"As its name indicates, in the infinite element method the
underlying domain is divided into infinitely many pieces. This
leads to a system of infinitely many equations for infinitely many
unknowns; but these can be reduced by analytical techniques to a
finite system when some sort of scaling is present in the original
problem. The simplest illustrative example, described carefully at
the beginning of the first chapter of the book, is the solution of
the Dirichlet problem in the exterior of some polygon. The exterior
is subdivided into annular regions by a sequence of geometrically
expanding images of the given polygon; these annuli are then
further subdivided. The resulting variational equations take the
form of a block tridiagonal Toeplitz matrix, with an inhomogeneous
term in the zero component. Various efficient methods are described
for solving such systems of equations. ... The infinfte element
method is, whereever applicable, an elegant and efficient approach
to solving problems in physics and engineering. Professor Yings
welcome book makes it available to the community of numerical
analysts and computational scientists. " (From the Preface by Peter
D. Lax)Die Infinite Elemente Methode wird hauptsachlich bei der
Berechnung singularer Loesungen partieller Differentialgleichungen
und bei deren Loesung von Gleichungen auf unbeschrankten Gebieten
angewandt. In dem Buch wird ein spezielles numerisches Verfahren
vorgestellt, das bisher noch relativ unbekannt geblieben ist.
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