相关论文: Model and computational advancements to full vecto…
In this article we study the two dimensional singularly perturbed heat equation in a circular domain. The aim is to develop a numerical method with a uniform mesh, avoiding mesh refinement at the boundary thanks to the use of a relatively…
The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on…
Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent generating complex 3D interface-fitted meshes. However, many…
In this article we present a systematic derivation of the Maxwell-Bloch equations describing amplification and laser action in a ring cavity. We derive the Maxwell-Bloch equations for a two-level medium and discuss their applicability to…
We analyze the amplification processes occurring in a nonlinear fiber, either driven with one or two pumps. After determining the solution for the signal and idler fields resulting from these amplification processes, we analyze the physical…
Nonlinear amplification is a powerful technique for generating ultrashort laser pulses with high peak power in fiber systems. However, the diversity of nonlinear amplification approaches and their inherent complexities present significant…
Atomistic simulations of heat transport in complex materials are costly and hard to converge. This has led to the development of several noise-reduction techniques applicable to equilibrium molecular-dynamics (MD) simulations. We analyze…
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble…
A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…
Metal additive manufacturing via laser-based powder bed fusion (PBF-LB/M) faces performance-critical challenges due to complex melt pool and vapor dynamics, often oversimplified by computational models that neglect crucial aspects, such as…
We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests:…
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…
This paper describes three-dimensional numerical simulations and Radio Frequency (RF) measurements of wave propagation in microwave-heated magnetized plasmas of ion sources. Full-wave solution of Maxwell's equations has been addressed…
Optical and optoelectronic approaches of performing matrix-vector multiplication (MVM) operations have shown the great promise of accelerating machine learning (ML) algorithms with unprecedented performance. The incorporation of…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
We present an implementation of the Maxwell-Bloch (MB) formalism for the study of x-ray emission dynamics from periodic multilayer materials whether they are artificial or natural. The treatment is based on a direct…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
We propose a robust simulation method for phospholipid membranes. It is based on a mixed three-field formulation that accounts for tangential fluidity (Boussinesq-Scriven law), bending elasticity (Canham-Helfrich model) and inextensibility.…
We focus on non-stationary Maxwell equations defined on a regular patch of elements as considered in the isogeometric analysis (IGA). We apply the time-integration scheme following the ideas developed by the finite difference community [M.…