Related papers: Passivity-preserving splitting methods for rigid b…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
In this letter, based on the exponential scalar auxiliary variable technology, we propose and study a new class of explicit energy-preserving splitting methods for solving the charged-particle dynamics. The energy-preserving property of…
We introduce an efficient split finite element (FE) discretization of a y-independent (slice) model of the rotating shallow water equations. The study of this slice model provides insight towards developing schemes for the full 2D case.…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For…
In this article, a brief description of Discrete Mechanics and Variational Integrators which preserve the symplectic structure of the flow will be provided and a Newton-Raphson algorithm that can be used to solve implicit equations on the…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…
Construction of splitting-step methods and properties of related non-negativity and boundary preserving numerical algorithms for solving stochastic differential equations (SDEs) of Ito-type are discussed. We present convergence proofs for a…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…
We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…
We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to…
The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a stabilizing term to the flow equation, which includes a…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
A key ingredient to achieving intelligent behavior is physical understanding that equips robots with the ability to reason about the effects of their actions in a dynamic environment. Several methods have been proposed to learn dynamics…