Efficient Numerical Method for Solving Quasiperiodic Elliptic Equations and Computing Quasiperiodic Homogenized Coefficients

This study presents a highly efficient algorithm for solving quasiperiodic elliptic equations and computing homogenized coefficients for quasiperiodic multiscale problems. The key innovations include the use of the projection method to transform the quasiperiodic problem into a higher-dimensional periodic system, a compressed storage format for the stiffness matrix, and a diagonal preconditioner to accelerate the iterative solver.