Related papers: On Particles and Splines in Bounded Domains
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically…
This short note introduces a novel diagnostic tool for evaluating the convection boundedness properties of numerical schemes across discontinuities. The proposed method is based on the convection boundedness criterion and the normalised…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…
We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…
This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a…
Many physical problems can be modelled by partial differential equations on unknown domains. Several examples can easily be found in the dynamics of free interfaces in fluid dynamics, solid mechanics or in fluid-solid interactions. To solve…
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…
We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satisfying geometric conditions at the boundary. We develop a…
We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection-diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard…
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded…
We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…
Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their…
Unfitted boundary methods are widely used to numerically solve partial differential equations (PDEs) on irregular domains, avoiding the computational burden of generating boundary-conforming grids. In the finite-difference framework,…
In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…
This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…