Complex variable reproducing kernel particle method for transient heat conduction problems

Abstract

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.