English
Related papers

Related papers: An explicit solution for implicit time stepping in…

200 papers

Numerical ice sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or…

Computational Physics · Physics 2023-08-16 Ed Bueler

This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step…

Numerical Analysis · Mathematics 2019-04-26 Rodolfo Ruben Rosales , Benjamin Seibold , David Shirokoff , Dong Zhou

This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…

Numerical Analysis · Mathematics 2025-10-27 Andrea Brugnoli , Denis Matignon , Joseph Morlier

A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…

In this work, we develop a class of stable and convergent numerical methods for the approximate solution of the viscoelastic Giesekus model in two space dimensions. The model couples the incompressible Navier--Stokes equations with an…

Numerical Analysis · Mathematics 2025-12-30 Endre Süli , Dennis Trautwein

We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations in the low Mach number regime. The method is based on finite differences on staggered grids and…

Numerical Analysis · Mathematics 2026-02-25 Andreu Martorell , Pep Mulet , Dionisio F. Yáñez

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…

Numerical Analysis · Mathematics 2022-07-27 Stein K. F. Stoter , Thi-Hoa Nguyen , René R. Hiemstra , Dominik Schillinger

The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment--fitting, local…

Numerical Analysis · Mathematics 2016-01-26 Maxim Olshanskii , Danil Safin

In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…

General Mathematics · Mathematics 2023-05-30 Aymen Laadhari , Ahmad Deeb

In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. This paper concerns resolvent…

Analysis of PDEs · Mathematics 2023-09-01 Maarten V. de Hoop , Masato Kimura , Ching-Lung Lin , Gen Nakamura

Simulations of the dynamic deformations of metal samples require elastic-plastic constitutive updates of the material behavior to be performed over a small time step between updates, as dictated by the Courant condition. Depending on the…

Materials Science · Physics 2007-05-23 S. N. Kuchnicki , A. M. Cuitino , R. A. Radovitzky

A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…

Optimization and Control · Mathematics 2014-11-19 L. Adam , J. V. Outrata , T. Roubicek

We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…

Fluid Dynamics · Physics 2016-08-31 Davide Modesti , Sergio Pirozzoli

This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…

Numerical Analysis · Computer Science 2013-11-13 Petr N. Vabishchevich

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Machine Learning · Computer Science 2025-06-06 Ruoxi Jiang , Xiao Zhang , Karan Jakhar , Peter Y. Lu , Pedram Hassanzadeh , Michael Maire , Rebecca Willett

An extension of the two-step staggered time discretization of linear elastodynamics in stress-velocity form to systems involving internal variables subjected to a possibly non-linear dissipative evolution is proposed. The original scheme is…

Numerical Analysis · Mathematics 2020-06-11 Tomáš Roubíček , Chrysoula Tsogka

In this work, we introduce a self-adaptive implicit-explicit (IMEX) time integration scheme, named IMEX-RB, for the numerical integration of systems of ordinary differential equations (ODEs), arising from spatial discretizations of partial…

Numerical Analysis · Mathematics 2025-07-28 Micol Bassanini , Simone Deparis , Francesco Sala , Riccardo Tenderini

In this article we design a finite volume semi-implicit IMEX scheme for the incompressible Navier-Stokes equations on evolving Chimera meshes. We employ a time discretization technique that separates explicit and implicit terms which…

Numerical Analysis · Mathematics 2023-08-08 Michele Giuliano Carlino , Walter Boscheri

In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of…

Numerical Analysis · Mathematics 2024-08-21 Gabriel R. Barrenechea , Ernesto Castillo , Douglas R. Q. Pacheco

Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…

Instrumentation and Methods for Astrophysics · Physics 2014-03-05 Benoit Commercon , Vincent Debout , Romain Teyssier