高波数强振荡Helmholtz方程的多尺度有限元精确高效解法OA

The Helmholtz equation has important applications in many fields such as acoustics and electromagnetics.However,its high wave number and strong oscillation characteristics lead to systematic difficulties in numerical simulations.Applying a novel multiscale finite element method combined with the embedding technique of multiscale basis functions,the strong oscillation microscopic characteristics of the original problem can be effectively captured,and a specific reduced-order finite-dimensional approximation space can be constructed.Compared with traditional methods,the novel method performs more excellently in capturing the details of wave phenomena.Especially in the case of high wave number,by applying local mesh refinement the high precision can still be maintained,and the computational efficiency can be optimized and the computational time can be reduced.Our research results validate that the multiscale finite element method is particularly suitable for dealing with complicated oscillation problems with multiscale characteristics,and it effectively improves the accuracy,stability and computational efficiency of the numerical solution of the Helmholtz equation,thus possessing significant advantages and application potentials.