eprintid: 4177
rev_number: 2
eprint_status: archive
userid: 1
dir: disk0/00/00/41/77
datestamp: 2023-11-09 16:15:50
lastmod: 2023-11-09 16:15:50
status_changed: 2023-11-09 15:57:50
type: article
metadata_visibility: show
creators_name: Hidayat, M.I.P.
creators_name: Wahjoedi, B.A.
creators_name: Parman, S.
creators_name: Megat Yusoff, P.S.M.
title: Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity
ispublished: pub
keywords: Delta functions; Finite difference method; Heat conduction, B splines; B-spline approximation; B-spline basis function; Complex domains; Generalized finite difference; Governing equations; Heat conduction problems; Meshless, Interpolation
note: cited By 14
abstract: 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.
date: 2014
publisher: Elsevier Inc.
official_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
id_number: 10.1016/j.amc.2014.05.031
full_text_status: none
publication: Applied Mathematics and Computation
volume: 242
pagerange: 236-254
refereed: TRUE
issn: 00963003
citation:   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.  ISSN 00963003