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Fast System Formation and Assembly f...
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Dudi Raghunath, Arvind.
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Fast System Formation and Assembly for Isogeometric Analysis.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Fast System Formation and Assembly for Isogeometric Analysis./
作者:
Dudi Raghunath, Arvind.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:
82 p.
附註:
Source: Masters Abstracts International, Volume: 81-05.
Contained By:
Masters Abstracts International81-05.
標題:
Aerospace engineering. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=22616124
ISBN:
9781088385111
Fast System Formation and Assembly for Isogeometric Analysis.
Dudi Raghunath, Arvind.
Fast System Formation and Assembly for Isogeometric Analysis.
- Ann Arbor : ProQuest Dissertations & Theses, 2019 - 82 p.
Source: Masters Abstracts International, Volume: 81-05.
Thesis (M.S.)--University of Colorado at Boulder, 2019.
This item must not be sold to any third party vendors.
Spline based basis functions offer greater accuracy than FEA basis functions. However, this accuracy comes at an increase in computational cost. This can be attributed to the system solution and system formation. In this thesis, we look to reduce cost due to system formation and assembly. There are many methods to decrease the cost. But the ones considered here maintain the element by element formation procedure. This is due to the fact that it simplifies the implementation. Hence, the reduction is concentrated on element formation. We present two approaches to this end and use the unsteady advection-diffusion problem as our model problem. The first method is to create C0 Bezier elements with the use of Bezier extraction. Along with this, we use the method of sum factorization which takes advantage of the tensor product structure of the Bernstein basis functions to reduce the cost of formation from O(p3d) to O(p2d+1), where p is the polynomial order of the basis functions and d is the spatial dimension. The second approach is to use Lagrange extraction and collocate on Gauss-Lobatto points. This approach takes advantage of the Kronecker δ property of Lagrange basis functions to reduce the cost of formation from O(p3d) to O(p2d+1). We finally present numerical results for a range of polynomial orders to support our theoretical cost calculations.
ISBN: 9781088385111Subjects--Topical Terms:
1002622
Aerospace engineering.
Subjects--Index Terms:
Spline based basis functions
Fast System Formation and Assembly for Isogeometric Analysis.
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Spline based basis functions offer greater accuracy than FEA basis functions. However, this accuracy comes at an increase in computational cost. This can be attributed to the system solution and system formation. In this thesis, we look to reduce cost due to system formation and assembly. There are many methods to decrease the cost. But the ones considered here maintain the element by element formation procedure. This is due to the fact that it simplifies the implementation. Hence, the reduction is concentrated on element formation. We present two approaches to this end and use the unsteady advection-diffusion problem as our model problem. The first method is to create C0 Bezier elements with the use of Bezier extraction. Along with this, we use the method of sum factorization which takes advantage of the tensor product structure of the Bernstein basis functions to reduce the cost of formation from O(p3d) to O(p2d+1), where p is the polynomial order of the basis functions and d is the spatial dimension. The second approach is to use Lagrange extraction and collocate on Gauss-Lobatto points. This approach takes advantage of the Kronecker δ property of Lagrange basis functions to reduce the cost of formation from O(p3d) to O(p2d+1). We finally present numerical results for a range of polynomial orders to support our theoretical cost calculations.
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