Abstract
The new generation of a generalized family of time discretized operators encompassing implicit and explicit representations that are unconditionally stable and which theoretically inherit Nth-order time accurate features developed in Part 1 are restricted here in Part 2 of the exposition to second-order time accurate operators. As such, unconditionally stable implicit representations are first described followed by unconditionally stable explicit representations. The theoretical design leading to computational algorithms with excellent algorithmic attributes for applicability to practical situations are also addressed for both the implicit and explicit unconditionally stable representations of time discretized operators. Attention is first focused on linear problems and extensions to nonlinear situations are subsequently briefly addressed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 291-329 |
| Number of pages | 39 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 192 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - Jan 17 2003 |
Bibliographical note
Funding 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.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.