Error estimation for simplifications of electrostatic models

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Rahimi, Amir;
  • Subject: QA75

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 simplificat... View more
  • References (17)
    17 references, page 1 of 2

    2.2 Defeaturing and Simplification Approaches . . . . . . . . . . . . . . 19 2.2.1 Surfaced Entity Based Techniques . . . . . . . . . . . . . . . 19 2.2.2 Volume Entity Based Features . . . . . . . . . . . . . . . . . 22 2.2.3 Explicit Entity Based Features . . . . . . . . . . . . . . . . . 23 2.2.4 CAD Model Dimension Reduction . . . . . . . . . . . . . . . 24 2.3 A Posteriori Error Estimation . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Adjoint Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5 Simplification Error Estimation . . . . . . . . . . . . . . . . . . . . . 31

    3 Electrostatic Problems 37 3.1 Variational Formulation and Finite Element Analysis for Electrostatics 41 3.2 Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    4 Goal-Oriented Simplification Error Estimation 49 4.1 Defeaturing and Model Simplification . . . . . . . . . . . . . . . . . 49 4.2 A Posteriori Error Estimation . . . . . . . . . . . . . . . . . . . . . . 51 4.2.1 Quantity of Interest (QoI) Error Estimation . . . . . . . . . . 52 4.2.2 Dual (adjoint) Model . . . . . . . . . . . . . . . . . . . . . . 56 4.2.3 Bounding Error in Constitutive Relation Error . . . . . . . . . 58

    5 Simplification Error Estimation for Different Feature Types of a Capacitor 63 5.1 Quantity of Interest (QoI) for Electrostatics Problems . . . . . . . . . 63 5.2 Internal Feature Simplification Error Estimation . . . . . . . . . . . . 64 5.3 Simplification Error Estimation for Boundary Features of a Capacitor 67 Conclusions and Future Work 109 7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

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