Title:
|
Implementation of a generalized exponential basis functions method for linear and non-linear problems
|
Author:
|
Mossaiby, Farshid; Ghaderian, M; Rossi, Riccardo
|
Other authors:
|
Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria; Universitat Politècnica de Catalunya. RMEE - Grup de Resistència de Materials i Estructures en l'Enginyeria |
Abstract:
|
This is the accepted version of the following article: Mossaiby, F., Ghaderian, M., Rossi, R. Implementation of a generalized exponential basis functions method for linear and non-linear problems. International Journal for Numerical Methods in Engineering [on line]. Jul 2015, which has been published in final form at http://dx.doi.org/10.1002/nme.4985. |
Abstract:
|
In this paper, we address shortcomings of the method of exponential basis functions (EBF) by extending it to general linear and non-linear problems. In linear problems, the solution is approximated using a linear combination of exponential functions. The coefficients are calculated such that the homogenous form of equation is satisfied on some grid. To solve non-linear problems, they are converted to into a succession of linear ones using a Newton-Kantorovich approach. The generalized exponential basis functions method (GEBF) developed can be implemented with greater ease compared to EBF, as all calculations can be performed using real numbers and no characteristic equation is needed. The details of an optimized implementation are described. We compare GEBF on some benchmark problems with methods in the literature, such as variants of the boundary element method, where GEBF shows a good performance. Also in a 3D problem, we report the run time of the proposed method compared to Kratos, a parallel, highly optimized finite element code. The results show that in this example, to obtain the same level of error much less computational effort is needed in the proposed method. Practical limitations might be encountered however for large problems because of dense matrix operations involved. |
Abstract:
|
Peer Reviewed |
Subject(s):
|
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica -Finite element method -Exponential functions -Linear systems -Nonlinear systems -Differential equations, Partial -Meshless methods -Exponential basis functions -Linear and non-linear problems -Partial differential equations -Newton-Kantorovich -Elements finits, Mètode dels -Funcions exponencials -Sistemes lineals -Sistemes no lineals -Equacions diferencials parcials |
Rights:
|
|
Document type:
|
Article - Submitted version Article |
Published by:
|
John Wiley & Sons
|
Share:
|
|