On a novel design of a new unified variational framework of discontinuous/continuous time operators of high order and equivalence

Ramdev Kanapady; Kumar K. Tamma

doi:10.1016/S0168-874X(03)00056-8

On a novel design of a new unified variational framework of discontinuous/continuous time operators of high order and equivalence

Ramdev Kanapady, Kumar K. Tamma

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper we present a novel design of a unified variational framework for both time continuous and discontinuous integration operators and also discuss in particular their equivalence via their respective spectral properties. As an added dimension, we also describe how the proposed approach enables the design of both time continuous/discontinuous high-order A-Stable schemes of order 2q, L-Stable schemes of order 2q - 1 and 2q - 2, and subsequently provide the requisite hierarchical computational structure of the resulting equations that is useful for time adaptive computations. In this regard, a new unified set of energy conserving and energy dissipating time discretized operators are described for both time continuous and discontinuous formulations for computational dynamics. Although the emphasis is placed on second-order systems, the developments also hold for first-order system representations.

Original language	English (US)
Pages (from-to)	727-749
Number of pages	23
Journal	Finite elements in analysis and design
Volume	39
Issue number	8
DOIs	https://doi.org/10.1016/S0168-874X(03)00056-8
State	Published - May 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 no. 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 contact no. DAAD19-01-2-0014. 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. Raju Namburu and Dr. Andrew Mark 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.

Keywords

Bi-discontinuous formulations
Continuous and discontinuous Galerkin and Petrov-Galerkin methods
Continuous/discontinuous time operators
High-order time integration operators
Weighted residual method

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10.1016/S0168-874X(03)00056-8

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abstract = "In this paper we present a novel design of a unified variational framework for both time continuous and discontinuous integration operators and also discuss in particular their equivalence via their respective spectral properties. As an added dimension, we also describe how the proposed approach enables the design of both time continuous/discontinuous high-order A-Stable schemes of order 2q, L-Stable schemes of order 2q - 1 and 2q - 2, and subsequently provide the requisite hierarchical computational structure of the resulting equations that is useful for time adaptive computations. In this regard, a new unified set of energy conserving and energy dissipating time discretized operators are described for both time continuous and discontinuous formulations for computational dynamics. Although the emphasis is placed on second-order systems, the developments also hold for first-order system representations.",

keywords = "Bi-discontinuous formulations, Continuous and discontinuous Galerkin and Petrov-Galerkin methods, Continuous/discontinuous time operators, High-order time integration operators, Weighted residual method",

author = "Ramdev Kanapady and Tamma, {Kumar K.}",

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 no. 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 contact no. DAAD19-01-2-0014. 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. Raju Namburu and Dr. Andrew Mark 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.",

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AB - In this paper we present a novel design of a unified variational framework for both time continuous and discontinuous integration operators and also discuss in particular their equivalence via their respective spectral properties. As an added dimension, we also describe how the proposed approach enables the design of both time continuous/discontinuous high-order A-Stable schemes of order 2q, L-Stable schemes of order 2q - 1 and 2q - 2, and subsequently provide the requisite hierarchical computational structure of the resulting equations that is useful for time adaptive computations. In this regard, a new unified set of energy conserving and energy dissipating time discretized operators are described for both time continuous and discontinuous formulations for computational dynamics. Although the emphasis is placed on second-order systems, the developments also hold for first-order system representations.

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On a novel design of a new unified variational framework of discontinuous/continuous time operators of high order and equivalence

Abstract

Bibliographical note

Keywords

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