8 papers
A High-Accuracy Numerical Homogenization Method for Quasiperiodic Hamilton--Jacobi Equations
Kai Jiang, Meng Li, Juan Zhang +1
In this work, we develop an accurate numerical homogenization method for computing effective Hamiltonians of quasiperiodic Hamilton--Jacobi equations (QHJEs) with convex Hamiltonia…
Accurately computing quasiperiodic parabolic equations within finite-size domains via modeling quasiperiodic boundary conditions
Xiaofang Han, Kai Jiang, Meng Li
Quasiperiodic parabolic equations (QPEs) describe various physical processes in systems with long-range order without decay, such as heat conduction, diffusion, and transport, and…
Geometric construction of superintegrable Poisson projection chains via Poisson centralizers
Kai Jiang, Guorui Ma, Ian Marquette +2
We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra of a complex semisim…
Quasiperiodic Elliptic Operators: Projection Method and Convergence Analysis
Kai Jiang, Jiaqi Tang, Qilong Zhai +1
Quasiperiodic elliptic operators (QEOs) serve as fundamental models in both mathematics and physics, as exemplified by their role in the numerical modeling of one-dimensional photo…
Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations
Kai Jiang, Meng Li, Juan Zhang +1
Numerically solving parabolic equations with quasiperiodic coefficients is a significant challenge due to the potential formation of space-filling quasiperiodic structures that lac…
Amplitude Expansion Phase Field Crystal (APFC) Modeling based Efficient Dislocation Simulations using Fourier Pseudospectral Method
Xinyi Wei, Yangshuai Wang, Kai Jiang +1
Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elastici…
Projection method for quasiperiodic elliptic equations and application to quasiperiodic homogenization
Kai Jiang, Meng Li, Juan Zhang +1
In this study, we address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection me…
Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems
Kai Jiang, Xueyang Li, Yao Ma +3
In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for quasiperiodic systems with concentrated spectral point distribution. Based on…