文档介绍：Finite Element Analysis
of Acoustic Scattering
Frank Ihlenburg
Springer
To Krystyna and Katja
Love’s not Time’s fool
— William Shakespeare, t 116
Preface
Als ¨uberragende Gestalt . . . tritt uns Helmholtz entgegen . . . Seine
außerordentliche Stellung in der Geschichte der Naturwissenschaf-
ten beruht auf einer ungew¨ohnlich vielseitigen, eindringenden Bega-
bung, innerhalb deren die mathematische Seite eine wichtige, f¨uruns
nat¨urlich in erster Linie in Betracht kommende Rolle spielt. (Felix
Klein, [84, p. 223])1
Waves are interesting physical phenomena with important practical appli-
cations. Physicists and engineers are interested in the reliable simulation
of processes in which waves are scattered from obstacles (scattering prob-
lems). This book deals with some of the mathematical issues arising in the
computational simulation of wave propagation and fluid–structure interac-
tion.
The linear mathematical models for wave propagation and scattering are
well-known. Assuming time-harmonic behavior, one deals with the Helm-
holtz equation ∆u + k2u = 0, where the wave number k is a physical
parameter. Our interest will be mainly in the numerical solution of exte-
rior boundary value problems for the Helmholtz equation which we call
Helmholtz problems for short.
The Helmholtz equation belongs to the classical equations of mathema-
tical physics. The fundamental questions about existence and uniqueness
1In Helmholtz we meet an overwhelming personality. His extraordinary position in
the history of science is based on his unusually diverse and rating talents, among
which the mathematical side, which for our present purpose is of primary importance,
plays an important role.
viii Preface
of solutions to Helmholtz problems were solved by the end of the 1950s; cf.,
., the monographs of Leis [87], Colton–Kress [39], and Sanchez Hubert–
Sanchez Palencia [107]. Those results of mathematical analysis form the
fundamental layer o