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

  • Pavel BochevEmail author
  • Paul Kuberry
  • Kara Peterson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10665)


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.


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



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.


  1. 1.
    Farhat, C., Lesoinne, M., Tallec, P.L.: Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput. Methods Appl. Mech. Engrg. 157(1–2), 95–114 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    de Boer, A., van Zuijlen, A., Bijl, H.: Review of coupling methods for non-matching meshes. Comput. Methods Appl. Mech. Engrg. 196(8), 1515–1525 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dohrmann, C.R., Key, S.W., Heinstein, M.W.: A method for connecting dissimilar finite element meshes in two dimensions. Int. J. Numer. Meth. Eng. 48(5), 655–678 (2000)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dohrmann, C.R., Key, S.W., Heinstein, M.W.: Methods for connecting dissimilar three-dimensional finite element meshes. Int. J. Numer. Meth. Eng. 47(5), 1057–1080 (2000)CrossRefzbMATHGoogle Scholar
  5. 5.
    Gunzburger, M.D., Peterson, J.S., Kwon, H.: An optimization based domain decomposition method for partial differential equations. Comput. Math. Appl. 37(10), 77–93 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gunzburger, M.D., Lee, H.K.: An optimization-based domain decomposition method for the Navier-Stokes equations. SIAM J. Numer. Anal. 37(5), 1455–1480 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Laursen, T.A., Heinstein, M.W.: Consistent mesh tying methods for topologically distinct discretized surfaces in non-linear solid mechanics. Int. J. Numer. Meth. Eng. 57(9), 1197–1242 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Parks, M., Romero, L., Bochev, P.: A novel lagrange-multiplier based method for consistent mesh tying. Comput. Methods Appl. Mech. Engrg. 196(35–36), 3335–3347 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Hecht, F.: New development in FreeFem++. J. Numer. Math. 20(3–4), 251–265 (2012)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Bochev, P., Ridzal, D.: Optimization-based additive decomposition of weakly coercive problems with applications. Comput. Math. with Appl. 71(11), 2140–2154 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© US Government (outside the US) 2018

Authors and Affiliations

  1. 1.Center for Computational ResearchSandia National LaboratoriesAlbuquerqueUSA

Personalised recommendations