  This paper deals with the discrete counterpart of 2D elliptic model problems
rewritten in terms of Boundary Integral Equations. The study is done within the
framework of Isogeometric Analysis based on B-splines. In such a context, the
problem of constructing appropriate, accurate and efficient quadrature rules
for the Symmetric Galerkin Boundary Element Method is here investigated. The
new integration schemes, together with row assembly and sum factorization, are
used to build a more efficient strategy to derive the final linear system of
equations. Key ingredients are weighted quadrature rules tailored for
B--splines, that are constructed to be exact in the whole test space, also with
respect to the singular kernel. Several simulations are presented and
discussed, showing accurate evaluation of the involved integrals and outlining
the superiority of the new approach in terms of computational cost and elapsed
time with respect to the standard element-by-element assembly.
