摘要
在重构核粒子法的基础上,引入复变量,讨论了复变量重构核粒子法.复变量重构核粒子法的优点是在构造形函数时采用一维基函数建立二维问题的修正函数.然后,将复变量重构核粒子法应用于瞬态热传导问题的求解,结合瞬态热传导问题的Galerkin积分弱形式,采用罚函数法引入本质边界条件,建立了瞬态热传导问题的复变量重构核粒子法,推导了相应的计算公式.与传统的重构核粒子法相比,复变量重构核粒子法具有计算量小、精度高的优点.最后通过数值算例证明了该方法的有效性.
On the basis of reproducing kernel particle method （RKPM）, the complex variable reproducing kernel particle method （CVRKPM） is discussed. The advantage of the CVRKPM is that the correction function of a 2-D problem is formed with 1-D basis function when the shape function is obtained. Then, we apply the complex variable method to two-dimensional transient heat conduction problems. In combination with the Galerkin weak form of transient heat conduction problems, the penalty method is employed to enforce the essential boundary conditions, the CVRKPM for transient heat conduction problems is investigated and the corresponding formulae are obtained. Compared with the conventional RKPM, the CVRKPM introduced in this paper has a higher precision and a lower computation cost. Some examples given in this paper verify the effectivity of the proposed method.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2008年第10期6047-6055,共9页
Acta Physica Sinica
基金
国家自然科学基金(批准号:10571118)
上海市重点学科建设项目(批准号:Y0103)资助的课题~~
关键词
重构核粒子法
复变量重构核粒子法
修正函数
瞬态热传导问题
reproducing kernel particle method, complex variable reproducing kernel particle method, correction function, transient heat conduction problems
