Effect of finite precision on em simulations for high-contrast biological media at low frequencies

At low frequencies, biological media are characterized by extremely high permittivities. As a result, the most commonly used simulation methods, i.e. finite-difference time domain (FDTD), finite element method (FEM), and domain integral equations (DIE), suffer from severe limitations in accuracy. These limitations are caused by the round-off errors in finite-precision floating point operations. Finite precision causes error accumulation in FDTD due to the large number of time steps required to simulate one period and to maintain stability. In FEM, finite precision causes the numerical derivative to collapse due to the dependence on the mesh size. While the DIE is hardly influenced by the mesh size, the extreme permittivities cause a large difference in the order of magnitude of the various terms in the DIE.