We propose a class of finite volume algorithms that are both simple and efficient for solving
numerically the shallow water equations with varying densities; shallow water flows in single …

Abstract Summation-by-Parts Finite Differences (SBP-FD) is an approach for approximation
of differential operators satisfying a discrete analogue of integration by parts analytic …

In this paper, we introduce a new framework for deriving partitioned implicit-exponential
integrators for stiff systems of ordinary differential equations and construct several time …

Deep learning is revolutionizing weather forecasting, with new data-driven models
achieving accuracy on par with operational physical models for medium-term predictions …

Within the context of fractional calculus, we investigate novel mathematical possibilities. In
this context, using the fractional dispersion relations for the fractional wave equation, we …

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine
propagator within a parallel iteration. It allows for large-scale parallelism that leads to …

High order exponential integrators require computing linear combination of exponential like
$\varphi $-functions of large matrices $ A $ times a vector $ v $. Krylov projection methods …

Despite the growing interest in parallel-in-time methods as an approach to accelerate
numerical simulations in atmospheric modeling, improving their stability and convergence …

Generally, discretization of partial differential equations (PDEs) creates a sequence of linear
systems $ A_k x_k= b_k, k= 0, 1, 2,..., N $ with well-known and structured sparsity patterns …

The goal of this project is to compare the performance of exponential time integrators with
traditional methods such as diagonally implicit Runge-Kutta methods in the context of …