OVERSHOOT OPTIMIZED NEWMARK-TYPE METHODS

Abstract

We propose a parameter set for the generalized-α class of time integration methods that allows to keep the beneficial damping properties of the algorithm including controllable dissipation of high frequency oscillations as well as second order of convergence for a large problem class. The benefits of the new parameter set are that the introduction of an additional parameter allows to lessen the
overshoot behavior in the transient phase leading to a more robust time integration. To assess the performance of the new parameters, we give a numerically tractable definition of overshoot for the class of algorithms and analyze the methods in terms of a multicriteria optimization problem taking overshoot as well as beneficial damping into account. Using nonlinear scalarization techniques, we
can then obtain full insight in how well the methods can perform and evaluate the classical as well as the new parameter sets. Some numerical test examples illustrate the findings.