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We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement uncertainties using a Bayesian approach. Further, we discuss the influence of numerical accuracy on the reconstruction result.
Parallel in time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel in time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet no sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups.
Temperature-based estimation of time of death (ToD) can be per-
formed either with the help of simple phenomenological models of corpse
cooling or with detailed mechanistic (thermodynamic) heat transfer mod-
els. The latter are much more complex, but allow a higher accuracy of
ToD estimation as in principle all relevant cooling mechanisms can be
taken into account.
The potentially higher accuracy depends on the accuracy of tissue and
environmental parameters as well as on the geometric resolution. We in-
vestigate the impact of parameter variations and geometry representation
on the estimated ToD based on a highly detailed 3D corpse model, that
has been segmented and geometrically reconstructed from a computed to-
mography (CT) data set, differentiating various organs and tissue types.
From that we identify the most crucial parameters to measure or estimate,
and obtain a local uncertainty quantifcation for the ToD.