Related papers: MultiWave: A computational lab for adaptive numeri…
Quantum trajectory methods can be used for a wide range of open quantum systems to solve the master equation by unraveling the density operator evolution into individual stochastic trajectories in Hilbert space. This C++ class library…
The Coherent Multiplex is formalized and validated as a scalable, real-time system for identifying, analyzing, and visualizing coherence among multiple time series. Its architecture comprises a fast spectral similarity layer based on cosine…
This paper develops an efficient Monte Carlo interior penalty discontinuous Galerkin method for electromagnetic wave propagation in random media. This method is based on a multi-modes expansion of the solution to the time-harmonic random…
Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
Motivated by simulations of ultrasound-enhanced drug delivery, this work presents the numerical analysis of a mathematical model that captures the influence of ultrasound waves on the diffusivity of the drug. The system under study consists…
In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber…
Metastability is one of the major encountered obstacle when performing long molecular dynamics simulations, and many methods were developed to address this challenge. The "Parallel Replica" (ParRep) dynamics is known for allowing to…
The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit…
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation…
In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together…
A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged…
A rezoning-type adaptive moving mesh discontinuous Galerkin method is proposed for the numerical solution of the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the simulation of perturbation…
In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law…
In this paper, we focus on the construction of a hybrid scheme for the approximation of non-Maxwellian kinetic models with uncertainties. In the context of multiagent systems, the introduction of a kernel at the kinetic level is useful to…
We are interested in numerically solving the Hamilton-Jacobi (HJ) equations, which arise in optimal control and many other applications. Oftentimes, such equations are posed in high dimensions, and this poses great numerical challenges.…
Programmable wireless environments enable the software-defined propagation of waves within them, yielding exceptional performance potential. Several building-block technologies have been implemented and evaluated at the physical layer. The…
Wave turbulence is by nature a multiple time scale problem for which there is a natural asymptotic closure. The main result of this analytical theory is the kinetic equation that describes the long-time statistical behaviour of such…
A challenging and fundamental research problem is the better understanding and control of the turbulent transport of heat in present-day tokamak fusion experiments. Recent developments in numerical methods along with enormous gains in…
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with…