相关论文: Finite-volume method and observability analysis fo…
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete spectral analysis, which is used to suggest optimal values of…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
State of health (SOH) estimation for lithium-ion battery modules with cells connected in parallel is a challenging problem, especially with cell-to-cell variations. Incremental capacity analysis (ICA) and differential voltage analysis (DVA)…
Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint…
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…
We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and…
Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion, water desalination, etc. Exactly-solvable models allow in-depth analyses…
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
The Steepest Entropy Ascent (SEA) ansatz, recently recognized as the fourth law of thermodynamics, governs the irreversible evolution of a system from a non-equilibrium state toward a unique maximum-entropy equilibrium. SEA builds upon the…
We compare the predicted phase behaviour of lead (Pb) using three different interatomic potential models, including an embedded atom method (EAM), a modified embedded atom method (MEAM), and a neural network-based machine-learned model in…
Reservoir simulators utilize numerical techniques to solve the governing equations of fluid flow in porous media and they are essential tool for oil and gas fields development. In practical reservoir simulation, the finite difference method…
Lithium-ion batteries (LIBs) of high energy density and light-weight design, have found wide applications in electronic devices and systems. Degradation mechanisms that caused by lithiation is a main challenging problem for LIBs with high…
Accounting for geometry-induced changes in the electronic distribution in molecular simulation is important for capturing effects such as charge flow, charge anisotropy and polarization. Multipolar force fields have demonstrated their…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
Lithium-ion battery (LIB) sources have played an essential role in self-sustained transportation energy systems and have been widely deployed in the last few years. To realize reliable battery maintenance, identifying its electrochemical…
Monitoring battery health is essential for ensuring safe and efficient operation. However, there is an inherent trade-off between assessment speed and diagnostic depth-specifically, between rapid overall health estimation and precise…