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Approximate Inverse of the Rao-Wilton-Glisson Basis Functions Gram Matrix via Monopolar Representation
  • Jonas Kornprobst ,
  • Josef Knapp ,
  • Thomas F. Eibert
Jonas Kornprobst
Technical University of Munich

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Josef Knapp
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Thomas F. Eibert
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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.