6533b86efe1ef96bd12cb280
RESEARCH PRODUCT
Computation of a few smallest eigenvalues of elliptic operators using fast elliptic solvers
Janne MartikainenJanne MartikainenTuomo RossiJari Toivanensubject
Applied MathematicsNumerical analysisMathematical analysisMathematicsofComputing_NUMERICALANALYSISGeneral EngineeringLanczos algorithmElliptic curveLanczos resamplingElliptic operatorMultigrid methodComputational Theory and MathematicsModeling and SimulationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONOrthogonalizationSoftwareEigenvalues and eigenvectorsMathematicsdescription
The computation of a few smallest eigenvalues of generalized algebraic eigenvalue problems is studied. The considered problems are obtained by discretizing self-adjoint second-order elliptic partial differential eigenvalue problems in two- or three-dimensional domains. The standard Lanczos algorithm with the complete orthogonalization is used to compute some eigenvalues of the inverted eigenvalue problem. Under suitable assumptions, the number of Lanczos iterations is shown to be independent of the problem size. The arising linear problems are solved using some standard fast elliptic solver. Numerical experiments demonstrate that the inverted problem is much easier to solve with the Lanczos algorithm that the original problem. In these experiments, the underlying Poisson and elasticity problems are solved using a standard multigrid method. Copyright © 2001 John Wiley & Sons, Ltd.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-07-17 | Communications in Numerical Methods in Engineering |