Fully explicit FEM formulation for NMR simulations using the Dufort- Frankel method

Resumo

In this paper we present a fully explicit finite element implementation for the simulation of the T2
relaxation and T1 recovery process in nuclear magnetic resonance experiments. We consider 2D domains defined
by images. We propose the combination of a lumped mass matrix and stable time-marching schemes to achieve
a fully explicit and stable simulation even with large time steps. The time-marching scheme we consider is the
Dufort-Frankel method which allows for large time-steps even for problems in the fast diffusion regime. We show
that the use of the lumped mass matrix adds a negligible amount of numerical error in comparison to the error
introduced by the discretization. We also show that this method compare favorably to the Explicit Euler in terms
of necessary number of time steps in order to achieve a reasonable threshold of numerical error.