Numerical solution of the ${\mathbb R}$-linear Beltrami equation

Abstract:

The $\mathbb {R}$-linear Beltrami equation appears in applications, such as the inverse problem of recovering the electrical conductivity distribution in the plane. In this paper, a new way to discretize the $\mathbb {R}$-linear Beltrami equation is considered. This gives rise to large and dense $\mathbb {R}$-linear systems of equations with structure. For their iterative solution, norm minimizing Krylov subspace methods are devised. In the numerical experiments, these improvements combined are shown to lead to speed-ups of almost two orders of magnitude in the electrical conductivity problem.