THE CONJUGATED VS. THE UNCONJUGATED INFINITE ELEMENT METHOD FOR THE HELMHOLTZ-EQUATION IN EXTERIOR DOMAINS

This work is devoted to a convergence study of infinite element (IE) d iscretizations for the Helmholtz equation in exterior domains. The dif ferent behavior of the conjugated and the unconjugated IE formulation is analyzed in context of (1) a formulation following a mathematical e xistence theory by Leis, (2) a formulation not based on an available e xistence theory following Burnett. Four variational formulations are p resented and the differences in implementing them are discussed. The e ffect of using or not using the complex conjugate in the weak formulat ion is carefully studied. The numerical and theoretical results clearl y indicate which of the four presented formulations is the most effici ent that can still give reliable results.