Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D  

作　　者：Adem Kaya 

机构地区：[1]Institut füur Mathematik,Universität Potsdam,Karl-Liebknecht-Str.,24-2514476 Potsdam/Golm,Germany

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第1期26-57,共32页高等学校计算数学学报（英文版）

摘　　要：An adapted-bubbles approach which is a modification of the residualfree bubbles(RFB)method,is proposed for the Helmholtz problem in 2D.A new two-level finite element method is introduced for the approximations of the bubble functions.Unlike the other equations such as the advection-diffusion equation,RFB method when applied to the Helmholtz equation,does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems.Adapted-bubbles(AB)are obtained by a simple modification of the sub-problems.This modification increases the accuracy of the numerical solution impressively.We provide numerical experiments with the AB method up to ch=5 where c is the wavenumber and h is the mesh size.Numerical tests show that the AB method is better by far than higher order methods available in the literature.

关 键 词：Helmholtz equation adapted-bubbles residual-free bubbles two-level finite element 

分 类 号：O175[理学—数学]