Exploitation of symmetry in graphs with applications to finite and boundary elements analysis

We present explicit and parametric forms of transformation matrices for three well-known and widely used symmetry groups: S-2v,C-2v and C-4v. Group representation theory is the most powerful method for exploiting symmetry. We propose an efficient algorithm for systematic generation of reducible representations that can be combined linearly to obtain the projection operators. The exact column spaces of these projection operators are calculated and integrated through special orderings, leading to exact explicit and parametric forms of transformation matrices. The transformation matrices could be used directly for block diagonalization of single-variable scalar field problems. Another algorithm is proposed to extend the application of the method to nonscalar and multivariable field problems. Finally, the generality and efficiency of the proposed method in relation to computation times and the accuracy of results are illustrated through examples from spectral decomposition, free vibration, buckling of FEMs and boundary element analysis of a symmetric field. Copyright (c) 2012 John Wiley & Sons, Ltd.