Finite difference method

About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.

Efficient Reformulation of Solid-Phase Diffusion in Physics-Based Lithium-Ion Battery Models

Abstract: Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms with an appropriate discretization or approximation for the solid phase. One of the major difficulties in simulating Li-ion battery models is the need for simulating solid-phase diffusion in a second dimension r. It increases the complexity of the model as well as the computation time/cost to a great extent. Traditional approach toward solid-phase diffusion leads to more difficulties, with the use of emerging cathode materials, which involve phase changes and thus moving boundaries. A computationally efficient representation for solid-phase diffusion is discussed in this paper. The operating condition has a significant effect on the validity, accuracy, and efficiency of various approximations for the solid-phase diffusion. This paper compares approaches available today for solid-phase reformulation and provides two efficient forms for constant and varying diffusivities in the solid phase. This paper introduces an efficient method of an eigenfunction based Galerkin collocation and a mixed order finite difference method for approximating/representing solid-phase concentration variations within the active materials of porous electrodes for a pseudo-two-dimensional model for lithium-ion batteries.

On stable numerical differentiation

Abstract: Based on a regularized Volterra equation, two different approaches for numeri- cal differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete fa- vorably with the variational regularization method for stable calculating the derivatives of noisy functions.

Numerical Approximation of Some Linear Stochastic Partial Differential Equations Driven by Special Additive Noises

Abstract: This paper is concerned with the numerical approximation of some linear stochastic partial differential equations with additive noises. A special representation of the noise is considered, and it is compared with general representations of noises in the infinite dimensional setting. Convergence analysis and error estimates are presented for the numerical solution based on the standard finite difference and finite element methods. The effects of the noises on the accuracy of the approximations are illustrated. Results of the numerical experiments are provided.