Related papers: On a Nonuniform Crank-Nicolson Scheme for Solving …
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
We demonstrate an approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of processes where the drift and diffusion coefficients are…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
We present a simple and robust strategy for the selection of sampling points in Uncertainty Quantification. The goal is to achieve the fastest possible convergence in the cumulative distribution function of a stochastic output of interest.…
We describe a short, reproducible workflow for applying finite differences on nonuniform grids determined by a positive weight function g. The grid is obtained by equidistribution, mapping uniform computational coordinates $\xi\in[0,1]$ to…
The adaptive spectral Koopman (ASK) method was introduced to numerically solve autonomous dynamical systems that lay the foundation of numerous applications across different fields in science and engineering. Although ASK achieves high…
The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
We present a numerical framework for computing nested quadrature rules for various weight functions. The well-known Kronrod method extends the Gauss-Legendre quadrature by adding new optimal nodes to the existing Gauss nodes for integration…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with respect to "Radici-Stra [SIAM J. Math. Anal. 55.3 (2023)]"…
We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with…
We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in…
The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrodinger equation. An adapted alternating-direction implicit method is used, along with a high-order finite difference…
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against…
This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture the singularities of "typical" solutions of time-fractional…
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…