Институт вычислительной математики
и математической геофизики

Abstracts

Numerical solution of differential and integral equations

Abstract Diffraction is the bending of waves around an obstacle such as the edge of a slit; it is the characteristics of waves of all types regardless of their nature or means of creation. In wave propagation studies when the lateral dimension of the area under consideration is not much greater than the wavelength, we can not describe some behaviors of the waves like bending round the obstacles and must take their nature specifically into account. That is, use the Huygens principal, which states that ``every point in a wave front is a source of wavelets''. This description enables us to see how the waves can hit and partially pass an obstacle. Hyperbolic equations are the mathematical means of describing wave propagation phenomena's and when approximated numerically they should carry out the same nature. In this paper we investigate the application of the Huygens principal when approximating two dimensional conservation Laws numerically. We demonstrate exactly how a ray of waves folds around an obstacle and show that this happens only when the numerical approximation takes into account all the surrounding nodes, (this is the case for example when linear or quadratic Finite Element Method is used), and it would not happen otherwise. We use different discretization methods in space and in each case numerical results are presented. Keywords: Diffraction; Numerical solution of hyperbolic equations; Boundary conditions; Finite differences.

Note. Abstracts are published in author's edition

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