A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

[1]  Grant P. Steven,et al.  Evolutionary natural frequency optimization of two‐dimensional structures with additional non‐structural lumped masses , 1997 .

[2]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[3]  Grant P. Steven,et al.  General evolutionary path for fundamental natural frequencies of structural vibration problems: towards optimum from below , 1996 .

[4]  B. Hobbs,et al.  Effects of geological inhomogeneity on high Rayleigh number steady state heat and mass transfer in fluid-saturated porous media heated from below , 1998 .

[5]  Grant P. Steven,et al.  Evolutionary optimization of maximizing the difference between two natural frequencies of a vibrating structure , 1997 .

[6]  Grant P. Steven,et al.  Effect of initial nondesign domain on optimal topologies of structures during natural frequency optimization , 1997 .

[7]  Grant P. Steven,et al.  Evolutionary natural frequency optimization of thin plate bending vibration problems , 1996 .

[8]  Grant P. Steven,et al.  A generalized evolutionary method for numerical topology optimization of structures under static loading conditions , 1998 .

[9]  J. Z. Zhu,et al.  The finite element method , 1977 .

[10]  Grant P. Steven,et al.  A generalized evolutionary method for natural frequency optimization of membrane vibration problems in finite element analysis , 1998 .

[11]  Chongbin Zhao,et al.  Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below , 1997 .