The dynamic change mode of land cover not only reflects the change characteristics of the land cover itself, but also reflects the influence exerted by external factors. Empirical mode decomposition is an effective time-frequency analysis method for nonlinear and nonstationary signals. In this paper, empirical mode decomposition firstly uses to each pixel time series to get its intrinsic mode functions, each intrinsic mode function relates to change mode with some time scale, clustering those intrinsic mode functions over the image, and different land cover change modes are obtained. The experimental dataset used is MODIS subset from the Jan 2011 to Dec 2020, located in the Ningxia Hui Autonomous Region, China. The clustering results of half-annual cycle and one-year cycle of intrinsic mode functions show the influence of local climate and policy factors on land cover change.

This paper presents a Finite Element Method (FEM) framework for solving the screened Poisson equation with a Dirac delta function as the forcing term. The singularity introduced by the delta function poses challenges for standard numerical methods, particularly in higher dimensions. To address this, we employ integrated Legendre basis functions, which yield sparse and structured system matrices characterized by a Banded-Block-Banded-Arrowhead ($B^3$-Arrowhead) form. In one dimension, the resulting linear system can be solved directly. In two and three dimensions, the equation can be efficiently solved using a generalized Alternating Direction Implicit (ADI) method combined with reverse Cholesky factorization. Numerical results in 1D, 2D, and 3D confirm that the method accurately captures the localized impulse response and reproduces the expected Green’s function behavior. The proposed approach offers a robust and scalable solution framework for partial differential equations with singular source terms and has potential applications in physics, engineering, and computational science.