scholarly journals A Hybrid Boundary Element Method-Reluctance Network Method for Open Boundary 3-D Nonlinear Problems

2014 ◽  
Vol 50 (2) ◽  
pp. 77-80 ◽  
Author(s):  
Douglas Martins Araujo ◽  
Jean-Louis Coulomb ◽  
Olivier Chadebec ◽  
Loic Rondot
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Nonlinear Problems ◽  
Open Boundary ◽  
Network Method ◽  
Reluctance Network ◽  
Element Method

scholarly journals Remarks on the boundary element method for strongly nonlinear problems

1993 ◽  
Vol 34 (4) ◽  
pp. 419-438 ◽  
Author(s):  
Keijo Ruotsalainen
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Nonlinear Problems ◽  
Monotone Operators ◽  
Heat Radiation ◽  
Optimal Order ◽  
Nonlinear Boundary Value Problems ◽  
Order Error ◽  
Strongly Nonlinear ◽  
Element Method

AbstractRecently in several papers the boundary element method has been applied to non-linear problems. In this paper we extend the analysis to strongly nonlinear boundary value problems. We shall prove the convergence and the stability of the Galerkin method in Lp spaces. Optimal order error estimates in Lp space then follow. We use the theory of A-proper mappings and monotone operators to prove convergence of the method. We note that the analysis includes the u4 -nonlinearity, which is encountered in heat radiation problems.

scholarly journals A FEM-Green Approach for Magnetic Field Problems with Open Boundaries

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1662
Author(s):  
Jacques Lobry
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Galerkin Approximation ◽  
Outer Region ◽  
Open Boundary ◽  
Element Approximation ◽  
Green Approach ◽  
Element Method

A new finite element method/boundary element method (FEM/BEM) scheme is proposed for the solution of the 2D magnetic static and quasi-static problems with unbounded domains. The novelty is an original approach in the treatment of the outer region. The related domain integral is eliminated at the discrete level by using the finite element approximation of the fundamental solutions (Green’s functions) at every node of the related mesh. This “FEM-Green” approach replaces the standard boundary element method. It is simpler to implement because no integration on the boundary of the domain is required. Then, the method leads to a substantially reduced computational burden. Moreover, the coupling with finite elements is more natural since it is based on the same Galerkin approximation. Some examples with open boundary and nonlinear materials are presented and compared with the standard finite element method.

Sign in / Sign up

Export Citation Format

Share Document