A composite collocation method with low-period elongation for structural dynamics problems

This paper presents a novel time integration algorithm for solving linear structural dynamic problems in the framework of the high-order collocation method. When two Gauss points in the integration interval are selected as collocation points, both an A-stable algorithm with third order accuracy and a non-dissipative algorithm with fourth order accuracy can be derived from a second order collocation polynomial. The only difference is that the former obtains a numerical solution at the middle point of the time interval, while the latter has a solution at the end of the interval. A new composite method is established through applying these two algorithms alternately, which combines the advantages of the numerical dissipation property of the third order algorithm and the high-order accuracy of the fourth order algorithm. The usage frequency of the two algorithms during the whole step-by-step integration procedure is an important parameter affecting the numerical dissipation, which is investigated in this study. As the algebraic equations systems solved by the two algorithms are exactly same, no extra computation effort is introduced.