We model ferromagnetic effects by using reduced scalar potential. An overlapping domain-decomposition technique is proposed to solve the underlying problem in unbounded domain. In the near-field, adjacent to the ferromagnetic object, we employ finite element discretization, while the far-field, going to infinity, is modelled through Green representation formulas. In this way, we circumvent the ...

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...

Effects of wall material on the channel capacity of an indoor multiple input multiple output (MIMO) system are investigated using a hybrid technique of the method of moments (MoM) and the finite difference time domain (FDTD) method with consideration of the Ricean K factor and the effective degrees of freedom (EDOF) of multiple paths. key words: MIMO, channel capacity, indoor channel, hybrid me...

In this work, we analyze three available domain decomposition methods. We also establish the convergence conditions. The theoretical analysis provides an interval in which a relaxation parameter has to be chosen in order to achieve convergence. Moreover, it allows the selection of the relaxation parameter so that convergence is achieved with the minimum number of iterations. Several example pro...

Recently, a combined approach of CFIE–BAE has been proposed by authors for solving external scattering problems in acoustics. CFIE stands for combined-field integral equations, and BAE is the method of boundary algebraical equation. The combined method is, essentially, a discrete analogue of the boundary element method (BEM), having none of its disadvantages. Namely, due to the discrete nature ...

This paper establishes a foundation of non-conforming boundary elements. We present a discrete weak formulation of hypersingular integral operator equations that uses Crouzeix–Raviart elements for the approximation. The cases of closed and open polyhedral surfaces are dealt with. We prove that, for shape regular elements, this non-conforming boundary element method converges and that, up to log...

At present, the main numerical modelling techniques for acoustic and (coupled) vibro-acoustic analysis are based on element based techniques, such as the finite element and boundary element method. Due to the huge computational efforts, the use of these deterministic techniques is practically restricted to lowfrequency applications. For high-frequency modelling, some alternative, probabilistic ...

In this paper we prove the L2 convergence rates for a fully discrete finite element procedure for approximating minimal, possibly unstable, surfaces. Originally this problem was studied by G. Dziuk and J. Hutchinson. First they provided convergence rates in the H1 and L2 norms for the boundary integral method. Subsequently they obtained the H1 convergence estimates using a fully discrete finite...

Green’s functions are important mathematical tools in mechanics and in other parts of physics. For instance, the boundary element method needs to know the Green’s function of the problem to compute its numerical solution. However, Green’s functions are only known in a limited number of cases, often under the form of complex analytical expressions. In this article, a new method is proposed to ca...

In this paper we prove an optimal error estimate for the H(curl)-conforming projection based p-interpolation operator introduced in [L. Demkowicz and I. Babuška, p interpolation error estimates for edge finite elements of variable order in two dimensions, SIAM J. Numer. Anal., 41 (2003), pp. 1195–1208]. This result is proved on the reference element (either triangle or square) K for regular vec...