Abstract: Newton-Lagrange Interpolations are widely used in
numerical analysis. However, it requires a quadratic computational
time for their constructions. In computer aided geometric design
(CAGD), there are some polynomial curves: Wang-Ball, DP and
Dejdumrong curves, which have linear time complexity algorithms.
Thus, the computational time for Newton-Lagrange Interpolations
can be reduced by applying the algorithms of Wang-Ball, DP and
Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong
algorithms, first, it is necessary to convert Newton-Lagrange
polynomials into Wang-Ball, DP or Dejdumrong polynomials. In
this work, the algorithms for converting from both uniform and
non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and
Dejdumrong polynomials are investigated. Thus, the computational
time for representing Newton-Lagrange polynomials can be reduced
into linear complexity. In addition, the other utilizations of using
CAGD curves to modify the Newton-Lagrange curves can be taken.
Abstract: In this paper, a new trend for improvement in semianalytical
method based on scale boundaries in order to solve the 2D
elastodynamic problems is provided. In this regard, only the
boundaries of the problem domain discretization are by specific subparametric
elements. Mapping functions are uses as a class of higherorder
Lagrange polynomials, special shape functions, Gauss-Lobatto-
Legendre numerical integration, and the integral form of the weighted
residual method, the matrix is diagonal coefficients in the equations
of elastodynamic issues. Differences between study conducted and
prior research in this paper is in geometry production procedure of
the interpolation function and integration of the different is selected.
Validity and accuracy of the present method are fully demonstrated
through two benchmark problems which are successfully modeled
using a few numbers of DOFs. The numerical results agree very well
with the analytical solutions and the results from other numerical
methods.