A Posteriori Error Estimation for Interface Simplifications in Elliptic Problems
17th World Congress on Computational Mechanics (WCCM), Munich, Germany
Simplifying complex computational geometries, also called defeaturing, is essential in industrial simulation pipelines. Defeaturing simplifies the meshing process and reduces the computational complexity of the simulation. Standard defeaturing methods typically rely on geometric criteria and ignore the underlying physics. In contrast, analysis-aware defeaturing offers a posteriori error estimates for geometry simplifications. It does so by combining the defeatured simulation output with the exact geometry information to guide the process. Introduced by Buffa, Chanon, and Vázquez for a single geometrical feature subject to Neumann boundary conditions in Poisson problems, the analysis-aware defeaturing framework has since been extended to various settings: multiple Neumann features in linear elasticity and Stokes flow problems, features subject to Dirichlet conditions, goal-oriented estimates, and adaptivity in combination with a posteriori estimates for the numerical error. However, the latter works only deal with geometrical features located on the boundary of the domain. In this work, we consider geometry simplifications of complex material interfaces within a computational domain. Even when interfaces are handled using immersed methods, accurately resolving complex features still requires expensive quadrature rules. Consequently, defeaturing remains an effective means of reducing the overall computational cost. In this context, we derive a reliable a posteriori estimator for the combined defeaturing and numerical error for a Poisson model problem with discontinuous diffusion coefficients. To capture the numerical component of the error, we employ a standard equilibrated flux reconstruction. To address the defeaturing error, we develop a reliable indicator by adapting the arguments from the boundary feature case to the interface case. In particular, we prove that the indicator’s effectivity index is independent of the feature’s size. This robustness is crucial for comparing features of different scales. Finally, we validate our approach through extensive numerical experiments.
Analysis-Aware Defeaturing of Dirichlet Features in Poisson Problems
13th International Conference on Isogeometric Analysis (IGA 2025), Eindhoven, Netherlands
Talk on certified a posteriori defeaturing error estimation, including goal-oriented estimates and features subject to Dirichlet boundary conditions.
Defeaturing Error Estimates for Poisson Problems with Dirichlet Features
14th European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Heidelberg, Germany
Geometry simplification, also known as defeaturing, is crucial for industrial simulations. It not only simplifies the meshing process but also reduces the computational costs of subsequent simulations by decreasing the number of degrees of freedom. Traditional defeaturing methods often rely on geometric criteria alone, overlooking the underlying physics of the problem. In contrast, analysis-aware defeaturing employs a posteriori error estimation, combining the defeatured simulation outputs with the exact geometry information to better inform the defeaturing process.
Analysis-Aware Defeaturing of Dirichlet Features in Poisson Problems
Schweizer Numerik Kolloquium, Basel, Switzerland
Talk on analysis-aware defeaturing of Dirichlet features in Poisson problems, including goal-oriented estimates. The abstract of the talk can be found here.
Galerkin Neural Network-POD for Acoustic and Electromagnetic Wave Propagation
16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Berlin, Germany
Talk on the POD-NN method for wave propagation in parameterized domains based on this preprint. The abstract of the talk can be found here.