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One does not usually talk about the values of the Dirac delta at a particular point, but rather its integral behaviour. 2 Fundamental solutions We develop here the fundamental solution (also called the freespace Green’s3 function) for Laplace’s Equation in two variables. The fundamental solution of a particular equation is the weighting function that is used in the boundary element formulation of that equation. It is therefore important to be able to find the fundamental solution for a particular equation.

3a an exact vector e (lying in 3D space) is approximated by a vector = 1 1 where 1 is a basis vector along the first coordinate axis (representing one degree of freedom in the system). 3: Showing how the Galerkin method maintains orthogonality between the residual vector r and the set of basis vectors 'i as i is increased from (a) 1 to (b) 2 to (c) 3. 3a). The Galerkin technique minimises this residual by making it orthogonal to '1 and hence to the approximating vector . 3b) is added, the approximating vector is = u1 1 + u2 2 and the residual is now also made orthogonal to '2 and hence to .

5. FEM: Sparse symmetric matrix generated. BEM: Fully populated nonsymmetric matrices generated. Comment: The matrices are generally of different sizes due to the differences in size of the domain mesh compared to the surface mesh. There are problems where either method can give rise to the smaller system and quickest solution - it depends partly on the volume to surface ratio. For problems involving infinite or semi-infinite domains, BEM is to be favoured. 6. FEM: Element integrals easy to evaluate.