期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (2)
This paper is devoted to a study of nonlinear Robin-type boundary value problems of second-order elliptic partial differential equations. Specifically......
期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (2)
We study the time-domain acoustic scattering problem by a cluster of small holes (i.e., sound-soft obstacles). Based on the retarded boundary integral......
期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (1)
In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., the potential-ground state map of t......
期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (2)
In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coeffi......
期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (2)
This paper presents an efficient multiscale approach for solving the time-domain Maxwell's equations with rapidly oscillating coefficients coupled to ......
期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (1)
Starting from Hadamard's method, we develop Babich's ansatz for the frequency-domain point-source elastic wave equations in an inhomogeneous medium in......
期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (2)
In this article, we study wave dynamics in the fractional nonlinear Schrodinger equation with a modulated honeycomb potential. This problem arises fro......
期刊： MULTISCALE MODELING & SIMULATION, 2021; 19 (1)
We present a first-principle based approach that leads from a many-particle description to a nonlinear, stochastic constitutive relation for the model......
期刊： MULTISCALE MODELING & SIMULATION, 2020; 18 (2)
We consider numerics/asymptotics for the rotating nonlinear Klein-Gordon (RKG) equation, an important PDE in relativistic quantum physics that can mod......
期刊： MULTISCALE MODELING & SIMULATION, 2020; 18 (2)
We study the anomalous electromagnetic scattering in the homogenization regime, by a subwavelength thin layer consisting of periodically distributed p......
期刊： MULTISCALE MODELING & SIMULATION, 2020; 18 (1)
The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driv......
期刊： MULTISCALE MODELING & SIMULATION, 2020; 18 (1)
In this paper, we propose a numerical method solving the one space dimensional semiclassical kinetic graphene model introduced in [O. Morandi and F. S......
期刊： MULTISCALE MODELING & SIMULATION, 2020; 18 (1)
The Laplacian Delta is the infinitesimal generator of isotropic Brownian motion, being the limit process of normal diffusion, while the fractional Lap......
期刊： MULTISCALE MODELING & SIMULATION, 2020; 18 (1)
This paper introduces a cascadic adaptive finite element method for nonlinear eigenvalue equations arising from quantum physics following the multilev......
期刊： MULTISCALE MODELING & SIMULATION, 2020; 18 (3)
We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic approximate low-dimensional struct......
