相关论文: Numerical Simulation of Macroscopic Traffic Equati…

Cellular automata (CA) play an important role in the development of computationally efficient microscopic traffic models and recently have gained considerable importance as a mean of optimising traffic control strategies. However, real-time…

In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…

We investigate the effects of numerical damping for oscillator simulation with spline methods. Numerical damping results in an artificial loss of energy and leads therefore to unreliable results in the simulation of autonomous systems, as…

Appropriate traffic regulations, e.g. planned road closure, are important in congested events. Crowd simulators have been used to find appropriate regulations by simulating multiple scenarios with different regulations. However, this…

We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…

In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the…

This work is a geometrical approach to the optimization problem motivated by transportation system management. First, an attempt has been made to furnish a comprehensive account of geometric programming based on the elementary Finsler…

One of the objectives of the pedestrian analysis is to evaluate the effects of proposed policy on the pedestrian facilities before its implementation. The implementation of a policy without pedestrian analysis might lead to a very costly…

We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…

The transport of scalar quantities passively advected by velocity fields with a small-scale component can be modeled at meso-scale level by means of an effective drift and an effective diffusivity, which can be determined by means of…

Parallel multiphysics simulations often suffer from load imbalances originating from the applied coupling of algorithms with spatially and temporally varying workloads. It is thus desirable to minimize these imbalances to reduce the time to…

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models,…

Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…

Inspired by path-integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids averaging over trajectories. To test the method,…

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…

Safety validation of autonomous driving systems is extremely challenging due to the high risks and costs of real-world testing as well as the rarity and diversity of potential failures. To address these challenges, we train a denoising…

Numeric simulations based on the Huygens-Fresnel method allow one to develop intuition about the behavior of coherent light in diffraction and interference experiments. They give an opportunity to numerically observe and appreciate a number…

The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…

Dense human flow has been a concern for the safety of public events for a long time. Macroscopic pedestrian models, which are mainly based on fluid dynamics, are often used to simulate huge crowds due to their low computational costs.…