ИСТИНА

The conventional volumetric integral equation (IE) approach in 3D electromagnetic modelling exploits the rectilinear meshes. However, with rectilinear meshes it is difficult to accurately model the effects arisen from the topography or/and bathymetry. Apparently, the most consistent way to address the problem is to represent the air-ground, or/and seawater-ground boundaries by curvilinear (high-order) meshes. We show that IE approach is capable to work in an efficient way with such meshes. The main challenge here is an accurate calculation of volumetric integrals of Green’s tensor over the domains (cells) with curvilinear boundaries. We demonstrate that by approximating the domain boundaries via Bezier surfaces and using the expansion of Green’s tensor via the piece-wise polynomial basis, one can calculate these integrals semi-analytically. Moreover, we show that such numerical scheme for integral calculation leads to computational loads which are comparable with those required by IE solutions with rectilinear meshes.