Related papers: Perfectly matched layers for the Boltzmann equatio…
In this article, global stabilization results for the Benjamin-Bona-Mahony-Burgers' (BBM-B) type equations are obtained using nonlinear Neumann boundary feedback control laws. Based on the $C^0$-conforming finite element method, global…
Perfectly Matched Layer (PML) is a widely adopted non-reflecting boundary treatment for wave simulations. Reducing numerical reflections from a discretized PML has been a long lasting challenge. This paper presents a new discrete PML for…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
In the paper, we develop spectral theory to analyze the sharp asymptotic behavior of solutions to the Boltzmann equation around global Maxwellians in a three-dimensional infinite layer $\mathbb{R}^2\times (-1,1)$. The isothermal diffuse…
A two-fluid Discrete Boltzmann Model(DBM) for compressible flows based on Ellipsoidal Statistical Bhatnagar-Gross-Krook(ES-BGK) is presented. The model has flexible Prandtl number or specific heat ratio. Mathematically, the model is…
The linear Boltzmann equation governs the absorption and scattering of a population of particles in a medium with an ambient field, represented by a Riemannian metric, where particles follow geodesics. In this paper, we study the possible…
In this research, a mid-infrared wide-angle ultra-broadband perfect absorber which composed of pyramid grating structure has been comprehensively studied. The structure was operated in the reststrahlem band of SiC and with the presence of…
Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every…
The simplified lattice Boltzmann method (SLBM) is a recent development in the lattice Boltzmann method (LBM) community, addressing the intrinsic limitations of the traditional LBM by directly evolving macroscopic quantities and maintaining…
A coarse-graining strategy, previously developed for polymer solutions, is extended here to mixtures of linear polymers and hard-sphere colloids. In this approach groups of monomers are mapped onto a single pseudoatom (a blob) and the…
Perfectly-Matched Layers (PML) are widely used in Particle-In-Cell simulations, in order to absorb electromagnetic waves that propagate out of the simulation domain. However, when charged particles cross the interface between the simulation…
Supersonic flow simulations face challenges in trans-scale modeling, numerical stability, and complex field analysis due to inherent nonlinear, nonequilibrium, and multiscale characteristics. The discrete Boltzmann method (DBM) provides a…
Consider the electromagnetic scattering of a time-harmonic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper is concerned with the numerical solutions of the transverse…
This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses Pn and filtered Pn expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically…
Finding reduced models of spatially-distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy…
The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wave lengths. In the worst, ABC are not even…
Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for…
This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a…
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling…
A systematic analysis of matched layers is undertaken with special attention to better understand the remarkable method of B\'erenger. We prove that the B\'erenger and closely related layers define well posed transmission problems in great…