Purpose The most used numerical method in electrical engineering resources is the finite element method (FEM). This paper aims to present the use of the finite volume method to solve differential systems that contain the curl-curl operator. Design/methodology/approach Two discretization approaches have been implemented and tested. In the first one, the authors present the approximation of the curl operator using the diamond scheme. The second approach, called the split-diamond scheme, is a dual version of the first for heterogeneous media. A comparison with FEM software is performed to validate the proposed approaches and highlight the advantages of the second method. Findings The authors validate the adaptation of the curl-curl operator on both schemes. The expected second-order spatial accuracy is obtained. For steep discontinuous media, the authors show that the split-diamond scheme greatly reduces the approximation errors. Originality/value Edge FEMs are usually used for the curl-curl operator because their basis functions naturally provide the continuity of the tangential component. The authors propose a finite volume method to solve the H-formulation obtained from Maxwell equations. The curl-curl operator is rewritten as div-grad to respect the requirements of the finite volume method. Inspired by an approximation of grad, the authors propose an approximation of curl operator. The flux expressions considered here to connect neighboring cells provide the continuity of the tangential component.
Poirier et al. (Tue,) studied this question.