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A Virtual Control Coupling Approach for Problems with Non-coincident Discrete Interfaces

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10665)

Abstract

Independent meshing of subdomains separated by an interface can lead to spatially non-coincident discrete interfaces. We present an optimization-based coupling method for such problems, which does not require a common mesh refinement of the interface, has optimal \(H^1\) convergence rates, and passes a patch test. The method minimizes the mismatch of the state and normal stress extensions on discrete interfaces subject to the subdomain equations, while interface “fluxes” provide virtual Neumann controls.

Keywords

  • PDE constrained optimization
  • Mesh tying
  • Transmission
  • Non-coincident interfaces
  • Optimal control
  • Virtual Neumann controls

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Acknowledgments

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, and the Laboratory Directed Research and Development program at Sandia National Laboratories.

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Correspondence to Pavel Bochev .

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Bochev, P., Kuberry, P., Peterson, K. (2018). A Virtual Control Coupling Approach for Problems with Non-coincident Discrete Interfaces. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_15

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_15

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-73441-5

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