Based on a posteriori error estimation a method to bound the error induced by simplifying the geometry of a model is presented. Error here refers to the solution of a partial differential equation and a specific quantity of interest derived from it. Geometry simplification specifically refers to replacing CAD model features with simpler shapes. The simplification error estimate helps to determine whether a feature can be removed from the model by indicating how much the simplification affects the physical properties of the model as measured by a quantity of interest. The approach in general can also be extended to other problems governed by linear elliptic equations. Strict bounds for the error are proven for errors expressed in the energy norm. The approach relies on the Constitutive Relation Error to enable practically useful and computationally affordable bounds for error measures in the energy error norm. All methodologies are demonstrated for a second order elliptic partial differential equation for electrostatic problems. Finite element simplification error estimation code is developed to calculate the simplification error numerically. Numerical experiments for some geometric models of capacitors show satisfactory results for the simplification error bounds for a range of different deafeaturing cases and a quantity of interest, linear in the solution of the electrostatic partial differential equation. Overall the numerically calculated bounds are always valid, but are more or less accurate depending on the type of feature and its simplification. In particular larger errors may be overestimated, while good estimates for small errors can be achieved. This makes the bound overall suitable to decide whether simplifying a feature is acceptable or not.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:709584 |
| Date | January 2016 |
| Creators | Rahimi, Amir |
| Publisher | Cardiff University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://orca.cf.ac.uk/99578/ |
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