The immersed boundary method as an inverse problem
Authors
Yan, Jianfeng
ORCID
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Other Contributors
Hicken, Jason
Henshaw, William D.
Sahni, Onkar
Zhang, Lucy T.
Henshaw, William D.
Sahni, Onkar
Zhang, Lucy T.
Issue Date
2020-08
Keywords
Aeronautical engineering
Degree
PhD
Terms of Use
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
Abstract
problem formulation is shown to be ill-posed. The ill-posedness is addressed by two complimentary strategies. The first strategy is to ensure that the enclosing domain tends to the true domain as the mesh is refined. The second strategy is to include a specialized, parameter-free regularization that is based on penalizing the difference between the control and the state on the boundary. The proposed inverse IBM is applied to the diffusion, advection, advection-diffusion, and linear elasticity equations using a high-order discontinuous Galerkin (DG) discretization. The numerical experiments demonstrate that the regularized scheme achieves optimal rates of convergence and that the reduced Hessian of the optimization problem has a bounded condition number as the mesh is refined.
Description
August 2020
School of Engineering
School of Engineering
Department
Dept. of Mechanical, Aerospace, and Nuclear Engineering
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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