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Numerical steepest descent for singular and oscillatory integrals

Presented by: 
Andrew Gibbs
Monday 9th December 2019 - 14:30 to 15:00
INI Seminar Room 1

Co-Authors: Daan Huybrechs, David Hewett

When modelling high frequency scattering, a common approach is to enrich the approximation space with oscillatory basis functions. This can lead to a significant reduction in the DOFs required to accurately represent the solution, which is advantageous in terms of memory requirements and it makes the discrete system significantly easier to solve. A potential drawback is that the each element in the discrete system is a highly oscillatory, and sometimes singular, integral. Therefore an efficient 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 have designed for this purpose, combining Numerical Steepest Descent (which works well for oscillatory integrals) with Generalised Gaussian quadrature (which works well for singular integrals).

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons