Related papers: On the integration of stochastic rigid body with g…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…
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…
Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…
We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…
In this paper we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schroedinger equation. We will design stochastic integrators which almost conserve the symplectic structure. The idea is…
The simulation of multi-body systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make the…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
This paper presents an analytical model and a geometric numerical integrator for a tethered spacecraft model that is composed of two rigid bodies connected by an elastic tether. This model includes important dynamic characteristics of…
In this work, we provide a specifc trigonometric stochastic numerical method for linear oscillators with high constant frequencies, driven by a nonlinear time-varying force and a random force. We present some theoretical considerations and…
We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…
In silico models of cardiac electromechanics couple together mathematical models describing different physics. One instance is represented by the model describing the generation of active force, coupled with the one of tissue mechanics. For…
In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the…
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 develop a rigorous analytical framework for a coupled stochastic fluid-rigid body system in $\mathbb{R}^3$. The model describes the motion of a rigid ball immersed in an incompressible Newtonian fluid subjected to both additive noise in…
We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…
In this article we show in details the derivation of an integration scheme for the dissipative particle dynamic model (DPD) using the stochastic Trotter formula [De Fabritiis et al., Physica A, 361, 429 (2006)]. We explain some subtleties…
Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in…