数学与系统科学研究院

计算数学所学术报告

报告人：        Huang Zhaohui

Institute of Computational Mathematics and Scientific/Engineering Computing , CAS

报告题目 Joint Adaptation Technique in Numerical Solution of PDEs & Parallel Computational Methods for Bose-Einstein Condensates

Abstract: Part I is concerned with the joint adaptation of the anisotropic finite element grids and the solvers in order to get both accurate and efficient numerical solutions. When generating an anisotropic finite element mesh, the foremost attention in the existing adaptive finite element methods is usually given to a suitable representation of the solutions on the constructed mesh (thus, to assure the accuracy of the solutions). Meanwhile, properties of the underlying anisotropic mesh including, mainly, the existence of the large angles, also have serious effect on the convergence of linear solvers developed for the resulting system of linear algebraic equations, (thus, on the efficiency of the solution process).

We propose that the anisotropic mesh generation and optimization should be jointly adapted together with the linear solver, and we also make suggestions on the modifications of the linear solvers for problems on anisotropic meshes so that an efficient and accurate numerical solution can be simultaneously achieved.

Finally, we implement parallel computing technology to study numerically the three-dimension structure of quantized vortices of Bose-Einstein con- densates(BECs) in Part II. For anisotropic cases, the bending process of vortices is described in detail with the decrease of Gross-Pitaevskii energy. A completely straight vortex and steady and symmetrical multiple vortex configurations are obtained. We analyze the effect of initial con- ditions and angular velocity on the number and shape of vortices.

报告时间：2004年5月18日  下午4：00

报告地点：科技综合楼三层报告厅