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Hybridizable discontinuous Galerkin method for solid mechanics.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Hybridizable discontinuous Galerkin method for solid mechanics./
Author:	Soon, SeeChew.
Description:	1 online resource (129 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 70-06, Section: B.
Contained By:	Dissertations Abstracts International70-06B.
Subject:	Civil engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9780549851974

Hybridizable discontinuous Galerkin method for solid mechanics.
Soon, SeeChew.

Hybridizable discontinuous Galerkin method for solid mechanics. - 1 online resource (129 pages)

Source: Dissertations Abstracts International, Volume: 70-06, Section: B.

Thesis (Ph.D.)--University of Minnesota, 2008.

Includes bibliographical references

In this Thesis, this criticism is addressed in the framework of second-order scalar elliptic equation, linear elasticity, and large-deformation elasticity by studying the so-called hybridizable discontinuous Galerkin (HDG) method. This method can be classified as a dual hybrid-mixed method whose new and most attractive feature is that it can be implemented more efficiently than any other known DG method for the same level of accuracy. This can be attributed to two main reasons. The first is that only the degrees of freedom associated with the approximation of the primary unknown (e.g., pressure, temperature, displacement) on the element boundaries, known as the hybrid unknown, are globally coupled. Moreover, since the corresponding stiffness matrix is symmetric, positive definite, and has a block-wise sparse structure, the method is easy to implement in the context of parallel and distributive computing. The second reason is that when polynomials of degree k are used for both the primary (e.g., pressure, temperature, displacement) and secondary (e.g., velocity, heat flux, stress) unknowns, both approximations converge with the optimal order of k + 1 for k ≥ 0. All other known DG methods provide a secondary unknown converging with order k and only for k ≥ 1. In addition, if k ≥ 2, an element-by-element post-processing generates a new approximation for primary unknown, which converges with order k + 2. The HDG method is thus more efficiently implementable and more accurate than any other DG methods.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9780549851974Subjects--Topical Terms:

561339
Civil engineering.
Subjects--Index Terms:

Discontinuous GalerkinIndex Terms--Genre/Form:

554714
Electronic books.

Hybridizable discontinuous Galerkin method for solid mechanics.
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500 $a Source: Dissertations Abstracts International, Volume: 70-06, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Stolarski, Henryk K.;Cockburn, Bernardo;Drescher, Andrew.
502 $a Thesis (Ph.D.)--University of Minnesota, 2008.
504 $a Includes bibliographical references
520 $a In this Thesis, this criticism is addressed in the framework of second-order scalar elliptic equation, linear elasticity, and large-deformation elasticity by studying the so-called hybridizable discontinuous Galerkin (HDG) method. This method can be classified as a dual hybrid-mixed method whose new and most attractive feature is that it can be implemented more efficiently than any other known DG method for the same level of accuracy. This can be attributed to two main reasons. The first is that only the degrees of freedom associated with the approximation of the primary unknown (e.g., pressure, temperature, displacement) on the element boundaries, known as the hybrid unknown, are globally coupled. Moreover, since the corresponding stiffness matrix is symmetric, positive definite, and has a block-wise sparse structure, the method is easy to implement in the context of parallel and distributive computing. The second reason is that when polynomials of degree k are used for both the primary (e.g., pressure, temperature, displacement) and secondary (e.g., velocity, heat flux, stress) unknowns, both approximations converge with the optimal order of k + 1 for k ≥ 0. All other known DG methods provide a secondary unknown converging with order k and only for k ≥ 1. In addition, if k ≥ 2, an element-by-element post-processing generates a new approximation for primary unknown, which converges with order k + 2. The HDG method is thus more efficiently implementable and more accurate than any other DG methods.
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538 $a Mode of access: World Wide Web
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653 $a Discontinuous Galerkin
653 $a Finite element
653 $a Hybrid
653 $a Linear elasticity
653 $a Scalar elliptic equations
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710 2 $a University of Minnesota. $b Civil Engineering. $3 1179810
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