Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

One of the promising branches of a pure mathematical field of science capable to push grid technology to a more advanced level is the theory of multidimensional differential geometry. In fact, many notions and characteristics of common surfaces such as metric tensors, their invariants, first and second groundforms, curvatures and torsions of lines, mean and Gauss curvatures of surfaces, and Christoffel symbols have already been used as natural elements in defining grid quality measures and formulating appropriate variational and differential grid techniques in a unified manner [1]. More general geometric objects such as regular multidimensional surfaces and Riemannian manifolds considered for generating adaptive grids are expected to become highly beneficial tools to boost grid technology. The paper gives an account of the geometrization of the popular comprehensive grid methods and presents an important extension of the methods, related to the application of the technique of Riemannian manifolds to the formulation of grid equations by developing some new procedures for the construction of metric tensors. Studies of the behavior of the grid lines and surfaces near boundary segments of the physical domains and surfaces are carried out. Some relations of the mean curvatures of the monitor surfaces to the Beltramian equations for grid generation are exhibited. On the basis of an analysis of equations with boundary and interior layers [2] a form of the monitor functions for generating layer-resolving grids is established. 1. Liseikin V.D. Grid Generation Methods, Berlin, Springer, 1999 2. Liseikin V.D. Layer Resolving Grids and Transformations for Singular Perturbation Problems, Ultrecht, VSP, 2001

Note. Abstracts are published in author's edition

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