相关论文: A Quasi-Helmholtz Projector Stabilized Full Wave S…
We study the Cauchy problem for a quasilinear wave equation with low-regularity data. A space-time $L^2$ estimate for the variable coefficient wave equation plays a central role for this purpose. Assuming radial symmetry, we establish the…
We present a sweeping preconditioner for quasi-optimal Domain Decomposition Methods (DDM) applied to Helmholtz transmission problems in periodic layered media. Quasi-optimal DD (QO DD) for Helmholtz equations rely on transmission operators…
In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms.…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless uncharged Dirac fields propagating in the outer region of de…
We investigate the Hatsugai-Kohmoto (HK) model on a square lattice, which describes both a Mott insulator at half-filling and a non-Fermi liquid phase on doping. Through the solution of this exactly solvable model with the inclusion of…
Meshless collocation with multiquadric radial basis functions (MQ-RBFs) delivers high accuracy for the three-dimensional Helmholtz equation but produces dense, severely ill-conditioned linear systems. We develop and evaluate three…
We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. The original WaveHoltz iteration for acoustic Helmholtz problems is a fixed-point iteration that…
We consider the Cauchy problem for the fifth-order modified Korteweg-de Vries equation (mKdV) under the periodic boundary condition. The fifth-order mKdV is an asymptotic model for shallow surface waves, and (in the perspective of…
Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution…
In this paper, we propose a spectral framework that embeds 1D and 2D quasiperiodic Helmholtz eigenvalue problems into higher-dimensional (2D and 4D) periodic spaces via the projection method \cite{jiang2014numerical, jiang2024numerical}. To…
This work is devoted to the construction of weakly nonlinear, highly oscillating, current vortex sheet solutions to the incompressible magnetohydrodynamics equations. Current vortex sheets are piecewise smooth solutions to the…
We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…
We study the well-posedness of the Cauchy problem with Dirichlet or Neumann boundary conditions associated to an H 1 -critical semilinear wave equation on a smooth bounded 2D domain {\Omega}. First, we prove an appropriate Strichartz type…
(Abridged) We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron MHD (EMHD). We argue there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. We…
A generalized Bose-Hubbard model in a two-mode approximation is applied to study the rotational dynamics of a direct-current atomtronic quantum interference device. Modified values of on-site interaction and pair-tunneling parameters of the…
We present in detail the recently developed multi-configurational symmetrized projector quantum Monte Carlo (MSPQMC) method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo method for a…
Stationary scattering of TE and TM waves propagating in an isotropic medium with planar symmetry is described by Bergmann's equation in one dimension. This is a generalization of Helmholtz equation which allows for developing transfer…