Beyond Automated Multilevel Substructuring: Domain Decomposition with Rational Filtering

DOI10.1137/17M1154527zbMath1394.65030arXiv1711.09487OpenAlexW2883603641WikidataQ129530302 ScholiaQ129530302MaRDI QIDQ3174778

Vassilis Kalantzis, Yousef Saad, Yuanzhe Xi

Publication date: 18 July 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.09487

zbMATH Keywords

Schur complementdomain decompositionparallel computingsymmetric generalized eigenvalue problemrational filtering

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Parallel numerical computation (65Y05)

Related Items

Multiscale modal analysis of fully-loaded spent nuclear fuel canisters, Complex moment-based eigensolver coupled with two Krylov subspaces, A spectral Newton-Schur algorithm for the solution of symmetric generalized eigenvalue problems, Fast Randomized Non-Hermitian Eigensolvers Based on Rational Filtering and Matrix Partitioning, Efficient Solution of Symmetric Eigenvalue Problems from Families of Coupled Systems, A Domain Decomposition Rayleigh--Ritz Algorithm for Symmetric Generalized Eigenvalue Problems, Distributed Solution of Laplacian Eigenvalue Problems

Uses Software

• ScaLAPACK
• PETSc
• MUMPS
• PRIMME
• FEAST
• SparseMatrix
• MPI
• Scotch

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
• PRIMME
• Designing rational filter functions for solving eigenvalue problems by contour integration
• Spectral Schur complement techniques for symmetric eigenvalue problems
• Nonlinear eigenvalue problems and contour integrals
• On correction equations and domain decomposition for computing invariant subspaces
• Kron's method for symmetric eigenvalue problems
• A projection method for generalized eigenvalue problems using numerical integration.
• Domain decomposition methods for eigenvalue problems
• A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems
• Computing Partial Spectra with Least-Squares Rational Filters
• Feast Eigensolver for Non-Hermitian Problems
• FEAST As A Subspace Iteration Eigensolver Accelerated By Approximate Spectral Projection
• Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
• The university of Florida sparse matrix collection
• Numerical Methods for Large Eigenvalue Problems
• A Hierarchical Low Rank Schur Complement Preconditioner for Indefinite Linear Systems
• The Lanczos Algorithm With Partial Reorthogonalization
• An Implementation and Evaluation of the AMLS Method for Sparse Eigenvalue Problems
• A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• Preconditioned Gradient-Type Iterative Methods in a Subspace for Partial Generalized Symmetric Eigenvalue Problems
• ScaLAPACK Users' Guide
• Domain decomposition approaches for accelerating contour integration eigenvalue solvers for symmetric eigenvalue problems
• A Fast Contour-Integral Eigensolver for Non-Hermitian Matrices
• An Automated Multilevel Substructuring Method for Eigenspace Computation in Linear Elastodynamics
• Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic
• Computation of Smallest Eigenvalues using Spectral Schur Complements
• An Algebraic Substructuring Method for Large-Scale Eigenvalue Calculation