W hen modelling high frequency scattering\, a common approach is to enrich the approximation space wit h oscillatory basis functions. This can lead to a significant reduction in the DOFs required to accu rately represent the solution\, which is advantage ous in terms of memory requirements and it makes t he discrete system significantly easier to solve. A potential drawback is that the each element in t he discrete system is a highly oscillatory\, and s ometimes singular\, integral. Therefore an efficie nt quadrature rule for such integrals is essential for an efficient scattering model. In this talk I will present a new class of quadrature rule we ha ve designed for this purpose\, combining Numerical Steepest Descent (which works well for oscillator y integrals) with Generalised Gaussian quadrature (which works well for singular integrals). LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR