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SIGA 2011
Kolman, Radek ; Linkeová, I. ; Okrouhlík, Miloslav ; Pařík, Petr
The conference SIGA 2011 aimed to bring together mathematicians, physicists, computer designers and engineers dealing with splines who are using them for the numerical solutions of partial differential equations of various problems in mechanics and physics. In computational mechanics, it is isogeometric analysis (IGA) which is being dynamically developed. This numerical method employs shape functions based on different types of splines (B-splines, NURBS, T-splines and many others), and the fields of unknown quantities are consequently described the same way as the geometry of the studied domain. In addition, this approach provides a higher degree of continuity than that offered by the classical finite element (FE) method based on Lagrangian polynomials. Isogeometric analysis aims to integrate FE ideas in CAD systems without necessity to regenerate mesh. The conference intends to create a forum for further discussion in multidisciplinary scientific areas involving mathematics, computer graphics, geometry, physics, engineering and software engineering, respectively.
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Analysis of classical and spectral finite element spatial discretization in one-dimensional elastic wave propagation
Kolman, Radek ; Plešek, Jiří ; Okrouhlík, Miloslav ; Gabriel, Dušan
The spatial discretization of continuum by finite element method introduces the dispersion error to numerical solutions of stress wave propagation. For higher order finite elements there are the optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefront. Spectral finite elements are of h-type finite element, where nodes have special positions along the elements corresponding to the numerical quadrature schemes, but the displacements along element are approximated by Lagrangian interpolation polynomials. In this paper, the classical and Legendre and Chebyshev spectral finite elements are tested in the one-dimensional wave propagation in an elastic bar.
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