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In the meshless scheme for solving volume integral equations (VIEs), one needs to evaluate hypersingular integrals over a small cylindrical domain excluded from the whole domain for the sake of regularizing integrands. Those integrals can be evaluated semi-numerically but the implementation may not be convenient. In this work, we present some new formulas which are purely analytical for those integrals...
In the reconstruction of dielectric objects by integral equation approach (IEA), the forward scattering integral equation (FSIE) and the inverse scattering integral equation (ISIE) are alternatively solved in the frame of distorted Born iterative method (DBIM) or its variations. In this work, we consider the reconstruction under a limited observation which is more practical. We use a DBIM-like Gauss-Newton...
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