A methodology based on a transfer function criterion to evaluate time integration algorithms

A methodology based on a transfer function criterion is developed to evaluate the performance of any time-integration algorithm, avoiding trial calculations. The procedure has been conducted on the frequency domain, comparing the exact transfer function with the numerical ones (developed herein) and, considering the most relevant aspects involved in the time integration techniques. This new criterion has been successfully applied to 18 of the most common time-integration methods in the field of Soil Dynamics. Moreover, three examples with known analytical solutions have been used to validate the conclusions drawn from the transfer function analysis. Finally, through the study of the different transfer functions, two numerical threshold values have been proposed in order to guarantee satisfactory results.

► A methodology to detect in advance and for any general case, how an algorithm could affect the numerical results.
► The influence of the main parameters and its combinations are analysed all together by the transfer function theory.
► This methodology has been successfully used in 18 schemes and three numerical examples.
► This methodology allows us to select the most suitable algorithm for every type of problem.
► Two threshold criteria have been proposed to guarantee satisfactory numerical results.