Issue link: https://resources.randsim.com/i/1492512
KRYLOV Method • Build subspace (Q) to reduce FEA model – Step 1 → Form K, M, C, and f at middle of the specified frequency range (ω 0 ) → symbolic assembly → .full file – Step 2 → Form Ǩ and Č where Ǩ(ω 0 ) = K - ω 0 2 M + iω 0 C and Č(ω 0 ) = C + 2iω 0 M – Step 3 → Factor Ǩ -1 using direct solver – Step 4 → Compute v 1 = g 1 /|g 1 | where g 1 = Ǩ -1 f and f(ω 0 ) = f r + if i – Step 5 → Compute v 2 = ǧ 2 /|ǧ 2 | where ǧ 2 =ǧ 2 –(v 1 •ǧ 2 )v 1 ǧ 2 = g 2 /|g 2 | and g 2 = –Ǩ -1 Čg 1 – Step 6 → Compute v n = ǧ n /|ǧ n | where ǧ n =ǧ n –(v n-1 •ǧ n )v 1 ǧ n = g n /|g n | and g n = –Ǩ -1 (Čg n-1 + Mg n-2 ) for n=3,dimQ • Steps 5 & 6 use Modified Gram-Schmidt Orthonormalization ‐ Generates a set of complex-value basis vectors {v 1 ,v 2 ,…,v n } that are almost orthonormal ‐ Structure preserving dimension reduction → subspace Q = span(v 1 , v 2 ,…,v n ) is used to reduce the harmonic FEA