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In this paper, we propose a new second-order fast finite difference scheme in time for solving the Tempered Time Fractional Advection-Dispersion Equation. Under the assumption that the solution is nonsmooth at the initial time, we…

We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a…

We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…

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…

Large-scale scientific simulations require significant resources to generate high-resolution time-varying data (TVD). While super-resolution is an efficient post-processing strategy to reduce costs, existing methods rely on a large amount…

We are interested in the high-order approximation of anisotropic, potential-driven advection-diffusion models on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

Alternative finite difference Weighted Essentially Non-Oscillatory (AFD-WENO) schemes allow us to very efficiently update hyperbolic systems even in complex geometries. Recent innovations in AFD-WENO methods allow us to treat hyperbolic…

This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…

Asymmetric distributed constraint optimization problems (ADCOPs) are an emerging model for coordinating agents with personal preferences. However, the existing inference-based complete algorithms which use local eliminations cannot be…

This paper proposes a first-order total variation diminishing (TVD) treatment for coarsening and refining of local timestep size in response to dynamic local variations in wave speeds for nonlinear conservation laws. The algorithm is…

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…

In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cases: the diffusion equation, the advection-diffusion equation…

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…

This work proposes a novel shape optimization framework for geometric inverse problems governed by the advection--diffusion equation, based on the coupled complex boundary method (CCBM). Building on recent developments [Afr22, Rab23, Rab25,…

Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…

Anomaly detection in complex, high-dimensional data, such as UAV sensor readings, is essential for operational safety but challenging for existing methods due to their limited sensitivity, scalability, and inability to capture intricate…

Solving compressible flows containing discontinuities remains a major challenge for numerical methods especially on unstructured grids. Thus in this work, we make contributions to shock capturing schemes on unstructured grids with aim of…

The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…

This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a…