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One of the main problems in computing the UTD surface diffracted fields on surfaces described by Non-Uniform Rational B-splines (NURBS) is due to the difficulty in determining the geodesic paths the electromagnetic waves takes along the surface. In this paper we discuss some of the numerical algorithms that are used for computing surface diffraction on NURBS surfaces

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In this paper we propose a technique for including UTD surface diffracted fields which are diffracted from curved convex objects into a multilevel fast multipole implementation (MLFMM) of the Finite Element Boundary Integral method. We use Non-Uniform Rational B-splines (NURBS) representation for efficiently describing arbitrarily shaped objects. The dyadic Green's function associated with UTD field scattered by these convex curved object is determined using a high frequency raybased method and then inserted at the various levels of the MLFMM. Results show that the proposed hybrid MLFMM-FEBI-UTD technique for convex object allows a significant reduction in memory storage and computational effort, preserving however the accuracy in the field estimates.