The presented method is based on Chaikin's algorithm for one-dimensional objects and utilizes Catmull-Clark surfaces to represent two-dimensional objects. On the basis of these two subdivision schemes, solutions to the heat equation are generated, demonstrating the applicability of the approach. The exactness of this solution and the performance of the algorithm are compared to a traditional FEM approach to the heat equation.
| Typ des Eintrags: | Bachelorarbeit |
|---|---|
| Erschienen: | 2015 |
| Autor(en): | Müller, Joel |
| Art des Eintrags: | Bibliographie |
| Titel: | A Subdivision-Based Approach to the Heat Equation for Simulation-Based Modeling |
| Sprache: | Englisch |
| Publikationsjahr: | 2015 |
| Kurzbeschreibung (Abstract): | In this thesis a subdivision-based method is presented for calculating numerical solutions to differential equations on the basis of a geometric representation that is also well suited for modeling. While modern CAD programs mainly use continuous representations, like B-splines or NURBS, numerical methods like FEM require a discrete mesh to perform the calculation on. The conversion between these two representations can become a hugely time consuming process. Utilizing the same representation for modeling and simulating objects speeds up the whole engineering process, as the need for mesh generation is eliminated. This also reduces the error made by approximating the geometry. As subdivision schemes are intuitive and efficient to use for modeling and visualizing complex geometries, they serve well as a basis for this method. The presented method is based on Chaikin's algorithm for one-dimensional objects and utilizes Catmull-Clark surfaces to represent two-dimensional objects. On the basis of these two subdivision schemes, solutions to the heat equation are generated, demonstrating the applicability of the approach. The exactness of this solution and the performance of the algorithm are compared to a traditional FEM approach to the heat equation. |
| Freie Schlagworte: | Business Field: Virtual engineering, Research Area: (Interactive) simulation (SIM), Subdivision surfaces, Physically based simulation, Computer aided engineering (CAE), Thermal simulation, Finite element method (FEM) |
| Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik 20 Fachbereich Informatik > Graphisch-Interaktive Systeme |
| Hinterlegungsdatum: | 13 Mai 2019 07:48 |
| Letzte Änderung: | 13 Mai 2019 07:48 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum