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PathFinder: a toolbox for oscillatory integrals by deforming into the complex plane

Presented by: 
Daan Huybrechs
Monday 9th December 2019 - 11:30 to 12:30
INI Seminar Room 1

We present PathFinder, a Matlab toolbox developed by Andrew Gibbs for the computation of oscillatory integrals. The methods are based on the numerical evaluation of line integrals in the complex plane, which mostly follow paths of steepest descent. The toolbox aims for automation and robustness: the path deformation is found fully automatically, but the paths correspond to those of steepest descent only if doing so has guarantees of correctness. We face a trade-off between achieving asymptotic orders of accuracy, i.e. increasing accuracy with increasing frequency much like asymptotic expansions, and reliable accuracy. In the toolbox we aim for the former, but give precedence to the latter. We conclude with an example of scattering integrals with phase functions that may have clusters of coalescing saddle points.

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