A reduced order model for the finite element approximation of eigenvalue problems
Fleurianne Bertrand, Daniele Boffi, Abdul Halim
Abstract
In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious time parameter. We use a POD approach and we present some theoretical results showing how to choose the optimal dimension of the POD basis. The results of our computations confirm the optimal behavior of our approximate solution. We compute the first eigenvalue and discuss how to approximate the next eigenmodes.
Topics & Concepts
Finite element methodEigenvalues and eigenvectorsOrder (exchange)Applied mathematicsMathematicsMixed finite element methodMathematical optimizationMathematical analysisCalculus (dental)PhysicsStructural engineeringEngineeringEconomicsFinanceDentistryMedicineQuantum mechanicsModel Reduction and Neural NetworksAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical Methods