NIFS-518

FULL TEXT (PDF, 585 KB)


Author(s):

J. Chen, N. Nakajima, M. Okamoto

Title:

Shift-and-Inverse Lanczos Algorithm for Ideal MHD Stability Analysis

Date of publication:

Nov. 1997

Key words:

Lanczos recursion with no re-orthogonalization, shift-and-inverse Lanczos recursion, Lanczos Phenomenon, gap stiffness, CAS3D2MN, CAS3D2MNvl

Abstract:

CAS3D and TERPSICHORE have been designed to analyze the global ideal MHD stability of three dimensional equilibria. Their critical part is t,o obtain the smallest eigenvalue and its corresponding eigenvector of a large but sparse real symmetric band matrix. In CAS3D the inverse iteration have been applied to do this and the spectral shift is computed by EISPACK eigensolver. It has been shown that application of such kind of software becomes very expensive in the sense of computational time and storage when matrix order and bandwidth become very large. Here this problem is resolved by using the Lanczos algorithm which is economical in CPU thne and storage and particularly suitable for very large scale problems. The version of CAS3D2MN with shift-and-inverse Lanczos algorithm is called CAS3D2MNvl. Practical calculations in CAS3D2MNvl indicate that the shift-and-inverse Lanczos recursion needs only 15 ~ 20 steps to calculate the smallest eigenvalue. The computation is reliable and efficient. The storage is much smaller and CPU time is saved significantly by 50 ~100 times compared with EISPACK subroutine. Finally the ballooning mode in three dimensional MHD equilibria has been mentioned briefly.

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