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Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity

In this paper, a new class of meshless methods based on local collocation and B-spline basis functions is presented for solving elliptic problems. The proposed approach is called as meshless local B-spline basis functions based finite difference (local B-FD) method. The method was straightforward to...

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Main Authors: Hidayat, M.I.P., Wahjoedi, B.A., Parman, S., Megat Yusoff, P.S.M.
Format: Article
Published: Elsevier Inc. 2014
Online Access:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84902458665&doi=10.1016%2fj.amc.2014.05.031&partnerID=40&md5=059cad51ba0e77d8c7a787f740a0dfbd
http://eprints.utp.edu.my/31146/
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spelling my.utp.eprints.311462022-03-25T09:01:30Z Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity Hidayat, M.I.P. Wahjoedi, B.A. Parman, S. Megat Yusoff, P.S.M. In this paper, a new class of meshless methods based on local collocation and B-spline basis functions is presented for solving elliptic problems. The proposed approach is called as meshless local B-spline basis functions based finite difference (local B-FD) method. The method was straightforward to develop and program as it was truly meshless. Only scattered nodal distribution was required hence avoiding at all mesh connectivity for field variable approximation and integration. In the method, any governing equations were discretized by B-spline approximation in the spirit of FD technique using local B-spline collocation i.e. any derivative at a point or node was stated as neighboring nodal values based on the B-spline interpolants. In addition, as B-spline basis functions pose favorable properties such as (i) easy to construct to any arbitrary order/degree, (ii) have partition of unity property, and (iii) can be easily designed to pose the Kronecker delta property, the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method. The applicability and capability of the present local B-FD method were demonstrated through several heat conduction problems with heat generation and spatially varying conductivity. © 2014 Elsevier Inc. All rights reserved. Elsevier Inc. 2014 Article NonPeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-84902458665&doi=10.1016%2fj.amc.2014.05.031&partnerID=40&md5=059cad51ba0e77d8c7a787f740a0dfbd Hidayat, M.I.P. and Wahjoedi, B.A. and Parman, S. and Megat Yusoff, P.S.M. (2014) Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity. Applied Mathematics and Computation, 242 . pp. 236-254. http://eprints.utp.edu.my/31146/
institution Universiti Teknologi Petronas
building UTP Resource Centre
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Petronas
content_source UTP Institutional Repository
url_provider http://eprints.utp.edu.my/
description In this paper, a new class of meshless methods based on local collocation and B-spline basis functions is presented for solving elliptic problems. The proposed approach is called as meshless local B-spline basis functions based finite difference (local B-FD) method. The method was straightforward to develop and program as it was truly meshless. Only scattered nodal distribution was required hence avoiding at all mesh connectivity for field variable approximation and integration. In the method, any governing equations were discretized by B-spline approximation in the spirit of FD technique using local B-spline collocation i.e. any derivative at a point or node was stated as neighboring nodal values based on the B-spline interpolants. In addition, as B-spline basis functions pose favorable properties such as (i) easy to construct to any arbitrary order/degree, (ii) have partition of unity property, and (iii) can be easily designed to pose the Kronecker delta property, the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method. The applicability and capability of the present local B-FD method were demonstrated through several heat conduction problems with heat generation and spatially varying conductivity. © 2014 Elsevier Inc. All rights reserved.
format Article
author Hidayat, M.I.P.
Wahjoedi, B.A.
Parman, S.
Megat Yusoff, P.S.M.
spellingShingle Hidayat, M.I.P.
Wahjoedi, B.A.
Parman, S.
Megat Yusoff, P.S.M.
Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity
author_facet Hidayat, M.I.P.
Wahjoedi, B.A.
Parman, S.
Megat Yusoff, P.S.M.
author_sort Hidayat, M.I.P.
title Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity
title_short Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity
title_full Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity
title_fullStr Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity
title_full_unstemmed Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity
title_sort meshless local b-spline-fd method and its application for 2d heat conduction problems with spatially varying thermal conductivity
publisher Elsevier Inc.
publishDate 2014
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-84902458665&doi=10.1016%2fj.amc.2014.05.031&partnerID=40&md5=059cad51ba0e77d8c7a787f740a0dfbd
http://eprints.utp.edu.my/31146/
_version_ 1738657206879911936
score 13.211869

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