The method of finite spheres in acoustic wave propagation through nonhomogeneous media: Inf-sup stability conditions

Williams L. Nicomedes, Klaus-Jürgen Bathe, Fernando J. S. Moreira, Renato C. Mesquita
Author affiliations

Authors

  • Williams L. Nicomedes Graduate Program in Electrical Engineering, Federal University of Minas Gerais, Belo Horizonte MG, Brazil
  • Klaus-Jürgen Bathe Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA, USA
  • Fernando J. S. Moreira Department of Electronics Engineering, Federal University of Minas Gerais, Belo Horizonte MG, Brazil
  • Renato C. Mesquita Department of Electronics Engineering, Federal University of Minas Gerais, Belo Horizonte MG, Brazil

DOI:

https://doi.org/10.15625/0866-7136/15336

Keywords:

acoustic waves, finite elements, finite spheres, inf-sup conditions, meshfree methods

Abstract

When the method of finite spheres is used for the solution of time-harmonic acoustic wave propagation problems in nonhomogeneous media, a mixed (or saddle-point) formulation is obtained in which the unknowns are the pressure fields and the Lagrange multiplier fields defined at the interfaces between the regions with distinct material properties. Then certain inf-sup conditions must be satisfied by the discretized spaces in order for the finite-dimensional problems to be well-posed. We discuss in this paper the analysis and use of these conditions. Since the conditions  involve norms of functionals in fractional Sobolev spaces, we derive ‘stronger’ conditions that are simpler in form. These new conditions pave the way for the inf-sup testing, a tool for assessing the stability of the discretized problems.

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Published

27-09-2020

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Scientific articles dedicated to Professor J.N. Reddy