A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics Part I. Formulation Original Research Article

A new class of time integration algorithms for dynamics is presented. The algorithms are based on finite element in time. The equations of motion are expressed in first-order form and the variables are interpolated via time polynomials. The unknown nodal variables are solved by the generalized Galerkin method. Algorithms of any desired order of time accuracy can be achieved by proper choice of the finite element interpolation in time. The salient feature of the algorithms is that it can be either asymptotic annihilating or non-dissipative. Besides, any desired algorithmic damping between these two extreme cases could be obtained. The algorithms are analysed in detail. The spectral characteristics equivalent to the upper diagonal, diagonal of the Padé approximations and other rational approximations are given.