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Title : Numerical methods for 1-D hyperbolic-type problems with free boundary
Author :

Faizal Makhrus, S.Kom., M.Sc., Ph.D. (1)

Date : 15 2015
Keyword : numerical method, hyperbolic type function,free boundary numerical method, hyperbolic type function,free boundary
Abstract : We study a 1-D hyperbolic-type problem with free boundary which describesthe motion of a piece of tape being peeled off from a surface. The graph of the solutionrepresents the shape of the tape, which displays contact angle dynamics at the free bound-ary (the location of peeling). The contact angle dynamics lead to singularities located onthe free boundary, which cause a slight difficulty. Under some assumptions, this problemcan be solved numerically by a so-called fixed domain method. This method is a numer-ical method which transforms the domain of the positive part of the solution into a fixeddomain using a change of variables and solves the problem in that domain. Although thismethod has a high accuracy, it can not be applied in some cases. Hence other numer-ical methods are chosen for solving a regularized problem, i.e., the singularities on thefree boundary are regularized by a smoothing function. The numerical methods are: twotypes of finite difference methods, the finite element method and discrete Morse flow. Inthis paper, the error of solving the regularized problem instead of the original problemis calculated. Since the choice of the parameter for smoothing function is important forthe accuracy, we propose a formula to estimate the optimal parameter in order to mini-mize the error. This formula is verified by numerical experiments and we find that it canestimate the optimal parameter. In addition, based on comparisons between the numeri-cal methods, we find that the finite difference methods have better performance than theother methods.
Group of Knowledge : Ilmu Komputer
Original Language : English
Level : Internasional
Status :
Published
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