Related papers: A Multilevel Monte Carlo Algorithm for Parabolic A…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
We use the Multi Level Monte Carlo method to estimate uncertainties in a Henry-like salt water intrusion problem with a fracture. The flow is induced by the variation of the density of the fluid phase, which depends on the mass fraction of…
In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate…
In this work, we consider a mathematical model for flow in a unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the flow is governed by Richards' equation. The submodels are…
Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…
Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
In this note, the existing porousMultiphaseFoam toolbox, developed initially for any two-phase flow in porous media is extended to the specific case of the Richards' equation which neglect the pressure gradient of the non-wetting phase.…
We consider conservation laws with discontinuous flux where the initial datum, the flux function, and the discontinuous spatial dependency coefficient are subject to randomness. We establish a notion of random adapted entropy solutions to…
This work is motivated by the need to develop efficient tools for uncertainty quantification in subsurface flows associated with radioactive waste disposal studies. We consider single phase flow problems in random porous media described by…
In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…