计算机工程与应用Issue(2)：26-29,4.DOI:10.3778/j.issn.1002-8331.1405-0047
求解任意波数的三维Helmholtz方程
Solution for three dimensional Helmholtz equations under arbitrary wave numbers
摘要
Abstract
The Adomian Decomposition Method(ADM)is employed in this paper to solve three dimensional Helmholtz equations under arbitrary wave numbers. Based on the ADM, the three dimensional Helmholtz differential equation becomes a recursive algebraic equation. Furthermore, the boundary conditions become simple algebraic equations which are suit-able for symbolic computation. By using boundary conditions, the closed-form series solution can be easily obtained. The main advantages of ADM are computational simplicity and do not involve any linearization or discretization. Finally, two numerical examples are presented to check the reliability of the proposed method for solving the three dimensional Helm-holtz equations with different wave numbers. The numerical results on three dimensional problems with known analytic solutions demonstrate that the ADM is quite accurate and readily implemented. Furthermore, the good convergence and the excellent numerical stability of the solution based on the ADM can also be found for high wave numbers. It means that the ADM is quite efficient and is practically well suited for solving three dimensional Helmholtz equations at different wave numbers.关键词
三维Helmholtz方程/Adomian分解法/波数Key words
three dimensional Helmholtz equations/Adomian decomposition method/wave numbers分类
数理科学引用本文复制引用
毛崎波..求解任意波数的三维Helmholtz方程[J].计算机工程与应用,2015,(2):26-29,4.基金项目
国家自然科学基金（No.51265037，No.11464031）；江西省高等学校科技落地项目（No.KJLD12075）；江西省教育厅科技项目（No.GJJ13524）。 （）
