000010968 001__ 10968
000010968 005__ 20141205155822.0
000010968 04107 $$aeng
000010968 046__ $$k2008-10-12
000010968 100__ $$aMeza-Fajardo, Kristel C.
000010968 24500 $$aThe Spectral Element Method (SEM): Formulation and Implementation of the Method for Engineering Seismology Problems

000010968 24630 $$n14.$$pProceedings of the 14th World Conference on Earthquake Engineering
000010968 260__ $$b
000010968 506__ $$arestricted
000010968 520__ $$2eng$$aVarious numerical methods have been proposed and used to investigate wave propagation in realistic earth media. Recently an innovative numerical method, known as the Spectral Element Method (SEM), has been developed and used in connection with wave propagation problems in 3D elastic media (Komatitsch and Tromp, 1999). The SEM combines the flexibility of a finite element method with the accuracy of a spectral method and it is not cumbersome in dealing with non-flat free surface and spatially variable anelastic attenuation. The SEM is a highly accurate numerical method that has its origins in computational fluid dynamics. One uses a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements that is adapted to the free surface and to the main internal discontinuities of the model. The wavefield on the elements is discretized using high-degree Lagrange interpolants, and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix, which greatly simplifies the algorithm. The most important property of the SEM is that the mass matrix is exactly diagonal by construction, which drastically simplifies the implementation and reduces the computational cost because one can use an explicit time integration scheme without having to invert a linear system. Furthermore, it allows an efficient parallel implementation. We sketch the formulation of the SEM in matrix form that is familiar to earthquake engineers. We demonstrate the efficiency and effectiveness of the method by implementing the proposed formulation to study various simple/canonical problems.

000010968 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000010968 653__ $$aspectral element method, elastodynamics, elastic wave propagation, perfectly matched layer, engineering seismology

000010968 7112_ $$a14th World Conference on Earthquake Engineering$$cBejing (CN)$$d2008-10-12 / 2008-10-17$$gWCEE15
000010968 720__ $$aMeza-Fajardo, Kristel C.$$iPapageorgiou, Apostolos S.
000010968 8560_ $$ffischerc@itam.cas.cz
000010968 8564_ $$s349528$$uhttps://invenio.itam.cas.cz/record/10968/files/03-03-0003.pdf$$yOriginal version of the author's contribution as presented on CD, Paper ID: 03-03-0003.
000010968 962__ $$r9324
000010968 980__ $$aPAPER