Collocation Methods

Abstract

In engineering boundary element methods almost all the codes are based on collocation methods. Here, first choose appropriate collocation points ik E I’ associated with the family of boundary element grids, $K = 1,...,N.$ Then, again with (2.3.2), find the coefficients, -y_N by solving the quadratic linear system of equations,

$$A{u_h}(\overrightarrow {{x_k}} ) = \sum\limits_{j = 1}^N A {\mu _j}({\overrightarrow x _k}){\gamma _j} = (\overrightarrow {{x_k}} ),k = 1,....N. $$

((3.0.1))

As we know from the special example in [46], the right choice of the collocation points Xk is significant for the stability and convergence of the approximation (3.0.1).