A solution procedure for solving nonlinear time-marching problems is presented. The nonsymmetric systems of equations arising from a Newton-type linearization of these time-marching problems are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High-speed flow computations demonstrate the effectiveness of these algorithms. © 1991.
CITATION STYLE
Johan, Z., & Hughes, T. J. R. (1991). A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids. Computer Methods in Applied Mechanics and Engineering, 87(2–3), 281–304. https://doi.org/10.1016/0045-7825(91)90009-U
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