Advances in grid generation by Olga V. Ushakova

By Olga V. Ushakova

Grid iteration bargains with using grids (meshes) within the numerical answer of partial differential equations by means of finite components, finite quantity, finite ameliorations and boundary components. Grid new release is utilized within the aerospace, mechanical engineering and medical computing fields. This publication offers new study within the box.

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But, there is no procedure to find the g�odesics and to link the specific parameters for them to ensure the parametrization extremeness. Does the best and unique parametrization exist? Even, if the positive answer exists, there is possibility to select other constructions with less metric distortion. Chebychev problem formulated in 1 856 [ 1 ] . This problem is devoted to selection of a conformal parametrization on the sphere (of the globe) to draw the geographical maps. Grave in his papers [2, 3] .

I= 1, . . , N - 1, j = 1 , . , M . 2). 5) will be described in the following section. 5). 5: A fragment of the grid obtained by the proposed method for the domain from Fig. 3. First we return to the domain with one protrusion presented in Fig. 3. 5) for e = 10- 2 is shown in Fig. 5. The grid lines j = const are directed from the lower to the upper boundaries of the domain. Comparing Fig. 5 with Fig. 2), one can see that the grid in Fig. 5 becomes involved in the protrusion, and large cells presented in Fig.

N 1 . - The monotonically increasing sequence tY = sU sCJv , i = 0, . . , N, tg = 0, tCJv = 1 is called the arrangement law. The arrangement law tfd along the boundary line j = M is defined analogously. The arrangement law along the other lines of the family is determined by the linear interpolation = [tY{ M - j ) + tfdj] /M . Then, the inner grid nodes are determined as follows: t1 fi ,j = To,j + t{ {fN,j - To,j ) , i = 1 , . . , N - 1 , j = 1 , . , M - 1 . (2. A . Charakhch'yan We call such grids quasi-one-dimensional.

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