An elastic model for meshfitting for the Level-set Method

An elastic model for meshfitting for the Level-set Method

den Hertog, Wilbert (TU Delft Electrical Engineering, Mathematics and Computer Science)

den Ouden-van der Horst, Dennis (mentor)
van den Dries, Bart (graduation committee)
Dubbeldam, Johan (graduation committee)

Delft University of Technology

Applied Mathematics

2019-06-27

The numerical errors involving the application of the level-set method to a problem can be minimized by fitting a mesh (usually a triangular mesh in two dimensions) to the zero level-set curve defined by the level-set function. These numerical errors depend on two things: the size and skewness of the triangles in the mesh. To fit the mesh, Timo Wortelboer derived a physical model using springs (Wortelboer, 2018). He also defined measures to quantify the quality of a fitted mesh. First, his model is analyzed, as well as the quality measures he defined. Then an introduction on linear isotropic elasticity is given, based on which an elastic model for meshfitting is derived. The Finite Element Method is used to solve the differential equations of the elastic model. Then an optimisation algorithm is introduced to change the Lamé parameters such that the quality of the mesh is improved even more. Lastly the spring model and the elastic model are compared, which results in the elastic model being better than the spring model.

Level Set Method
Numerical Analysis
Finite Element Method
Partial Differential Equations
Mathematical Physics
mesh fitting
elasticity

http://resolver.tudelft.nl/uuid:fb7820dd-7792-48a1-bc0c-cb3dd26861ba

Student theses

bachelor thesis

© 2019 Wilbert den Hertog