Acceleration Techniques for Newton's Non-linear Iterative Scheme Acceleration Techniques for Newton's Non-linear Iterative Scheme Acceleration Techniques for Newton's Non-linear Iterative Scheme
نویسنده
چکیده
The solution of non-linear sets of algebraic equations is usually obtained by the Newton's method, exhibiting quadratic convergence. For practical simulations, a signiicant computational eeort consists in the evaluation of the Jacobian matrices. In this paper, we propose and experiment various methods to speed the convergence process either by re-using information from previous iterates or by bypassing the Jacobian evaluations. These methods are applied to the solution of hyperbolic PDE's arising in CFD problems. A signiicant improvement is obtained in terms of computation cost compared to the crude Newton's approach. Abstract The solution of non-linear sets of algebraic equations is usually obtained by the Newton's method, exhibiting quadratic convergence. For practical simulations, a signiicant computational eeort consists in the evaluation of the Jacobian matrices. In this paper, we propose and experiment various methods to speed the convergence process either by re-using information from previous iterates or by bypassing the Jacobian evaluations. These methods are applied to the solution of hyperbolic PDE's arising in CFD problems. A signiicant improvement is obtained in terms of computation cost compared to the crude Newton's approach.
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