Spectral element method pdf

The spectral element method introduced here is a highorder variational method for the spatial approximation of elasticwave equations. Equations of motion of a body discretised using spectral finite elements. Abstract the spectral element method sem is a high order numerical method for solving partial di. For most discretizations finite difference, finite volume, finite element, spectral element, etc.

Classical finiteelement methods have been successfully applied to the study of wave propagation in 3d sedimentary basins e. The spectral element method for seismic wave propagation theory. Loworder finite element methods usually use n 1 or n 2, while in the spectral element method for seismic wave propagation n is usually chosen between 4 and 10. Spectral element method mathematics and computer science. Computing characteristic matrices of spectral finite elements. Photonic nanojet analysis by spectral element method. Boyd university of michigan ann arbor, michigan 481092143 email. Spectral elements in a nutshell snapshot of the displacement. Spectral element method in structural dynamics wiley.

This work aims especially at understanding a further numerical approach, the socalled spectral. Finite and spectral element methods in three dimensions. Spectral element method in structural dynamics is a concise and timely introduction to the spectral element method sem as a means of solving problems in structural dynamics, wave propagations, and other related fields. Originally developed to address problems in fluid dynamics, the sem combines the flexibility of a finite element. A spectral element fourier smoothed profile method for large eddy simulations of complex viv problems. The spectralelement method in seismology institute of. The mass matrix is diagonal by construction in this method, which drastically reduces the computational cost and allows an efficient parallel implementation.

Introduction to finite and spectral element methods using. These lectures provide an introduction to the sem for graduate students in earth science. Introduction to the spectral element method for threedimensional. Shape functions in the spectral finite element method. Approximating displacement, strain and stress fields. Pdf photonic nanojet analysis by spectral element method. In essence, it can be considered as a fe method formulated in. Solving equations of motion of a body discretised using spectral finite elements. We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic. Spectral finite element method sfem is an ef fective tool to solve wave prop agation probl ems. Chebyshev and fourier spectral methods second edition john p.