Authors’ summary: A simplified \(h\)-version of the adaptive boundary elements is proposed for the eigenvalue analysis of the Helmholtz equation. The new scheme considers the effect of each local boundary element refinement, not on the eigenvalue but on the eigenvector, which is devised for possible application of the conventional adaptive mesh construction strategy for boundary value problems.
In this paper, for improvement of computational efficiency, the local analysis for obtaining the eigenvector is employed. The error indicator of the eigenvector in place of that of the eigenvalue, the global value, decides selectively the boundary elements to be refined. Utility of the proposed method is compared, through some examples, with those previously developed.