An h-adaptive spacetime-discontinuous Galerkin method for linear elastodynamics

Reza Abedi; Robert B. Haber; Shripad Thite; Jeff Erickson

doi:10.3166/remn.15.619-642

An h-adaptive spacetime-discontinuous Galerkin method for linear elastodynamics

Reza Abedi, Robert B. Haber, Shripad Thite, Jeff Erickson

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

Abstract

We present an h-adaptive version of the spacetime-discontinuous Galerkin (SDG) finite element method for linearized elastodynamics (Abedi et al., 2006). The adaptive version inherits key properties of the basic SDG formulation, including element-wise balance of linear and angular momentum, complexity that is linear in the number of elements and oscillationfree shock capturing. Unstructured spacetime grids allow simultaneous adaptation in space and time. A localized patch-by-patch solution process limits the cost of reanalysis when the error indicator calls for more refinement. Numerical examples demonstrate the method's performance and shock-capturing capabilities.

Original language	English (US)
Pages (from-to)	619-642
Number of pages	24
Journal	European Journal of Computational Mechanics
Volume	15
Issue number	6
DOIs	https://doi.org/10.3166/remn.15.619-642
State	Published - 2006

Keywords

Adaptive analysis
Discontinuous Galerkin
Elastodynamics
Shocks
Spacetime

ASJC Scopus subject areas

Modeling and Simulation
Mechanics of Materials
Mechanical Engineering

Online availability

10.3166/remn.15.619-642

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title = "An h-adaptive spacetime-discontinuous Galerkin method for linear elastodynamics",

abstract = "We present an h-adaptive version of the spacetime-discontinuous Galerkin (SDG) finite element method for linearized elastodynamics (Abedi et al., 2006). The adaptive version inherits key properties of the basic SDG formulation, including element-wise balance of linear and angular momentum, complexity that is linear in the number of elements and oscillationfree shock capturing. Unstructured spacetime grids allow simultaneous adaptation in space and time. A localized patch-by-patch solution process limits the cost of reanalysis when the error indicator calls for more refinement. Numerical examples demonstrate the method's performance and shock-capturing capabilities.",

keywords = "Adaptive analysis, Discontinuous Galerkin, Elastodynamics, Shocks, Spacetime",

author = "Reza Abedi and Haber, {Robert B.} and Shripad Thite and Jeff Erickson",

note = "Funding Information: The authors gratefully acknowledge the contributions of Shuo-Heng Chung, Yong Fan, Michael Garland, and Yuan Zhou to this work. Support from the Center for Process Simulation and Design (CPSD) is gratefully acknowledged. The U.S. National Science Foundation supports research in CPSD via grant NSF DMR 01-21695.",

year = "2006",

doi = "10.3166/remn.15.619-642",

language = "English (US)",

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journal = "European Journal of Computational Mechanics",

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AU - Abedi, Reza

AU - Haber, Robert B.

AU - Thite, Shripad

AU - Erickson, Jeff

N1 - Funding Information: The authors gratefully acknowledge the contributions of Shuo-Heng Chung, Yong Fan, Michael Garland, and Yuan Zhou to this work. Support from the Center for Process Simulation and Design (CPSD) is gratefully acknowledged. The U.S. National Science Foundation supports research in CPSD via grant NSF DMR 01-21695.

PY - 2006

Y1 - 2006

N2 - We present an h-adaptive version of the spacetime-discontinuous Galerkin (SDG) finite element method for linearized elastodynamics (Abedi et al., 2006). The adaptive version inherits key properties of the basic SDG formulation, including element-wise balance of linear and angular momentum, complexity that is linear in the number of elements and oscillationfree shock capturing. Unstructured spacetime grids allow simultaneous adaptation in space and time. A localized patch-by-patch solution process limits the cost of reanalysis when the error indicator calls for more refinement. Numerical examples demonstrate the method's performance and shock-capturing capabilities.

AB - We present an h-adaptive version of the spacetime-discontinuous Galerkin (SDG) finite element method for linearized elastodynamics (Abedi et al., 2006). The adaptive version inherits key properties of the basic SDG formulation, including element-wise balance of linear and angular momentum, complexity that is linear in the number of elements and oscillationfree shock capturing. Unstructured spacetime grids allow simultaneous adaptation in space and time. A localized patch-by-patch solution process limits the cost of reanalysis when the error indicator calls for more refinement. Numerical examples demonstrate the method's performance and shock-capturing capabilities.

KW - Adaptive analysis

KW - Discontinuous Galerkin

KW - Elastodynamics

KW - Shocks

KW - Spacetime

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An h-adaptive spacetime-discontinuous Galerkin method for linear elastodynamics

Abstract

Keywords

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