Abstract: An apparatus, system, and method may operate to solve a first equation associated with a structure of the form {??2MR+i?BR+[(1+i?)KR+i(K4R)]}Y=FR. The apparatus and system may include a definition module to define an intermediate matrix C=(1+i?)LM?1KRLM?T+iLM?1K4RLM?T, a first computation module to compute a plurality of eigenvalues and eigenvectors for a second equation C?C=?C?C, a second computation module to compute a matrix P=?CTLM?1UR and a matrix R=VRTLM?T?C, an equation solving module to solve a third equation of the form (D(?)+PQ(?)R)Z=?CTLM?1FR for Z, wherein D(?)=??2I+?C and Q(?)=i??R, and a product formation module to form a product Y=LM?T?CZ, wherein the product Y is a matrix having a plurality of vectors corresponding to the plurality of load vectors acting on the structure and included in the matrix F.