Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation
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In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...
In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...
The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned so ...
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 ...
In this paper we prove the global in time well-posedness of the following non-local diffusion equation with αε[0,2/3): ∂tu={(−Δ)−1u}Δu+αu2,u(t=0)=u0. The initial condition u0 is positive, rad ...
Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We descr ...
Problems that exhibit multiple time scales arise naturally in many scientific and engineering fields. For transient, distributed process systems, the corresponding models consist of partial differential equations (PDEs), possibly coupled to ordinary differ ...
In the first part of these notes, we deal with first order Hamiltonian systems in the form Ju'(t) = del H(u(t)) where the phase space X may be in infinite dimensional so as to accommodate some partial differential equations. The Hamiltonian H is an element ...
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as w ...
In this paper we introduce the framework of Partial difference Equations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with decentralized control schemes. Both leaderless and leader-follower models are considered. PdEs mimic ...