Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems
-
Stefano Giani
,
Luka Grubišić
,
Luca Heltai
und
Ornela Mulita
Abstract
We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is motivated by the analysis of inexact (perturbed) inverse iteration algorithms in numerical linear algebra. We couple the perturbed inverse iteration approach with mesh refinement strategy based on residual estimators. We demonstrate our approach on model problems in two and three dimensions.
Funding source: Hrvatska Zaklada za Znanost
Award Identifier / Grant number: IP-2019-04-6268
Funding statement: Luka Grubišić was supported by the Croatian Science Foundation grant HRZZ IP-2019-04-6268. Luka Grubišić is also thankful to the hospitality of the research visit to Scuola Internazionale Superiore di Studi Avanzati where the work has started. Ornela Mulita is thankful to the University of Zagreb for the hospitality during her collaborative research visit there. Luca Heltai was partially supported by the National Research Projects (PRIN 2017) “Numerical Analysis for Full and Reduced Order Methods for the efficient and accurate solution of complex systems governed by Partial Differential Equations”, funded by the Italian Ministry of Education, University, and Research.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Reliable Methods of Mathematical Modeling
- Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional
- A Priori and a Posteriori Error Analysis of the Crouzeix–Raviart and Morley FEM with Original and Modified Right-Hand Sides
- A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid
- On the Energy Stable Approximation of Hamiltonian and Gradient Systems
- Reliability and Efficiency of DWR-Type A Posteriori Error Estimates with Smart Sensitivity Weight Recovering
- A Locking-Free DPG Scheme for Timoshenko Beams
- Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems
- Energy Contraction and Optimal Convergence of Adaptive Iterative Linearized Finite Element Methods
- Quasi-Optimal and Pressure Robust Discretizations of the Stokes Equations by Moment- and Divergence-Preserving Operators
- Contractive Local Adaptive Smoothing Based on Dörfler’s Marking in A-Posteriori-Steered p-Robust Multigrid Solvers
- Uniform Preconditioners of Linear Complexity for Problems of Negative Order
- An Exact Realization of a Modified Hilbert Transformation for Space-Time Methods for Parabolic Evolution Equations
Artikel in diesem Heft
- Frontmatter
- Reliable Methods of Mathematical Modeling
- Optimal Convergence Rates for Goal-Oriented FEM with Quadratic Goal Functional
- A Priori and a Posteriori Error Analysis of the Crouzeix–Raviart and Morley FEM with Original and Modified Right-Hand Sides
- A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid
- On the Energy Stable Approximation of Hamiltonian and Gradient Systems
- Reliability and Efficiency of DWR-Type A Posteriori Error Estimates with Smart Sensitivity Weight Recovering
- A Locking-Free DPG Scheme for Timoshenko Beams
- Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems
- Energy Contraction and Optimal Convergence of Adaptive Iterative Linearized Finite Element Methods
- Quasi-Optimal and Pressure Robust Discretizations of the Stokes Equations by Moment- and Divergence-Preserving Operators
- Contractive Local Adaptive Smoothing Based on Dörfler’s Marking in A-Posteriori-Steered p-Robust Multigrid Solvers
- Uniform Preconditioners of Linear Complexity for Problems of Negative Order
- An Exact Realization of a Modified Hilbert Transformation for Space-Time Methods for Parabolic Evolution Equations
