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High-Order Adaptive Extended Stencil Finite Element Methods for Applications with Curved Boundaries.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	High-Order Adaptive Extended Stencil Finite Element Methods for Applications with Curved Boundaries./
Author:	Delaney, Tristan Joseph.
Description:	1 online resource (113 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
Contained By:	Dissertation Abstracts International79-01B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355150735

High-Order Adaptive Extended Stencil Finite Element Methods for Applications with Curved Boundaries.
Delaney, Tristan Joseph.

High-Order Adaptive Extended Stencil Finite Element Methods for Applications with Curved Boundaries. - 1 online resource (113 pages)

Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

High-order numerical methods for PDE discretizations have attracted significant interests for scientific and engineering applications in recent years. For engineering problems with complex geometries, achieving high-order convergence is decidedly challenging, especially with curved boundaries. The existing high-order finite element methods based on isoparametric elements require the definition of curved volumetric elements to represent the geometry accurately and ensure the validity of their variational formulations. However, these high-order elements have much stricter mesh quality requirements due to the possibilities of internal foldings of the elements, which are very hard to detect. In addition, poor mesh quality may also lead to potential loss of the completeness of the basis functions. Some recently proposed alternatives such as isogeometric analysis and NURBS-enhanced FEM can achieve high-order convergence but are very complicated and also have even stricter requirement on mesh quality.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355150735Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

High-Order Adaptive Extended Stencil Finite Element Methods for Applications with Curved Boundaries.
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100 1 $a Delaney, Tristan Joseph. $3 1180752
245 1 0 $a High-Order Adaptive Extended Stencil Finite Element Methods for Applications with Curved Boundaries.
264 0 $c 2017
300 $a 1 online resource (113 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
500 $a Adviser: Xiangmin Jiao.
502 $a Thesis (Ph.D.) $c State University of New York at Stony Brook $d 2017.
504 $a Includes bibliographical references
520 $a High-order numerical methods for PDE discretizations have attracted significant interests for scientific and engineering applications in recent years. For engineering problems with complex geometries, achieving high-order convergence is decidedly challenging, especially with curved boundaries. The existing high-order finite element methods based on isoparametric elements require the definition of curved volumetric elements to represent the geometry accurately and ensure the validity of their variational formulations. However, these high-order elements have much stricter mesh quality requirements due to the possibilities of internal foldings of the elements, which are very hard to detect. In addition, poor mesh quality may also lead to potential loss of the completeness of the basis functions. Some recently proposed alternatives such as isogeometric analysis and NURBS-enhanced FEM can achieve high-order convergence but are very complicated and also have even stricter requirement on mesh quality.
520 $a In our recent work, we have developed the adaptive extended stencil finite element method (AES-FEM), which has less dependent on mesh quality. In this dissertation, we extend the AES-FEM to achieve high order convergence on geometries with curved boundaries and Neumann boundary conditions. AES-FEM uses high-degree polynomial basis functions to accurately discretize the PDE. In the interior, AES-FEM uses piecewise linear test functions for simplicity and efficiency. For elements adjacent to the curved boundary, we construct new superparametric elements, whose test functions are piecewise linear in the parametric space but curved in the real space to capture the curved geometry accurately. We construct these superparametric elements using simplices with curved faces and edges defined by the curved geometry.
520 $a As another contribution, we propose a new strategy for enforcing Neumann boundary conditions for weighted residual methods in the variational formulations, which only require integrating the Neumann boundary conditions over small regions on the boundary. The method is consistent with the variational problem and simplifies some of the implementation, and it allows enforcing Neumann boundary conditions even for boundaries with discontinuous normal directions. We present the method both for AES-FEM as well as generalized finite difference (GFD) methods. We present results of our method applied to second-order elliptic problems on curved boundaries.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a State University of New York at Stony Brook. $b Applied Mathematics and Statistics. $3 1179106
773 0 $t Dissertation Abstracts International $g 79-01B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10281664 $z click for full text (PQDT)