CAJ | 학술논문

提出通过Adomian分解法求解任意波数的三维Helmholtz方程。通过Adomian分解法可以把三维Helmholtz微分方程转换成递归代数公式，并进一步把其边界条件转换成适用符号计算的简单代数公式。利用边界条件可以很容易得到方程的解析解表达式。Adomian分解法的主要特点在于计算简单快速，并且不需要进行线性化或离散化。最后通过数值计算以验证Adomian分解法求解任意波数下三维Helmholtz方程的有效性。数值计算结果表明：Adomian分解法的计算结果非常接近精确解，并且该方法在大波数情况下还具有良好的收敛性。
제출통과Adomian분해법구해임의파수적삼유Helmholtz방정。통과Adomian분해법가이파삼유Helmholtz미분방정전환성체귀대수공식，병진일보파기변계조건전환성괄용부호계산적간단대수공식。이용변계조건가이흔용역득도방정적해석해표체식。Adomian분해법적주요특점재우계산간단쾌속，병차불수요진행선성화혹리산화。최후통과수치계산이험증Adomian분해법구해임의파수하삼유Helmholtz방정적유효성。수치계산결과표명：Adomian분해법적계산결과비상접근정학해，병차해방법재대파수정황하환구유량호적수렴성。
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.