Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme

Abstract This paper discusses the application of the multizone decomposition technique with multiquadric scheme for the numerical solutions of a time-dependent problem. The construction of the multizone algorithm is based on a domain decomposition technique to subdivide the global region into a number of finite subdomains. The reduction of ill-conditioning and the improvement of the computational efficiency can be achieved with a smaller resulting matrix on each subdomain. The proposed scheme is applied to a hypothetical linear two-dimensional hydrodynamic model as well as a real-life nonlinear two-dimensional hydrodynamic model in the Tolo Harbour of Hong Kong to simulate the water flow circulation patterns. To illustrate the computational efficiency 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 efficiency of the multizone technique is improved substantially with faster convergence without significant degradation in accuracy.

[1]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[2]  M. Floater,et al.  Multistep scattered data interpolation using compactly supported radial basis functions , 1996 .

[3]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[4]  R. E. Carlson,et al.  Improved accuracy of multiquadric interpolation using variable shape parameters , 1992 .

[5]  R. E. Carlson,et al.  The parameter R2 in multiquadric interpolation , 1991 .

[6]  X. Z. Mao,et al.  A Multiquadric Interpolation Method for Solving Initial Value Problems , 1997 .

[7]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[8]  Y. Hon,et al.  Multiquadric method for the numerical solution of a biphasic mixture model , 1997 .

[9]  R. E. Carlson,et al.  Sparse approximate multiquadric interpolation , 1994 .

[10]  M. Golberg,et al.  Improved multiquadric approximation for partial differential equations , 1996 .

[11]  E. J. Kansa,et al.  Application of the Multiquadric Method for Numerical Solution of Elliptic Partial Differential Equations , 2022 .

[12]  E. J. Kansa.  A strictly conservative spatial approximation scheme for the governing engineering and physics equations over irregular regions and inhomogeneously scattered nodes , 1992 .