The objectives and motivation of the exposition presented in Parts 1 and 2 are to fundamentally describe from new perspectives the generic design, development and formal theory towards a new generation of a generalized family of time discretized operators possessing excellent algorithmic attributes as related to the notion of stability and accuracy, and, which also closely mimic the properties of the exact solution of dynamic systems including providing practically useful forms. Subsequently, avenues that also lead to various other time discretized operators are described. In Part 1, the generalized theoretical developments and representations of time discretized operators which theoretically inherit Nth order accuracy for dynamic systems is first designed and proposed which encompass both implicit and explicit unconditionally stable representations of the time discretized operators. Whereas Part 1 primarily focuses on the fundamental theoretical developments and rigor of the generalized representations as related to stability, accuracy and the like, in Part 2 we specifically focus attention towards practical second-order time accurate representations including also assessing the algorithmic attributes and extensions to nonlinear situations. Also described as particular cases are the consequences leading to various other time discretized operators. Simple illustrative numerical examples are then presented to demonstrate the excellent algorithmic and numerical properties of selected implicit and explicit secondorder time discretized operators which closely mimic the properties of the exact solutions including nonlinear dynamic response situations.
|Original language||English (US)|
|Number of pages||34|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Jan 17 2003|
Bibliographical noteFunding Information:
The authors are very pleased to acknowledge support in part by Battelle/US Army Research Office (ARO) Research Triangle Park, North Carolina, under grant number DAAH04-96-C-0086, and by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army, Army Research Laboratory (ARL) under contract number DAAD19-01-2-0014. Dr. Raju Namburu is the technical monitor. The content does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. Support in part by Dr. Andrew Mark and Dr. Raju Namburu of the IMT and CSM Computational Technical Activities and the ARL/MSRC facilities is also gratefully acknowledged. Special thanks are due to the CIS Directorate at the US Army Research Laboratory (ARL), Aberdeen Proving Ground, Maryland. Other related support in form of computer grants from the Minnesota Supercomputer Institute (MSI), Minneapolis, Minnesota is also gratefully acknowledged.