The Portable, Extensible Toolkit for Scientific Computation (PETSc), is a suite of data
structures and routines for the scalable (parallel) solution of scientific applications modeled …

In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

Approximation rate bounds for emulations of real-valued functions on intervals by deep
neural networks (DNNs) are established. The approximation results are given for DNNs …

We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

This manual describes the use of PETSc for the numerical solution of partial differential
equations and related problems on high-performance computers. The Portable, Extensible …

Spatial discretizations of time-dependent partial differential equations usually result in a
large system of semi-linear and stiff ordinary differential equations. Taking the structures into …

The main purpose of the paper is to show how to use implicit–explicit Runge–Kutta methods
in a much more general context than usually found in the literature, obtaining very effective …

In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the
Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization …

In this paper, we present a convergence analysis of a weak Galerkin finite element method
(WG-FEM) using polygonal meshes for the semilinear singularly perturbed time-dependent …

In this paper we introduce a space-dependent multiscale model to describe the spatial
spread of an infectious disease under uncertain data with particular interest in simulating the …