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Scattering of Guided Waves in Plates and Cylinders
Published in Subhendu K. Datta, Arvind H. Shah, Elastic Waves in Composite Media and Structures, 2019
Subhendu K. Datta, Arvind H. Shah
The geometry of the plate with a delamination and its dimensions are shown in Fig. 6.11. Also shown are the contours C and B used to develop the equations governing the displacements at the nodes in RI ∪ B. These are given by equation (6.2.57). As in the previous section, an adaptive integration scheme is used to obtain the Green’s functions in the frequency domain. The system of equations (6.2.57) is solved by a biconjugate gradient method. Details are given in Datta et al. (1992b) (see the previous section).
Methods of Solving Systems of Algebraic Equations
Published in M. Necati Özişik, Helcio R.B. Orlande, Marcelo José Colaço, Renato Machado Cotta, Finite Difference Methods in Heat Transfer, 2017
M. Necati Özişik, Helcio R.B. Orlande, Marcelo José Colaço, Renato Machado Cotta
Another iterative method, which is highly vectorizable, is the biconjugate gradient method. This method performs very well, with a high rate of convergence. The method is fully described in Press et al. (1992) along with the subroutine LINBCG needed for its implementation. A basic algorithm, which uses a preconditioning matrix à for solving the linear system Ax = b, can be described in the following steps:
GMRES based numerical simulation and parallel implementation of multicomponent multiphase flow in porous media
Published in Cogent Engineering, 2020
Saltanbek T. Mukhambetzhanov, Danil V. Lebedev, Nurislam M. Kassymbek, Timur S. Imankulov, Bazargul Matkerim, Darkhan Zh. Akhmed-Zaki
There are several well-known methods for solving systems of algebraic equations of this type; direct methods, such as the Gauss method or LU decomposition, are not suitable for systems with sparse matrices since there is the possibility of overflow (Higham, 2011). The Conjugate gradient method (CG) is designed for systems with symmetric matrices, and the Biconjugate Gradient Method (BiCG) has slow convergence (Van der Vorst, 2003). In this work, system (8) was solved by the iterative method GMRES, which is a widely used Krylov subspace method (Saad, 2003).