High-accuracy adaptive modeling of the energy distribution of a meniscus-shaped cell culture in a Petri dish

Cylindrical Petri dishes embedded in a rectangular waveguide and exposed to a polarized electromagnetic wave are often used to grow cell cultures. To guarantee the success of these cultures, it is necessary to enforce that the specific absorption rate distribution is sufficiently high and uniform over the Petri dish. Accurate numerical simulations are needed to design such systems. These simulations constitute a challenge due to the strong discontinuity of electromagnetic material properties involved, the relative low field value within the dish cultures compared with the rest of the domain, and the presence of the meniscus shape developed at the liquid boundary. The latter greatly increases the level of complexity of the model in terms of geometry and intensity of the gradients/singularities of the field solution. In here, we employ a three-dimensional (3D) hp-adaptive finite element method using isoparametric elements to obtain highly accurate simulations. We analyze the impact of the geometrical modeling of the meniscus shape cell culture in the hp-adaptivity. Numerical results showing the error convergence history indicate the numerical difficulties arisen due to the presence of a meniscus-shaped object. At the same time, the resulting energy distribution shows that to consider such meniscus shape is essential to guarantee the success of the cell culture from the biological point of view.