RT Journal Article ID 7193bb2d745d9103 A1 Kanaun, Sergey T1 Fast Calculation of Elastic Fields in a Homogeneous Medium with Isolated Heterogeneous Inclusions JF International Journal for Multiscale Computational Engineering JO JMC YR 2009 FD 2009-09-01 VO 7 IS 4 SP 263 OP 276 K1 elastic fields K1 heterogeneous medium K1 integral equations K1 Gaussian approximating functions K1 Toeplitz matrix K1 fast Fourier transform AB This work is devoted to the calculation of static elastic fields in a homogeneous medium with a finite number of isolated heterogeneous inclusions. First, the problem is reduced to the solution of integral equations for strain fields inside the inclusions. Then, Gaussian approximating functions are used for discretization of these equations. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms. The method is mesh-free, and the coordinates of the approximating nodes is the only geometrical information required in the method. If such nodes compose a regular lattice, the matrix of the discretized problem will have Toeplitz structure. By the calculation of matrix-vector products with such matrices, the fast Fourier transform technique may be used. The latter essentially accelerates the process of the iterative solution of the disretized problem. The results of calculations of elastic fields in a 2-D medium with an isolated heterogeneous inclusion and with several inclusions are presented. PB Begell House LK https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,232871fc3b0df9a5,7193bb2d745d9103.html