Related papers: Transformed implicit-explicit DIMSIMs with strong …
We propose an explicit partitioned (loosely coupled) scheme for fluid structure interaction (FSI) problems, specifically designed to achieve high computational efficiency in modern engineering simulations. The FSI problem under…
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact…
We present implicit and explicit versions of a numerical algorithm for solving a Volterra integro-differential equation. These algorithms are an extension of our previous work, and cater for a kernel of general form. We use an appropriate…
In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the…
We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse…
In this paper we combine a flexible covariant formulation of the shallow water equations with the semi-implicit numerical scheme developed over the years by Casulli and collaborators. After adopting an orthogonal, but non-orthonormal,…
We present a divergence-free semi-implicit finite volume scheme for the simulation of the ideal magnetohydrodynamics (MHD) equations which is stable for large time steps controlled by the local transport speed at all Mach and Alfv\'en…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of…
The main goal of this paper is to investigate the order reduction phenomenon that appears in the integral deferred correction (InDC) methods based on implicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class of stiff…
A numerical search approach is used to design high-order diagonally implicit Runge-Kutta (DIRK) schemes equipped with embedded error estimators, some of which have identical diagonal elements (SDIRK) and explicit first stage (ESDIRK). In…
In this paper, the design and analysis of high order accurate IMEX finite volume schemes for the compressible Euler-Poisson (EP) equations in the quasineutral limit is presented. As the quasineutral limit is singular for the governing…
Strong stability preserving (SSP) Runge-Kutta methods are often desired when evolving in time problems that have two components that have very different time scales. Where the SSP property is needed, it has been shown that implicit and…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
We consider solving the Laplace-Beltrami problem on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We…
In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
In this paper implicit and explicit exact difference schemes (EDS) for system $\textbf{x}' = A\textbf{x}$ of three linear differential equations with constant coefficients are constructed. Numerical simulations for stiff problem and for…