On the Convergence of a Dual-Primal Substructuring Method

Abstract

In the Dual-Primal FETI method, introduced by Farhat et al., the domain is decomposed into non-overlapping subdomains, but the degrees of freedom on crosspoints remain common to all subdomains adjacent to the crosspoint. The continuity of the remaining degrees of freedom on subdomain interfaces is enforced by Lagrange multipliers and all degrees of freedom are eliminated. The resulting dual problem is solved by preconditioned conjugate gradients. We give an algebraic bound on the condition number, assuming only a single inequality in discrete norms, and use the algebraic bound to show that the condition number is bounded by C(1+log2(H/h)) for both second and fourth order elliptic self-adjoint problems discretized by conforming finite elements, as well as for a wide class of finite elements for the Reissner-Mindlin plate model.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADA436826

Entities

People

  • Jan Mandel
  • Radek Tezaur

Organizations

  • University of Colorado Boulder

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Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Colorado
  • Computational Fluid Dynamics
  • Computational Science
  • Continuity
  • Convergence
  • Differential Equations
  • Equations
  • Euler Equations
  • Formulas (Mathematics)
  • Inequalities
  • Interpolation
  • Mathematics
  • Notation
  • Partial Differential Equations

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  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)