Boundary integral

This paper compares experimental data for aluminium and steel specimens with two methods of solving the forward problem in the thin-skin regime. The first approach is a 3D Finite Element / Boundary Integral Element method (TRIFOU) developed by EDF/RD Division (France). The second approach is specialised for the treatment of surface cracks in the thin-skin regime developed by the University of Surrey (England). In the thin-skin regime, the electromagnetic skin-depth is small compared with the depth of the crack. Such conditions are common in tests on steels and sometimes on aluminium. 

D Finite Element / Boundary Integral Element method (TRIFOU)... 

TRIFOU is a combined Finite Elements/Boundary Integral formulation code. The BIM formulation in vacuum is suitable for NDT simulation where the probe moves in the air around the test block. The FEM formulation needs more calculation time, but tetrahedral elements enable a large variety of specimens and defect geometries to be modelled. TRIFOU uses a formulation of Maxwell Equations using magnetic field vector h, where h is decomposed as h = hs + hr (hj source field, and hr reaction field). 

Integral terms extending on R are reduced to iJc using Boundary Integral Elements on the boundaries of the FEM domain (especially the influence of the source field hs). Inside the FEM domain, edge elements are used to compute the reaction field. 

Insurance in pressure boundary integrity of NPP unit is strongly influenced by technical capabilities and efficiency of metal examination system. Ordinary ultrasonic examination tools and procedures have limitations in flaw sizing and positioning. The problems arise for welds and repair zones of welds made by filler materials of austenitic type. 

AUGUR information on inspected zones as applied to pearlitic and austenitic weld materials reduces level of ISI results uncertainty and therefore gives additional insurance of pressure boundary integrity. 

Arzhaev A T, Kiselyov VA., Badalyan V.G., Vopilkin A.Kb., Strelkov B.R,Vanukov V.N., Aladinsky V. V, Makhanev V.O. Field application of Augur)> ultrasonic system during RBMK NPP Unit ISI and its impact on pressure boundary integrity. In Ageing of Materials and Methods for the Assessment of Lifetimes of Engineering Plant, R K. Penny (Ed.), 1997, pp. 97-104. 

D. B. Ingham and M. A. Kelmanson. Boundary Integral Equation Analysis of Singular, Potential and Biharmonic Problems. Heidelberg Springer Verlag, 1994. 

Meiron (12) and Kessler et al. (13) have shown that numerical studies for small surface energy give indications of the loss-of-existence of the steady-state solutions. In these analyses numerical approximations to boundary integral forms of the freeboundary problem that are spliced to the parabolic shape far from the tip don t satisfy the symmetry condition at the cell tip when small values of the surface energy are introduced. The computed shapes near the tip show oscillations reminiscent of the eigensolution seen in the asymptotic analyses. Karma (14) has extended this analysis to a model for directional solidification in the absence of a temperature gradient. 

Pratt, L. R., Tawa, G.J., Hummer, G., Garcia, A. E., and Corcelli, S. A. (1997). Boundary integral methods for the poisson equation of continuum dielectric solvation models. Int.J. Quant. Chem. 64, 121-141. 

Abstract. A method for the computation of eigenvalues of quantum billiard is offered. This method is based on combining of boundary integral method and thermofield dynamics formalism. 

In this work we use thermofield dynamics formalism (Takahashi et.al., 1996 Das, 1997) and boundary integral method (Li et.al., 1995) to get temperature dependence in the billiard energy level spectrum. Instead of the zero-temperature Green s function we use finite-temperature one which is obtained within the TFD formalism. 

Before proceeding to finite-temperature treatment we briefly describe the boundary integral method for zero-temperature case, which was introduced to solve this type of problem (Berry et al, 1984 Tiago et al, 1997). 

In the case of finite temperature a similar approach can be used based on the boundary integral method, where instead of the zero temperature Green s function, finite-temperature Green s function derived within TFD formalism is used. Introducing finite-temperature within the thermofield dynamics formalism is based on two steps, doubling of the Hilbert space and Bogolyubov transformations (Takahashi et.ah, 1996 Ademir, 2005). 

Using in-boundary integral method for this Green s function gives us finite-temperature analog of the matrix given in Eq. (5),... 

Atkinson, K.E., 1997, The numerical solution of boundary integral equations, Cambridge University Press, Cambridge. 

The function w(x0) is a superposition of a single-layer potential of density du/dn (first boundary integral),... 

A double-layer potential of density w(x) (second boundary integral) and... 

For any point in the domain and boundary, the fundamental solutions in the boundary integrals of eqn. (10.82) can be written in matrix form as... 

Low Reynolds number flows with boundary integral representation have been used to describe rheological and transport properties of suspensions of solid spherical particles, as well as for numerical solution of different problems, including particle-particle interaction, the motion of a particle near a fluid interface or a rigid wall, the motion of particles in a container, and others. 

The direct boundary integral formulation was used to simulate suspended spheres in simple shear flow. The viscosity was then calculated by integration of the surface tractions on the moving wall. Figure 10.28 shows a typical mesh for the domain and spheres for these simulations in this mesh, the box has dimensions of 1 x 1 x 1 (Length units)3 and 40 spheres of radius of 0.05 length units. 

B.A. Davis. Investigation of non-linear flows in polymer mixing using the boundary integral method. PhD thesis, University of Wisconsin-Madison, Madison, 1995. 

H. Power and L. C. Wrobel. Boundary Integral Methods in Fluid Mechanics. Computational Mechanics Publications, 1995. 

C. Pozrikidis. Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University, 1992. 

A.M. Linkov Boundary Integral Equations in Elasticity Theory. 2002... 

This will be symbolized here by if o) = KVnf(a ) = Rf(a). If the normal gradient is specified, this defines a classical Neumann boundary condition on a, which determines a unique solution of the Schrodinger equation in the enclosed volume r. The value of the boundary integral is... 

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