Remarks on numerical methods for conformal mapping of multiply connected domains and applications – Tom DeLillo (Wichita State University)

December 13, 2019 @ 2:00 pm – 2:30 pm
Seminar Room 1
Newton Institute

Conformal maps from multiply connected domains with circular boundaries to physical domains and complex velocity potentials for potential flow problems can be represented by Laurent series in the circle domains. The linear systems arising in the computation of the truncated series have a block structure in the form of the discrete Fourier transform plus low rank matrices representing the interaction of the circles plus certain auxiliary parameters such as the conformal moduli or the circulations of the flow. The conjugate gradient method can be used to solve these systems efficiently. We will give an outline of this approach. Time permitting, we will also give several examples of conformal map calculations.