Component-Based Reduced Basis for Eigenproblems

Abstract

A component-based approach is introduced for fast and flexible solution of parameter-dependent eigenproblems. We consider a shifted version of the eigenproblem where the left hand side operator corresponds to an equilibrium between the stiffness operator and a weighted mass operator. This permits to apply the Static Condensation Reduced Basis Element method, a domain synthesis approach with reduced basis approximation at the intradomain level. We provide eigenvalue a posteriori error estimators and we present various numerical results of modal analysis of structures. We are able to obtain several orders of magnitude speed-up compared to a classical Finite Element Method.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 17, 2013
Accession Number
ADA587593

Entities

People

  • A. T. Patera
  • D. B. Huynh
  • D. J. Knezevic
  • S. Vallaghe

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computational Science
  • Computations
  • Condensation
  • Connectors
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Elastic Properties
  • Equations
  • Estimators
  • Frequency
  • Mechanics
  • Modulus Of Elasticity
  • Partial Differential Equations
  • Vibration

Fields of Study

  • Engineering

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Software Engineering.