Multi-zone Decomposition for Simulation of Time-dependent Problems using the Multiquadric Scheme

This paper discusses the application of the multi-zone decomposition technique with Multiquadric scheme for the numerical solutions of a time-dependent problem. The construction of the multi-zone algorithm is based on a domain decomposition technique to subdivide the global region into a number of nite subdomains. The reduction of ill-conditioning and the improvement of the computational eeciency can be achieved with a smaller resulting matrix on each sub-domain. The proposed scheme is applied to a hypothetical linear two-dimensional hydrodynamic model as well as a real-life non-linear two-dimensional hydrodynamic model in the Tolo Harbour of Hong Kong to simulate the water ow circulation patterns. To illustrate the computational eeciency and accuracy of the technique, the numerical results are compared with those solutions obtained from the same problem using a single domain Multiquadric scheme. The computational eeciency of the multi-zone technique is improved substantially with faster convergence without signiicant degradation in accuracy.