By Olga V. Ushakova

Grid iteration offers with using grids (meshes) within the numerical answer of partial differential equations through finite parts, finite quantity, finite modifications and boundary components. Grid new release is utilized within the aerospace, mechanical engineering and medical computing fields. This e-book provides new examine within the box.

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43, No. 9, 1 1 69 (200 1). , Numerical investigation of compression of deuterium in a con­ ical target under a strong cumulation effect, Pril. Mekhan. i Tekhnieh. Fiz. (J. Appl. Meehan. 4, 22 ( 1 994). , Numerical study of a spontaneous electromagnetic field in­ duced by annular cumulative jets in conical targets, Plasma Physics Reports 24, No. 4, 349 ( 1 998). , Numarical study 0 shock compression of graphite and its con­ version to diamond in conical targets, Technieal Physics 48, No. 6, 727 (2003).

N - 1 ; j = 1 , . . , m - 1 defines a grid consisting of only convex quadrangles. The set of such grids is called a convex grid set and denoted by D. 1). 3) takes the form N-I M -l In the method [6], the grid 1( 6 ) (G) = min. The function j. Then, at each � x� + �y� + � x�+1 + � Y�+1 ' 2Jk ( 1 . 4) where the factor 112 introduced to simplify formulas for derivatives of 1( 6 ) = = 4 LLL 'Pk. 5) G is generated from an iteration process for solving the problem 1( 6) has the following disadvantage.

1 ), if c = 0 and Tij = 1, the iteration process stops after the first iteration and yields the quasi-one-dimensional grid defined by (2. 1 ). Clearly, if 0 < c « 1 , even the first iteration yields a grid that is close to a quasi-one-dimensional one in the subdomains where small distortions of lines of the selected family are enough to preserve the convexity of cells. To reduce the computational cost we use a special choice of the iteration parameter Tij and iterations on subsets of grid nodes.

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