Related papers: A positivity preserving convergent event based asy…
In this paper, we improve the original Lagrange multiplier approach \cite{ChSh22,ChSh_II22} and introduce a new energy correction approach to construct a class of robust, positivity/bound-preserving, mass conserving and energy dissipative…
Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…
As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure. These systems are associated with non-increasing entropy…
The scalability of massively parallel algorithms is a fundamental question in computer science. We study the scalability and the efficiency of a conservative massively parallel algorithm for discrete-event simulations where the discrete…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
High-dimensional portfolio optimization faces significant computational challenges under complex constraints, with traditional optimization methods struggling to balance convergence speed and global exploration capability. To address this,…
Event cameras respond to brightness changes in the scene asynchronously and independently for every pixel. Due to the properties, these cameras have distinct features: high dynamic range (HDR), high temporal resolution, and low power…
We consider numerical approximations for a phase field dendritic crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation together. We propose two efficient,…
This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal…
For a system of partial differential equations (PDEs) $F = 0$ admitting a local (point, contact, or higher) symmetry $X$ with the characteristic $\varphi$, invariant solutions satisfy the reduced system $F = \varphi = 0$. We propose a…
We address a class of schemes for the Euler equations with the following features: the space discretization is staggered, possible upwinding is performed with respect to the material velocity only and the internal energy balance is solved,…
This paper deals with the construction of numerical stable solutions of random mean square Fisher-KPP models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique…
In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum…
In this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods,…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
Mass-conservative reaction-diffusion systems have recently been proposed as a general framework to describe intracellular pattern formation. These systems have been used to model the conformational switching of proteins as they cycle from…
We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling. The scheme is fully discrete and structure preserving in…
In this paper, we develop numerical methods for solving Stochastic Differential Equations (SDEs) with solutions that evolve within a hypercube $D$ in $\mathbb{R}^d$. Our approach is based on a convex combination of two numerical flows, both…
The shear shallow water model is an extension of the classical shallow water model to include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non-conservative products. We develop a high-order entropy…
A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its…