“…The mode superposition methods were originally proposed for transient heat diffusion problems [Biot, 1957;Gallagher and Mallet, 1971;Shih and Skladany, 1983], structural dynamics [Clough and Penzien, 1975], and the diffusion-convection equation [Nickell et al, 1979], and make use of a reduced transformation matrix which contains a number of the leftmost eigenvectors of a generalized eigenproblem with the same size as the finite element grid. Several techniques exist for finding the eigenpairs of sparse matrices [e.g., Parlett, 1980;Bathe, 1982;Hughes, 1987] and computer routines are also available [Bathe and Wilson, Paper number 92WR02331.…”