The purpose of the paper is to introduce a novel cell boundary element (CBE) method for the convection dominated diffusion equation. The CBE method can be viewed as a Petrov-Galerkin type method defined on the skeleton of a mesh. The proposed method utilizes continuity of normal flux on each inter-element boundary. By constructing a local basis (mesh-oriented element) that is dependent upon the...

The indirect boundary element method for the Helmholtz equation in three dimensions is of great interest and practical value for many problems in acoustics as it is capable of treating infinitely thin plates and allows coupling of interior and exterior scattering problems. In the present paper we provide a new approach for treatment of boundary integrals, including hypersingular, singular, and ...

This paper presents an efficient and novel geometric flow-driven method for mesh optimization of segmented tetrahedral meshes with non-manifold boundary surfaces. The presented method is composed of geometric optimization and topological transformation techniques, so that both location and topology of vertices are optimized. Non-manifold boundary can be divided into manifold surface patches hav...

A boundary element method is applied for the numerical solution of a boundary value problem for a two-dimensional steady-state bioheat transfer model of the human eye. The human eye is modeled as comprising four distinct homogeneous regions. The boundary condition on the outer surface of the cornea is non-linear due to heat radiation. An iterative approach is used to treat the non-linear heat r...

In this paper we introduce and analyze two least squares methods for second order elliptic di erential equations with mixed boundary conditions These methods extend to problems which involve oblique derivative boundary conditions as well as nonsym metric and inde nite problems as long as the original problem has a unique solution With the methods to be developed Neumann and oblique boundary con...

Article history: Received 14 January 2011 Received in revised form 31 May 2011 Accepted 8 July 2011 Available online xxxx

Article history: Received 1 October 2013 Available online 21 November 2013 Submitted by J. Shi

Article history: Received 30 May 2012 Received in revised form 2 May 2013 Accepted 19 August 2013 Available online 25 September 2013

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