Combining cellular automata and lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition
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Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
A bottom-up modelling approach together with a set of calibration methodologies is presented to predict residential building occupants' time-dependent activities, for use in dynamic building simulations. The stochastic model to predict activity chains is c ...
We propose a novel method for the analysis of spatially distributed data from an exponential family distribution, able to efficiently treat data occurring over irregularly shaped domains. We consider a generalized linear framework and extend the work of Sa ...
A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates becaus ...
An analysis of a multiscale symmetric interior penalty discontinuous Galerkin finite element method for the numerical discretization of elliptic problems with multiple scales is proposed. This new method, first described in [A. Abdulle, C.R. Acad. Sci. Par ...
Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...
Bedload transport rate in mountain rivers is highly fluctuating and has strong stochastic behavior even under steady flow conditions. Its stochastic description thus offers deeper insights into its dynamics than the deterministic one. As a random quantity, ...
In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...
Liquid-phase sintering (LPS) is a consolidation process for metallic and ceramic powders. At given temperature conditions, the process occurs with constant amount of liquid phase. However, the evolution of solid-particle shape is observed, namely, the roun ...
