A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem

In this paper,a meshless regularization method of fundamental solutions is proposed for a two-dimensional,two-phase linear inverse Stefan problem.The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions.Furthermore,the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution.Therefore,regularization is necessary in order to obtain a stable solution.Numerical results for several benchmark test examples are presented and discussed.

Agent-based modeling of COVID-19 outbreaks for New York state and UK:Parameter identification algorithm

This paper uses Covasim,an agent-based model(ABM)of COVID-19,to evaluate and scenarios of epidemic spread in New York State(USA)and the UK.Epidemiological parameters such as contagiousness(virus transmission rate),initial number of infected people,and probability of being tested depend on the region's demographic and geographical features,the containment measures introduced;they are calibrated to data about COVID-19 spread in the region of interest.At the first stage of our study,epidemiological data(numbers of people tested,diagnoses,critical cases,hospitalizations,and deaths)for each of the mentioned regions were analyzed.The data were characterized in terms of seasonality,stationarity,and dependency spaces,and were extrapolated using machine learning techniques to specify unknown epidemiological parameters of the model.At the second stage,the Optuna optimizer based on the tree Parzen estimation method for objective function minimization was applied to determine the model's unknown parameters.The model was validated with the historical data of 2020.The modeled results of COVID-19 spread in New York State and the UK have demonstrated that if the level of testing and containment measures is preserved,the number of positive cases in New York State remain the same during March of 2021,while in the UK it will reduce.

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

We propose a new moving pseudo-boundary method of fundamental solutions(MFS)for the determination of the boundary of a three-dimensional void(rigid inclusion or cavity)within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary.The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions.We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear leastsquares minimization.The feasibility of this new method is illustrated in several numerical examples.