Geodesic
Effective computation of restoring force vector in finite element method
Kybernetika, Tome 43 (2007) no. 6, pp. 767-776 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and equations.
We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and equations.
Classification : 35L15, 65M06, 65M60, 65Y20, 74B05, 74H15, 74S05, 74S20
Keywords: FEM; stiffness matrix; restoring force vector; computational efficiency of algorithm; e-invariants 
@article{KYB_2007_43_6_a1,
     author = {Balazovjech, Martin and Halada, Ladislav},
     title = {Effective computation of restoring force vector in finite element method},
     journal = {Kybernetika},
     pages = {767--776},
     year = {2007},
     volume = {43},
     number = {6},
     mrnumber = {2388391},
     zbl = {1138.65087},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007_43_6_a1/}
}
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Balazovjech, Martin; Halada, Ladislav. Effective computation of restoring force vector in finite element method. Kybernetika, Tome 43 (2007) no. 6, pp. 767-776. http://geodesic.mathdoc.fr/item/KYB_2007_43_6_a1/

[1] Archuleta R. J.: Experimental and Numerical Three-dimensional Simulations of Strike-slip Earthquakes. Ph.D. Thesis. University of California, San Diego 1976

[3] Felippa C. A.: Introduction to Finite Element Methods (ASEN 5007). Lecture notes. University of Colorado, Boulder 2005

[4] Moczo P., Kristek, J., Bystrický E.: Efficiency and optimization of the 3D finite-difference modeling of seismic ground motion. J. Comp. Acoustics 9(2) (2004), 593–609 | DOI | MR

[5] Reddy J. N.: An Introduction to the Finite Element Method, McGraw-Hill, New York 199.