6 papers · 1 filter
A High-Accuracy Numerical Homogenization Framework for Quasiperiodic Hamilton--Jacobi Equations
Kai Jiang, Meng Li, Juan Zhang +1
In this work, we develop an accurate numerical homogenization framework for computing effective Hamiltonians of quasiperiodic Hamilton--Jacobi equations (QHJEs) with convex Hamilto…
Accurately computing quasiperiodic parabolic equations within finite-size domains via modeling quasiperiodic boundary conditions
Xiaofang Han, Kai Jiang, Meng Li
Quasiperiodic systems exhibit long-range order without decay and are naturally posed on the whole space. However, in practical applications, computations are performed on finite do…
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…
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…
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…
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…