相关论文: High-order stochastic integration schemes for the …
We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…
We formulate and test a hybrid fluid-Monte Carlo scheme for the treatment of elastic collisions in gases and plasmas. While our primary focus and demonstrations of applicability are for moderately collisional plasmas, as described by the…
The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a…
The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…
Three schemes, whose expressions are not too complex, are selected for the numerical integration of a system of stochastic differential equations in the Stratonovich interpretation: the integration methods of Heun, Milstein, and…
In this paper we describe a numerical algorithm for integrating the multicomponent, reacting, compressible Navier-Stokes equations, targeted for direct numerical simulation of combustion phenomena. The algorithm addresses two shortcomings…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that…
The dynamics of burning plasmas in tokamaks are crucial for advancing controlled thermonuclear fusion. This study applies the NeuralPlasmaODE, a multi-region multi-timescale transport model, to simulate the complex energy transfer processes…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
The explicit semi-Lagrangian method method for solution of Lagrangian transport equations as developed in [Natarajan and Jacobs, Computer and Fluids, 2020] is adopted for the solution of stochastic differential equations that is consistent…
In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is…
Because most chemical or biological experiments are performed under conditions of controlled pressure and temperature, it is important to simulate the isobaric-isothermal ensemble at the atomic level to reveal the microscopic mechanism. By…
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…
In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov--Fokker--Planck system coupled with Poisson or Amp\`ere equation. Splitting methods…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…