Spectral Element Method - Discussion

Discussion

The spectral method expands the solution in trigonometric series, a chief advantage being that the resulting method is of very high order. This approach relies on the fact that trigonometric polynomials are an orthonormal basis for . The spectral element method chooses instead high degree piecewise polynomial basis functions, also achieving a very high order of accuracy.Spectral element Method is relatively new computational technique,where the element is defined using higher order polynomial. Such polynomials are usually orthogonal Chebyshev polynomial or very high order Lobatto polynomial over non-uniformly spaced nodes.in SEM computational error decreases exponentially as the order of approximating polynomial.therefore fast convergence of solution to exact solution realized with lesser degree freedom of structure in camparison with FEM In Structural health Monitoring FEM can be used for detecting large flaws in the structure as the flaws size reduced there is a need to use high frequency wave with very small wave length therefore there is a need to fine the FEM mesh, But computational time required will be more and solution will not be exact hence SEM is used for detecting small flaws. by using SEM computational errors is avoided and time for computation will be less. non- uniformity of nodes helps to make mass matrix diagonal which helps saving time and memory and also much usefull for adopting Central Difference Method(CDM) The disadvantage of SEM includes modeling of complex geometry, compare to FEM