Multimodal Higher Order FDTD Analysis

FIGURE 7.1 (a) Geometry of an arbitrarily curved waveguide with a varying cross section, (b) Transverse cut of a three-port Y-junction comprising two ducts of elliptical cross section and different dimensions 

The elements of matrices W (z = A,. .., E) describe the fundamental curvature details. Hence, after enforcing the boundary constraints, one receives 

For the sufficient annihilation of vector parasites, equations (7.4) are direedy advanced in the time domain via the conventional, (2.14)-(2.20), or the nonstandard, (3.70)-(3.81), HO FDTD schemes. The above procedure provides E and H values at specific planes inside the bend. These values are next inserted as excitation terms in the FDTD formulas to proceed with the update mechanism in the usual manner. 

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