A scalable two-level domain decomposition eigensolver for periodic Schrödinger eigenstates in anisotropically expanding domains
DOI10.1137/23m161848xMaRDI QIDQ6623717
Lambert Theisen, Benjamin Stamm
Publication date: 24 October 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
finite element methoddomain decompositionpreconditioningSchrödinger equationiterative methodscoarse spaces
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convergence of inexact inverse iteration with application to preconditioned iterative solvers
- Domain decomposition methods for the numerical solution of partial differential equations
- Domain decomposition methods for eigenvalue problems
- Homogenization of a spectral problem in neutronic multigroup diffusion.
- Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2D
- Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. III.
- The \(J\)-method for the Gross-Pitaevskii eigenvalue problem
- Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation
- A robust and efficient line search for self-consistent field iterations
- On the scalability of the Schwarz method
- A novel domain decomposition framework for the ground state solution of Bose-Einstein condensates
- Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet-to-Neumann maps
- Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps
- Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method
- The Finite Element Method: Theory, Implementation, and Applications
- Two-Level Discretization Techniques for Ground State Computations of Bose-Einstein Condensates
- Julia: A Fresh Approach to Numerical Computing
- Deflation of Conjugate Gradients with Applications to Boundary Value Problems
- Domain Decomposition Preconditioners for Multiscale Flows in High-Contrast Media
- Analysis of a Quadratic Programming Decomposition Algorithm
- Domain Decomposition Preconditioners for Multiscale Flows in High Contrast Media: Reduced Dimension Coarse Spaces
- Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton's Method
- Toward Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations
- An Introduction to Domain Decomposition Methods
- Templates for the Solution of Algebraic Eigenvalue Problems
- Domain decomposition approaches for accelerating contour integration eigenvalue solvers for symmetric eigenvalue problems
- Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-sized Subdomains: Part II
- An Automated Multilevel Substructuring Method for Eigenspace Computation in Linear Elastodynamics
- A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
- Energy-adaptive Riemannian optimization on the Stiefel manifold
- Iterative Methods and Preconditioners for Systems of Linear Equations
- A Robust Algebraic Multilevel Domain Decomposition Preconditioner for Sparse Symmetric Positive Definite Matrices
- Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency
- Adaptive GDSW Coarse Spaces for Overlapping Schwarz Methods in Three Dimensions
- Analysis of the divide-and-conquer method for electronic structure calculations
- New Developments in Molecular Orbital Theory
- Methods of conjugate gradients for solving linear systems
- Analysis of the Schwarz Domain Decomposition Method for the Conductor-like Screening Continuum Model
- Convergence Analysis of Direct Minimization and Self-Consistent Iterations
- A Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains
- Density Functional Theory
- Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices
- Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems
- The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem
- On Optimal Convergence Rates for Discrete Minimizers of the Gross–Pitaevskii Energy in Localized Orthogonal Decomposition Spaces
- BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation
- Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems
- Modified-operator method for the calculation of band diagrams of crystalline materials
- Fully algebraic domain decomposition preconditioners with adaptive spectral bounds
- Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-\(\kappa\) regime
- Riemannian Newton methods for energy minimization problems of Kohn-Sham type
This page was built for publication: A scalable two-level domain decomposition eigensolver for periodic Schrödinger eigenstates in anisotropically expanding domains