Improved Discretization of the Full First-Order Magnetic Field Integral Equation

Abstract

The inaccuracy of the classical magnetic field integral equation (MFIE) is a long-studied problem. We investigate one of the potential approaches to solve the accuracy problem: higher-order discretization schemes. While these are able to offer increased accuracy, we demonstrate that the accuracy problem may still be present. We propose an advanced scheme based on a weak-form discretization of the identity operator which is able to improve the high-frequency MFIE accuracy considerably -without any significant increase in computational effort or complexity.

Accuracy Analysis of Div-Conforming Hierarchical Higher-Order Discretization Schemes for the Magnetic Field Integral Equation

“…In order to be on the safe side regarding the possibly negative influence of ker G 𝜶 LO ,𝜷 LO on the one hand and to ensure a sufficient accuracy improvement on the other hand, slightly larger values -𝛾 0.5 = 0.5, 𝛾 1.0 = 0.8, and 𝛾 1.5 = 0.925 -are chosen in the following. The underlying mesh refinement analyses for these proposed values of 𝛾 𝑝 , 𝑝 ∈ {0.5, 1.0}, have been presented in [34].…”

“…The approaches with div-conforming basis functions often choose curl-conforming testing functions or a mixture of curl-and div-conforming ones [23]- [26]. Furthermore, it was demonstrated that div-conforming HO expansion approaches may improve the accuracy of both the EFIE and MFIE [27]- [34], where it remains unclear whether the MFIE inaccuracy issues are really completely resolved or only partially. More recently, it was proposed to improve the accuracy of the high-frequency RWG MFIE by applying a weak-form (WF) discretization scheme for the discretized identity operator while working with classical div-conforming RWG testing functions [26].…”

“…In particalur, we demonstrate that a hierarchical HO basis [28]- [30] is only capable of curing the MFIE inaccuracies in part and additional measures seem to be required to boost the MFIE accuracy to really good levels. Preliminary results regarding the accurate full first-order discretization of the MFIE only are found in [34].…”

Accuracy Analysis of Div-Conforming Hierarchical Higher-Order Discretization Schemes for the Magnetic Field Integral Equation

“…The approaches with div-conforming basis functions often choose curl-conforming testing functions or a mixture of curl-and div-conforming ones [23]- [26]. Furthermore, it was demonstrated that div-conforming HO expansion approaches may improve the accuracy of both the EFIE and MFIE [27]- [34], where it remains unclear whether the MFIE inaccuracy issues are really completely resolved or only partially. More recently, it was proposed to improve the accuracy of the high-frequency RWG MFIE by applying a weak-form (WF) discretization scheme for the discretized identity operator while working with classical div-conforming RWG testing functions [26].…”

“…In particalur, we demonstrate that a hierarchical HO basis [28]- [30] is only capable of curing the MFIE inaccuracies in part and additional measures seem to be required to boost the MFIE accuracy to really good levels. Preliminary results regarding the accurate full first-order discretization of the MFIE only are found in [34].…”