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The conjugated vs. the unconjugated infinite element method for the Helmholtz equation in exterior domains

by K. Gerdes

(Report number 1996-11)

Abstract
This work is devoted to a convergence study of infinite element (IE) discretizations for the Helmholtz equation in exterior domains. The different behavior of the conjugated and the unconjugated IE formulation is analyzed in context of 1.) a formulation following a mathematical existence theory by Leis, 2.) a formulation not based on an available existence theory following Burnett. Four variational formulations are presented and the differences in implementing them are discussed. The effect of using or not using the complex conjugate in the weak formulation is carefully studied. The numerical and theoretical results clearly indicate which of the four presented formulations is the most efficient that can still give reliable results.

Keywords:

@Techreport{G96_194,
  author = {K. Gerdes},
  title = {The conjugated vs. the unconjugated infinite element method for the Helmholtz equation in exterior domains},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-11.pdf },
  year = {1996}
}

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