The value of numerical amplification matrices in time integration methods

摘要

Several frequently overlooked concepts in linear elastodynamics are reviewed. First that the amplification matrix may be obtained numerically and if obtained this way, it may give some extra information on the programmed algorithm. Second that the adequate dimension of that matrix depends on the algorithm at hand. Such dimension equals the number of independent initial conditions that must be prescribed. Third that those initial conditions should be consistent with the problem at hand and with the algorithm. Overshooting phenomena present in some time integration algorithms may be a consequence of overlooking such issues.