Model reduction techniques seek approximate solutions of a problem with a large number of DOFs within a subspace of small dimension. Component Mode Synthesis (CMS) methods form a large class of reduction methods where the subspace is selected a priori. Introducing a posteriori error estimation and iterative correction significantly extends the range of applications of reduction methods. The pap...

in this paper a method is presented in details to solve a nonlinear partial differential equation which has many applications in engineering fields. the boundary condition is mixed to be able to define the value of function on its variation on the boundary. examples are given to demonstrate the accuracy and efficiency of the method.

In this note we prove in the case of a Lipschitz interface the stability of the coupling of finite and boundary element methods when the direct boundary integral equation with single and double layer potentials is used only. In particular we prove an ellipticity estimate of the coupled bilinear form. Hence we can use standard arguments to derive stability and error estimates for the Galerkin di...

The paper studies the thermal rise in the human eye caused by time harmonic electromagnetic waves. An eye has been illuminated by a high frequency plane wave with power density 5.0 mW/cm. Such a problem has been considered as an electromagnetic scattering problem since part of EM energy is transmitted to the eye and part of it is reflected. The total electric field inside an eye and related Spe...

This paper studies the expected return of a stock investment with a stop-loss strategy. The probability density function for the investment value is formulated as the solution for a boundary value problem of a partial differential equation. Then, the expected value is manipulated as a function of the stop-loss probability. Two examples are solved by an analytic method. Finally, we design a boun...

The interior transmission problem (ITP) is a boundary value problem arising in inverse scattering theory which has important applications in qualitative methods. In this paper, we propose a coupled boundary element and finite element method for the ITP. The coupling procedure is realized by applying the direct boundary integral equation method to define the so-called Dirichlet-to-Neumann (DtN) ...

Applications of three-dimensional Galerkin boundary element methods require the numerical evaluation of many four-dimensional integrals. In this paper we explore the possibility of using extrapolation quadrature. To do so, one needs appropriate error functional expansions. The treatment here is limited to integration over a region T1×T2, where T1 and T2 are planar triangular elements in a hangi...

Boundary and finite element modeling approach to the assessment of electrostatic field on human head generated by Video Display Units (VDU’s) are compared and discussed. Attention is focused to the field distribution over the surface of the face. The mathematical formulation for the assessment of the electrostatic field is based on the Laplace equation for the electric scalar potential. The ele...

on Γ := {(x1, 0) : x1 ∈ R}, where k > 0 (the wavenumber) is some arbitrary positive constant. This boundary value problem can arise when modelling the acoustic scattering of an incident wave by a planar surface with spatially varying acoustical properties [1]. The total acoustic field u ∈ C(U)∩C(U) satisfies (1)– (2) where the wavenumber k = 2πμ/c, with μ being the frequency of the incident wav...

In this paper, the natural boundary element method (NBEM) for an anisotropic hyperbolic problem in an exterior elliptic domain is investigated. By the theory of the natural boundary reduction (NBR), the natural integral equation (NIE) and the Poisson integral formula of the problem considered are obtained, and the numerical method of the NIE is given. Finally, some numerical examples are presen...