A Parallel Augmented Subspace Method for Eigenvalue Problems

A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in the multigrid method, solving the ei...

[1]  I. Babuska,et al.  Finite element-galerkin approximation of the eigenvalues and Eigenvectors of selfadjoint problems , 1989 .

[2]  Hehu Xie,et al.  A type of multilevel method for the Steklov eigenvalue problem , 2014 .

[3]  Randolph E. Bank,et al.  An optimal order process for solving finite element equations , 1981 .

[4]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[5]  J. Pasciak,et al.  New convergence estimates for multigrid algorithms , 1987 .

[6]  Hamilton-Jacobi Equations,et al.  Multigrid Methods for , 2011 .

[7]  Hehu Xie,et al.  A multi-level correction scheme for eigenvalue problems , 2011, Math. Comput..

[8]  Hehu Xie,et al.  A full multigrid method for eigenvalue problems , 2016, J. Comput. Phys..

[9]  G. Burton.  Sobolev Spaces , 2013 .

[10]  Andrew Knyazev,et al.  Preconditioned Eigensolvers - an Oxymoron? , 1998 .

[11]  Jinchao Xu,et al.  Iterative Methods by Space Decomposition and Subspace Correction , 1992, SIAM Rev..

[12]  Andrew V. Knyazev,et al.  A subspace preconditioning algorithm for eigenvector/eigenvalue computation , 1995, Adv. Comput. Math..

[13]  A. Knyazev,et al.  Efficient solution of symmetric eigenvalue problems using multigridpreconditioners in the locally optimal block conjugate gradient method , 2001 .

[14]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[15]  F. Chatelin.  Spectral approximation of linear operators , 2011 .

[16]  Hehu Xie,et al.  A Multilevel Correction Type of Adaptive Finite Element Method for Eigenvalue Problems , 2012, SIAM J. Sci. Comput..

[17]  Vicente Hernández,et al.  SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems , 2005, TOMS.

[18]  Hehu Xie,et al.  Fast Eigenpairs Computation with Operator Adapted Wavelets and Hierarchical Subspace Correction , 2018, SIAM J. Numer. Anal..

[19]  Herbert L. Strauss,et al.  Quantum Mechanics, an Introduction , 1968 .

[20]  James H. Bramble,et al.  The analysis of multigrid methods , 2000 .

[21]  Wolfgang Hackbusch,et al.  On the Computation of Approximate Eigenvalues and Eigenfunctions of Elliptic Operators by Means of a Multi-Grid Method , 1979 .

[22]  Sophia Blau,et al.  Analysis Of The Finite Element Method , 2016 .

[23]  D. Sorensen.  Numerical methods for large eigenvalue problems , 2002, Acta Numerica.

[24]  E. D'yakonov,et al.  Minimization of the computational labor in determining the first eigenvalues of differential operators , 1980 .

[25]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[26]  Andrew V. Knyazev,et al.  Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method , 2001, SIAM J. Sci. Comput..

[27]  Merico E. Argentati,et al.  Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc , 2007, SIAM J. Sci. Comput..

[28]  Jinchao Xu.  A new class of iterative methods for nonselfadjoint or indefinite problems , 1992 .

[29]  Hehu Xie,et al.  A full multigrid method for eigenvalue problems , 2014, J. Comput. Phys..

[30]  D. Sorensen.  IMPLICITLY RESTARTED ARNOLDI/LANCZOS METHODS FOR LARGE SCALE EIGENVALUE CALCULATIONS , 1996 .