Minimizing The 3D Solenoidal Basis Set in Method of Moments Based Volume Integral Equation
Keywords:
Divergence-free, method of moments (MoM), solenoidal edge basis functionAbstract
A method for completely minimizing a 3D-solenoidal basis set, and identifying its linearly independent basis functions in method of moments (MoM) based volume integral equation (VIE) is presented. The method uses the connecting information of the geometric mesh and the properties of the 3D solenoidal basis function to remove the null space of the basis set. Consequently, the approach is not prone to numerical inaccuracies due to finite machine precision resulting from matrix manipulations. In addition, our method is not restricted to simply connected or contiguous mesh regions; it is applicable to a wide variety of complicated mesh regions featuring holes and voids. Finally, an expression for determining the minimum number of linearly independent solenoidal basis functions in a given tetrahedral mesh is presented.
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References
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