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Subspace correction multi-level methods for elliptic eigenvalue problems. (English) Zbl 1071.65549

Summary: We apply the ideas of domain decomposition and multi-grid methods to PDE-based eigenvalue problems represented in two equivalent variational formulations. To find the lowest eigenpair, we use a “subspace correction” framework for deriving the multiplicative algorithm for minimizing the Rayleigh quotient of the current iteration. By considering an equivalent minimization formulation proposed by G. Mathew and V. Reddy [IEEE Trans. Signal Process. 42, 663–673 (1994)], we can use the theory of multiplicative Schwarz algorithms for non-linear optimization developed by X.-C. Tai and M. Espedal [SIAM J. Numer. Anal. 35, 1558–1570 (1998; Zbl 0915.65063)] to analyse the convergence properties of the proposed algorithm. We discuss the application of the multiplicative algorithm to the problem of simultaneous computation of several eigenfunctions also formulated in a variational form. Numerical results are presented.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms

Citations:

Zbl 0915.65063
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References:

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