CAJ | 학술논문

对于二维 Helmholtz 方程问题，本文提出一种基于积分核级数展开的多极边界元方法，推导证明了二维 Helmholtz 方程的多极展开定理，给出了多极边界元法计算公式和计算过程，分析了截断误差，说明截断误差可由截断项数控制，并给出一个可广泛应用于实际计算的截断项数的近似表达式。
대우이유 Helmholtz 방정문제，본문제출일충기우적분핵급수전개적다겁변계원방법，추도증명료이유 Helmholtz 방정적다겁전개정리，급출료다겁변계원법계산공식화계산과정，분석료절단오차，설명절단오차가유절단항수공제，병급출일개가엄범응용우실제계산적절단항수적근사표체식。
@@@@A kind of Fast Multipole Boundary Element Method (FM-BEM) based on series expansion of integral kernel is proposed to solve two-dimensional (2-D) Helmholtz equation problems in this paper. A theorem of multipole expansion is derived and proved for the fundamental solution. Numerical formulas and computational process of the FM-BEM are obtained for 2-D Hel-mholtz equation problems. The truncation error is analyzed and proved to be controlled by a truncation number . A refined ap-proximate expression of is finally derived for practical science and engineering computation.