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This paper concerns the fast, highly accurate, and exponentially convergent solution of three sets of integral equations pertaining to two-dimensional generalized microstrip or microslot structures. The analysis relies on Nyström's method with due regard to all singular integrals and slowly converging series that appear in the kernels; the sophisticated treatment and efficient computation of such series and integrals is of paramount importance, entailing the use of advanced techniques. As a result of our specialized treatment, the discretization procedures developed herein: a) fully account for both the singular nature of the kernels and the singularities of the solution at the edges; b) obviate the need for taking inner products with testing functions; c) appear to converge exponentially versus matrix size; and d) enable expressing all matrix elements via single, finite sums. Detailed numerical examples and case studies illustrate the simplicity, flexibility, and remarkable efficiency of the algorithms.

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