A novel computational procedure called the scaled boundary
finite-element method is described which combines the advantages of
the finite-element and boundary-element methods: Of the
finite-element method that no fundamental solution is required and
thus expanding the scope of application, for instance to anisotropic
material without an increase in complexity and that singular
integrals are avoided and that symmetry of the results is
automatically satisfied. Of the boundary-element method that the
spatial dimension is reduced by one as only the boundary is
discretized with surface finite elements, reducing the data
preparation and computational efforts, that the boundary conditions
at infinity are satisfied exactly and that no approximation other
than that of the surface finite elements on the boundary is
introduced. In addition, the scaled boundary finite-element method
presents appealing features of its own: an analytical solution inside
the domain is achieved, permitting for instance accurate stress
intensity factors to be determined directly and no spatial
discretization of certain free and fixed boundaries and interfaces
between different materials is required. In addition, the scaled
boundary finite-element method combines the advantages of the
analytical and numerical approaches. In the directions parallel to
the boundary, where the behaviour is, in general, smooth, the
weighted-residual approximation of finite elements applies, leading
to convergence in the finite-element sense. In the third (radial)
direction, the procedure is analytical, permitting e.g.
stress-intensity factors to be determined directly based on their
definition or the boundary conditions at infinity to be satisfied
exactly. In a nutshell, the scaled boundary finite-element method is
a semi-analytical fundamental-solution-less boundary-element method
based on finite elements. The best of both worlds is achieved in two
ways: with respect to the analytical and numerical methods and with
respect to the finite-element and boundary-element methods within the
numerical procedures. The book serves two goals: Part I is an
elementary text, without any prerequisites, a primer, but which using
a simple model problem still covers all aspects of the method and
Part II presents a detailed derivation of the general case of
statics, elastodynamics and diffusion.