A magnetic type integral operator which is stable till extremely low frequencies

We introduce a new magnetic field integral equation that does not suffer from low-frequency numerical cancelations even for extremely low frequencies (10-40Hz). The new equation is obtained by symmetrizing the standard MFIE with its dual equation and by using appropriately chosen quasi-Helmholtz projectors. When compared to mixed discretized MFIEs, the new equation maintains the favorable properties of mixed discretizations even without using high precision integration rules. Numerical results confirm the theoretical developments and show the effectiveness of the new scheme

A multiplicative Calderón preconditioner for the electric field integral equation

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High-order div- and quasi curl-conforming basis functions for calderon multiplicative preconditioning of the EFIE

A new high-order Calderon multiplicative preconditioner (HO-CMP) for the electric field integral equation (EFIE) is presented. In contrast to previous CMPs, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of high-order quasi curl-conforming basis functions. Like its predecessors, the HO-CMP can be seamlessly integrated into existing EFIE codes. Numerical results demonstrate that the linear systems of equations obtained using the proposed HO-CMP converge rapidly, regardless of the mesh density and of the order of the current expansion