Abstract
This paper derives two new integrated and explicit boundary conditions, named the “explicit normal version” and “explicit tangential versions” respectively for electromagnetic fields at an arbitrary interface between two anisotropic media. The new versions combine two implicit boundary equations into a single explicit matrix formula and reveal the boundary values linked by a 3 × 3 matrix, which depends on the interface topography and model property tensors. We analytically demonstrate the new versions equivalent to the common implicit boundary conditions and their application to transformation of the boundary values in the boundary integral equations. We also give two synthetic examples that show recovery of the boundary values on a hill and a ridge, and highlight the advantage of the new versions of being a simpler and more straightforward method to compute the electromagnetic boundary values.
Highlights
The boundary conditions are often expressed in two equations―continuity of the tangential components and discontinuity of the normal components of electromagnetic field intensities ( E, H ) [1]
This paper derives two new integrated and explicit versions of the boundary conditions, called the explicit “normal” and “tangential” versions respectively. They successfully combine two common implicit boundary equations into a single explicit linear matrix formula without altering their applicability to interfaces that have arbitrary topography and two anisotropic media. These new versions consistently present the boundary values of electromagnetic field intensities ( E, H ) linked by a 3 × 3 matrix, which can be calculated with the known interface topography (n) and tensors of model electric permittivity (ε ), conductivity (σ ) and magnetic permeability (μ )
Two new integrated and explicit boundary conditions, termed the “normal” and “tangential” versions, have been presented in this paper for electromagnetic fields at an arbitrary interface between two anisotropic media. These two versions both achieve combination of two implicit boundary equations into a single explicit linear matrix form, and consistently reveal that the boundary values are linked by a 3 × 3 boundary matrix dependent on the interface topography and electric conductivity or magnetic permeability tensors of the media
Summary
The boundary conditions are often expressed in two equations―continuity of the tangential components and discontinuity of the normal components of electromagnetic field intensities ( E, H ) [1]. This paper derives two new integrated and explicit versions of the boundary conditions, called the explicit “normal” and “tangential” versions respectively They successfully combine two common implicit boundary equations into a single explicit linear matrix formula without altering their applicability to interfaces that have arbitrary topography and two anisotropic media. These new versions consistently present the boundary values of electromagnetic field intensities ( E, H ) linked by a 3 × 3 matrix, which can be calculated with the known interface topography (n) and tensors of model electric permittivity (ε ), conductivity (σ ) and magnetic permeability (μ ). Two synthetic experiments of utilizing the new versions are conducted, and show the advantage of the new versions of being a simpler and more straightforward method to recover the whole boundary values at arbitrary interfaces
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