The embedded curved boundary method for orthogonal simulation meshes (Q1383032)

This article considers the problem of representing curved boundary data in an orthogonal mesh. Whereas unstructured finite element meshes usually allow a precise representation of those data in orthogonal meshes this is in general more difficult. However, since orthogonal meshes enjoy a number of implementational advantages their use might be favourable. In order to make use of these advantages in the presence of curved boundary data the so called embedded curved boundary technique is developed. Here the boundary data structure is superimposed onto the orthogonal grid, and taken into account in the resulting linear systems. The author discusses a suitable data structure, the derivation of the resulting equations for elliptic problems and the problem of the computation of the gradients and curls near the structure boundaries. Finally, numerical results for the space-charge-limited flow between curved electrodes are presented.