Abstract
Dual formulations are more reliable and accurate in computing energy-related global quantities such as inductances and capacitances by providing the upper and lower bounds of the true values of the global energy-related quantities. Existing dual formulations adopt different variables belongs to totally different finite element spaces and thus will produce totally different algebraic matrix equations to be solved separately. In this work, two recently proposed dual formulations for open region problems where the coefficient matrices are exactly the same, are generalized to solve problems with general boundary conditions for cases with reduced full model or other scenarios. Two numerical examples are computed to show the accuracy of the proposed formulations.
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