Exploiting Multilevel Preconditioning Techniques in Eigenvalue Computations

摘要: In the Davidson method, any preconditioner can be exploited for iterative computation of eigenpairs. However, convergence eigenproblem solver may poor a high quality preconditioner. Theoretically, this counter-intuitive phenomenon with method is remedied by Jacobi--Davidson approach, where preconditioned system restricted to appropriate subspaces codimension one. it not clear how solved accurately and efficiently in case good The obvious approach introduces instabilities that hamper convergence. In paper, we show incomplete decomposition based on multilevel approaches used stable way. We also these preconditioners improved when better approximations eigenvalue interest become available. additional costs updating are negligible. Furthermore, our leads initial guess wanted eigenpair nearby eigenvalues. illustrate ideas MRILU