### Friday, July 18

10:30 AM-12:30 PM

*Building 300, Room 300*

## MS76

Numerical Solution of Elliptic PDEs in Unbounded Domain

In a variety of applications involving scientific and engineering computations one needs to solve partial differential equations in unbounded domains. For the standard numerical methods, such as the finite element and finite difference methods, it is difficult to extend the conventional techniques of convergence and error analysis for numerical methods for solving BVPs in an infinite domain. In engineering treatment, it is quite common to replace the original problem by one in a finite sub-domain which is considered to be "sufficiently large." In order to get sufficient accuracy of the solution, one may need to increase the sub-domain, and the whole computation process is considerably time consuming. On the other hand, it is impossible to reduce the infinite domain to be a finite sub-domain for some problems such as wave propagation. Consequently, extensive research was devoted to the development of efficient and accurate numerical methods to solve the BVPs in unbounded domains, e.g. the infinite element method, the boundary element method, the coupling of finite element and boundary element
method, and finite element method with approximate boundary conditions on the artificial boundary. The domain decomposition method is also often applied to the infinite domains.

**Organizer: Weimin Xue**

*Hong Kong Baptist University, Hong Kong*

**10:30 A Dirichlet-Neumann Alternating Method in Infinite Domain: Algorithm and Convergence Analysis**
- De-Hao Yu, Academia Sinica, People's Republic of China;
*Weimin Xue*, Organizer; and Hong-Ci Huang, Hong Kong Baptist University, Hong Kong
**11:00 A Finite Element Method for Exterior Poisson Boundary Value Problem in Three Dimensions**
- Xiaonan Wu, Hong Kong Baptist University, Hong Kong
**11:30 Infinite Element Method for Viscous Incompressible Flow in Infinite Domains**
- Long-an Ying, Beijing University, People's Republic of China

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*MMD, 3/31/97*

*tjf, 5/29/97*

*MMD, 6/3/97*