Orthogonal Element Function And Its Application In Engineering

A series of orthogonal finite element function is presented by group method and finite element method. In continuous analysis there are famous function called consonance function ( the sine and cosine function), for disperse analysis there are sinusoid transform and cosine transform to be used, in continuous-disperse analysis recently there is wavelet transform to be applied to. Is there still other function can be used in continuous-disperse analysis? The paper first used normal representation theory of group to construct a group space and used self-cognation operator to get eigenvector of the operator, the eigenvector is orthogonal to each other. From the existed finite element the node bases of element is constructed. Consider symmetry of periodic area we get the symmetry transform group, act the eigenvector of self-cognation operator on the node bases element function, a series of orthogonal function is constructed. The functions is applied to make analysis of symmetry structure. By applied Γалёркин method the function is used to solute partial differential equation, the method greatly reduce the computation. An example is presented in the paper, the result show the accuracy of this method. According to the rudely divided element space included in the finely divided element space, the recurrence equation of relation between the two element space image is also presented in the paper. Used the recurrence equation to proceed signal, the result show the potential application of proposed method. The orthogonal finite element method have both advantage of wavelet analysis and cosine transform.