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Talk

Computing with spherical geometries: from implicit solvation models to stochastic homogenisation

  • Benjamin Stamm (Rheinisch-Westfälische Technische Hochschule Aachen)
A3 01 (Sophus-Lie room)

Abstract

In this talk, a framework to solve elliptic interface problems on geometries involving spherical shapes is presented. Applications range from implicit solvation models in computational chemistry to electrostatic interaction of charged dielectric spheres to stochastic homogenisation with spherical inclusions. One of the main issues of elliptic problems is that the Green’s function is decaying very slowly. Therefore, the strategy is in all cases the same: we first transform the problem into an integral equation allowing for capturing the right asymptotic behaviour of the solution towards infinity. The integral equation is subsequently discretised by means of spherical harmonics on each sphere. In particular in the case of stochastic homogenisation, this approach allows for a new strategy of the corrector problem as one can solve problems on the unbounded domain where the stochastic medium is embedded in an infinite continuous medium. Numerical illustrations will underline the methodological developments.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss