A two-level spectral preconditioning for the finite element method

An efficient auxiliary space preconditioning (ASP) was proposed for the linear matrix equation that was formed by the frequency-domain finite element method. A new two-level spectral preconditioning utilizing auxiliary space preconditioning is presented to solve the linear system. This technique is...

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Bibliographic Details
Main Authors: Zi He, Weiying Ding, Ningye He, Rushan Chen
Format: Conference Proceeding
Language:English
Subjects:
Convergence
Eigenvalues and eigenfunctions
Equations
Finite element analysis
Iterative methods
Sparse matrices
Vectors
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Summary:An efficient auxiliary space preconditioning (ASP) was proposed for the linear matrix equation that was formed by the frequency-domain finite element method. A new two-level spectral preconditioning utilizing auxiliary space preconditioning is presented to solve the linear system. This technique is a combination of ASP and a low-rank update spectral preconditioning, in which the restarted deflated generalized minimal residual GMRES with the newly constructed spectral two-step preconditioning is considered as the iterative method for solving the system. Numerical experiments indicate that the proposed preconditioning is efficient and can significantly reduce the iteration number.