This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the magnetic and electric fields on the boundary as inputs and outputs. Suitable expressions for the energy stored in the region and the energy absorbed from the boundaries are introduced, and used to show that the FDTD system is dissipative under a generalized Courant-Friedrichs-Lewy condition. Based on the concept of dissipation, a powerful theoretical framework to investigate the stability of FDTD methods is devised. The new method makes FDTD stability proofs simpler, more intuitive, and modular. Stability conditions can indeed be given on the individual components (e.g. boundary conditions, meshes, embedded models) instead of the whole coupled setup. As an example of application, we derive a new subgridding method with material traverse, arbitrary grid refinement, and guaranteed stability. The method is easy to implement and has a straightforward stability proof. Numerical results confirm its stability, low reflections, and ability to handle material traverse.

The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be particularly challenging in scenarios where a setup is composed of multiple components, such as grids of different resolution, advanced boundary conditions, reduced-order models, and lumped elements. We propose a dissipation theory for 3-D FDTD inspired by the principle of energy conservation. We view the FDTD update equations for a 3-D region as a dynamical system, and show under which conditions the system is dissipative. By requiring each component of an FDTD-like scheme to be dissipative, the stability of the overall coupled scheme follows by construction. The proposed framework enables the creation of provably stable schemes in an easy and modular fashion, since conditions are imposed on the individual components, rather than on the overall coupled scheme as in existing approaches. With the proposed framework, we derive a new subgridding scheme with guaranteed stability, low reflections, support for material traverse and arbitrary (odd) grid refinement ratio.

A wearable microsystem for low-latency automatic sleep stage classification and REM sleep detection in rodents is presented. The detection algorithm is implemented digitally to achieve low latency and is optimized for low complexity and power consumption. The algorithm uses both EEG and EMG signals as inputs. Experimental results using off-line signals from nine mice show REM detection sensitivity and specificity of 81.69% and 93.83%, respectively, with a latency of 39µs. The system will be used in a non-disruptive closed loop REM sleep suppression microsystem to study the effects of REM sleep deprivation on memory consolidation.

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