By C. A. Brebbia
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E. 97) where J0 is a Bessel function of the first kind and Y0 is one of the second kind. „ . 101) In general we can write a constant c, instead of \ for a non-smooth boundary. 102) From now on the usual boundary element matrix technique can be applied. 12). 103) for the case of a threedimensional medium, for which the boundary at Γχ will be a sphere of radius tending to infinity. 104) The minus sign in front of the right-hand side integral comes from the fact that the normal on Γ ^ is in the opposite direction to the radial coordinate, dö, άφ are the differentials of the angles in spherical polar coordinates.
Note that the variation of du/dn velocities is the one expected. 27 28 • u=2 25 2k 23 26 i · 1 · ■ · i ·—i 22 21 · . · 20 19 18 17 i · i · ■ · . 8 Prescribed conditions and solution for constant elements, (a) Values ofu and du/dn prescribed along boundary; (b) computed values for u and du/δη along boundary 44 POTENTIAL PROBLEMS Values of u inside the domain agree well with the finite elements results and the cell collocation solution (developed in Lau and Brebbia4). The cell collocation method for this case is similar to a curvilinear finite difference technique.
Q + q = 0. 32) μ are called dipoles and give rise to an alternative indirect formulation. 1 Similar arguments can also be applied to problems such as those present in elasticity (Chapter 4) and the argument can even be extended to non-self-adjoint problems but for these cases the fundamental solution for the adjoint operator may be difficult to find. 30). 32) are the starting relationships for the source approach. 34) on the other part. 36) are frequently used. Conversely we can use a dipole type formulation, but this is slightly more cumbersome as it involves second derivatives of the potential and in consequence is applied less frequently.