ACCELERATED SUBSPACE ITERATION METHOD FOR GEN-ERALIZED EIGENPROBLEMS USING DYNAMIC CONDENSA-TION TECHNIQUE

Ｎ－ＥＲＡＬＩＺＥＤ ＥＩＧＥＮＰＲＯＢＬＥＭＳ ＵＳＩＮＧ ＤＹＮＡＭＩＣ ＣＯＮＤＥＮＳＡ－ＴＩＯＮ ＴＥＣＨＮＩＱＵＥTX＠瞿祖清＠华宏星＠傅志方ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｏｂｌｅｍｏｆｄｅｔｅｒｍｉｎｉｎｇａｓｕｆｉｃｉｅｎｔｎｕｍｂｅｒｏｆ...

ACCELERATED SUBSPACE ITERATION METHOD FOR GENERALIZED EIGENPROBLEMS USING DYNAMIC CONDENSATION TECHNIQUE

The subspace iteration method is a method which combines the simultaneous inverse iteration method and the Rayleigh Ritz procedure. Since the Rayleigh Ritz procedure is usually time consuming, the solution time used in the subspace iteration method rises rapidly as the dimension of the subspace increases. An accelerated subspace iteration method for generalized eigenproblems is derived by obtaining a new subspace. The new subspace is composed of a dynamic condensation matrix, which relates the deformations associated with the master and slave degrees of freedom of a full model, and an identity matrix. Since the new subspace has nothing to do with the eigenpairs of the reduced model, there is no need to adopt the Rayleigh Ritz procedure in every iteration. This makes the proposed method computationally much more efficient and easier to be accelerated. The accelerated method converges any integer times as fast as the basic subspace iteration method. An eigenvalue shifting technique is also applied to make the stiffness matrix non singular, to accelerate the convergence and to calculate the eigenpairs in any given frequency range. Numerical examples demonstrate that the proposed method is feasible.