计算机工程与应用
計算機工程與應用
계산궤공정여응용
COMPUTER ENGINEERING AND APPLICATIONS
2013年
13期
40-42,84
,共4页
Helmholtz型方程%配点法%楔形基函数%区域分解法
Helmholtz型方程%配點法%楔形基函數%區域分解法
Helmholtz형방정%배점법%설형기함수%구역분해법
Helmholtz-type equations%collocation method%ridge basis function%domain decomposition method
基于楔形基函数和无网格配点法，提出了一种求解Helmholtz型方程区域分解法。该方法克服了在求解大规模问题时用一般的全域配点法所带来的配置矩阵为非对称满阵，且高度病态的问题。通过数值结果表明，该算法在求解Helm-holtz型方程降低系数矩阵条件数的同时，也能够降低误差，并达到满意的收敛效果。
基于楔形基函數和無網格配點法，提齣瞭一種求解Helmholtz型方程區域分解法。該方法剋服瞭在求解大規模問題時用一般的全域配點法所帶來的配置矩陣為非對稱滿陣，且高度病態的問題。通過數值結果錶明，該算法在求解Helm-holtz型方程降低繫數矩陣條件數的同時，也能夠降低誤差，併達到滿意的收斂效果。
기우설형기함수화무망격배점법，제출료일충구해Helmholtz형방정구역분해법。해방법극복료재구해대규모문제시용일반적전역배점법소대래적배치구진위비대칭만진，차고도병태적문제。통과수치결과표명，해산법재구해Helm-holtz형방정강저계수구진조건수적동시，야능구강저오차，병체도만의적수렴효과。
A meshless collocation method for Helmholtz-type equations is developed, which is based on domain decomposition method and ridge basis function. This method overcomes the ill-conditioned problems caused by much larger condition number of the coefficient matrix when collocation method is used for solving Helmholtz-type equations defined large-scale regions. According to numerical example and analysis, it is seen that the method Helmholtz-type equations slows down the condition number of the coefficient matrix and calculation errors, and can achieve satisfactory results.
