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Mehrgitter Verfahren für die Ausbreitung von Aktionspotentialen entlang von Muskelfasern
Bearbeiter Tobias Walter
Betreuer Dr.-Ing. Nehzat Emamy
Prüfer Prof. Dr. rer. nat. habil. Miriam Mehl

The neuro-muscular system is a complex multiscale coupled system, for which some chemo-
electro-mechanical models are available. Realistic simulations of such models are computationally
extremely demanding. One computationally challenging part of the model is the propagation of the
action potential along muscle fibers. This propagation is well described by the monodomain partial
differential equation (PDE). The PDE is coupled with a set of nonlinear ordinary differential
equations (ODEs) resulting for example from the Hodgkin and Huxley (1952) model, which
resemble ionic currents at the cell membrane. To reduce the computational cost, we would like to
apply the multigrid techniques. A literatures survey is required to find out the proper technique for
our special case of coupled system.
The purpose of the project is to :

  • Implement the multigrid technique for the 1D diffusion problem as the first step.
  • Implement and test some ideas for multigrid solution of the coupled system of PDE and ODEs.

The method would be implemented in the under develop C++ code.