Periodic boundary conditions in element free Galerkin method

Abstract

If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -The purpose of this paper is to introduce a new methodology to implement periodic and anti-periodic boundary conditions in the element free Galerkin method (EFGM). Design/methodology/approach -This paper makes use of the interpolating moving least squares (IMLS) in the EFGM to implement periodic and anti-periodic boundary conditions. This fact allows imposing periodic and anti-periodic boundary conditions in a way similar to the one used by the finite element method. Findings -EFGM generally uses the moving least squares to obtain its shape functions. So, these functions do not possess the Kronecker delta property. As a consequence, the imposition of essential, as well as periodic and anti-periodic boundary conditions needs other techniques to do it. When EFGM makes use of IMLS the shape functions satisfy the Kronecker delta property. As consequence the periodic boundary conditions implementation can be done in a direct way, similar to the FEM. Originality/value -IMLS provides a new way of periodic boundary conditions implementation in EFGM. This kind of implementation provides an easy and direct way in comparison to usual existing methods. With this technique EFGM can now easily take advantage of electrical machines symmetry.

Meshless Methods for Computation of Overhead Transmission Lines Electromagnetic Fields

“…It was originally proposed by [5] and it belongs to a class of global weak-form meshless methods, which are based on the global Galerkin weak-form for the problem equations. The Moving Least Squares approximation is often used to construct shape functions, and a set of background cells are required to evaluate the integrals resulted from the weak-form [6]- [9]. This work consists in the computational modeling of three-phase transmission line (TL) with uniform parameters.…”