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2016•PORTO Publications Open Repository TOrino (Politecnico di Torino)Requires access

On the Hierarchical Preconditioning of the Combined Field Integral Equation

Simon B. Adrian, Francesco P. Andriulli, Thomas F. Eibert

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Abstract

This paper analyzes how hierarchical bases preconditioners constructed for the Electric Field Integral Equation (EFIE) can be effectively applied to the Combined Field Integral Equation (CFIE). For the case where no hierarchical solenoidal basis is available (e.g., on unstructured meshes), a new scheme is proposed: the CFIE is implicitly preconditioned on the solenoidal Helmholtz subspace by using a Helmholtz projector, while a hierarchical non-solenoidal basis is used for the non-solenoidal Helmholtz subspace. This results in a well-conditioned system. Numerical results corroborate the presented theory.

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What this paper is about

This paper analyzes how hierarchical bases preconditioners constructed for the Electric Field Integral Equation (EFIE) can be effectively applied to the Combined Field Integral Equation (CFIE). For the case where no hierarchical solenoidal basis is available (e.g., on unstructured meshes), a new scheme is proposed: the CFIE is implicitly preconditioned on the solenoidal Helmholtz subspace by using a Helmholtz projector, while a hierarchical non-solenoidal basis is used for the non-solenoidal Helmholtz subspace. This results in a well-conditioned system. Numerical results corroborate the presented theory.

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Available abstract

This paper analyzes how hierarchical bases preconditioners constructed for the Electric Field Integral Equation (EFIE) can be effectively applied to the Combined Field Integral Equation (CFIE). For the case where no hierarchical solenoidal basis is available (e.g., on unstructured meshes), a new scheme is proposed: the CFIE is implicitly preconditioned on the solenoidal Helmholtz subspace by using a Helmholtz projector, while a hierarchical non-solenoidal basis is used for the non-solenoidal Helmholtz subspace. This results in a well-conditioned system. Numerical results corroborate the presented theory.

Key concepts: Solenoidal vector field, Electric-field integral equation, Mathematics, Integral equation, Subspace topology, Helmholtz free energy, Helmholtz equation, Polygon mesh

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