**Authors:** J. Kornprobst, J. Knapp, T. F. Eibert

**Source:** FERMAT, Volume 34, Communication 1, Jul.-Aug., 2019

**Abstract:** Starting from the monopolar representation of the Rao-Wilton-Glisson (RWG) functions, an approximate inverse (AI) of the RWG Gram matrix is constructed, where only 3x3 matrices for all individual triangles have to be inverted. The inversion of the Gram matrix is, however, only approximate, since it results as the inverse of a product of singular matrices, which is not easily obtained. The AI is shown to be an effective preconditioner for the RWG Gram matrix and is in particular useful for ill-conditioned Gram matrics on distorted meshes.

**Index Terms:** Gram matrix, Rao-Wilton-Glisson functions, preconditioner, matrix inversion

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