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Example text

Thus, the boundary-value problem can be posed in the following fashion with uc as the unknown function: ∇ 2 uc = 0 with uc = −up on . Second, for many practical cases it will be difficult to find a particular solution. For example, the values of “b” may be provided in a tabular form applied at a series of points in . 50) The domain term can be computed by dividing the domain into a number of internal cells (Fig. 8) and performing numerical integration over these cells. 8. Internal cells for domain term integration.

2. Streamline solution at interior points for fluid flow. FE Nodes x-coord. y-coord. 7. Integration over a small circular boundary ε. 2. Function u is the solution that we seek for the governing Laplace’s equation. Therefore, u satisfies the Laplace’s equation in the entire domain [eqn. 1)]. Since u∗ is the fundamental solution to a point source at P, it also satisfies the Laplace’s equation for the entire domain , except at the point p [eqn. 6)]. Let us isolate this point by putting an arbitrarily small circular region (or a spherical region in 3-D) ε around the point bounded by ∈ (Fig.

We will use weighted residual technique in the rest of the book for deriving boundary element equations. The materials presented up to this point in this chapter would be adequate for a general understanding of the fundamentals of the boundary element formulation. Very often the approach outlined thus far would be found in boundary element literature that describes the basic methodology. The next section on indirect method, therefore, is presented briefly for the sake of completeness. 5. Indirect method In the direct method, the physical quantities themselves are used as the unknown variables to be solved by numerical means.

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