Fast Boundary Element Methods

Boundary element methods as described in Chapter 12 result in dense stiffness matrices. In particular, both the storage requirements and the numerical amount of work to compute all entries of a boundary element stiffness matrix is quadratic in the number of degrees of freedom. Hence there is a serious need to derive and to describe fast boundary element methods which exhibit an almost linear, up to some polylogarithmic factors, behavior in the number of degrees of freedom. Here we constrict our considerations to the case of a two—dimensional model problem, for the three—dimensional case, see, for example, [117].