Preconditioning Newton-Krylor Methods for Variably Saturated Flow

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In this paper, we compare the effectiveness of three preconditioning strategies in simulations of variably saturated flow. Using Richards' equation as our model, we solve the nonlinear system using a Newton-Krylov method. Since Krylov solvers can stagnate, resulting in slow convergence, we investigate different strategies of preconditioning the Jacobian system. Our work uses a multigrid method to solve the preconditioning systems, with three different approximations to the Jacobian matrix. One approximation lags the nonlinearities, the second results from discarding selected off-diagonal contributions, and the third matrix considered is the full Jacobian. Results indicate that although the Jacobian is more accurate, ... continued below

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120 Kilobytes pages

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Woodward, C. & Jones, J January 7, 2000.

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In this paper, we compare the effectiveness of three preconditioning strategies in simulations of variably saturated flow. Using Richards' equation as our model, we solve the nonlinear system using a Newton-Krylov method. Since Krylov solvers can stagnate, resulting in slow convergence, we investigate different strategies of preconditioning the Jacobian system. Our work uses a multigrid method to solve the preconditioning systems, with three different approximations to the Jacobian matrix. One approximation lags the nonlinearities, the second results from discarding selected off-diagonal contributions, and the third matrix considered is the full Jacobian. Results indicate that although the Jacobian is more accurate, its usage as a preconditioning matrix should be limited, as it requires much more storage than the simpler approximations. Also, simply lagging the nonlinearities gives a preconditioning matrix that is almost as effective as the full Jacobian but much easier to compute.

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120 Kilobytes pages

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  • XIII International Conference on Computational Methods in Water Resources, Calgary, Alberta (CA), 06/25/2000--06/29/2000

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  • Report No.: UCRL-JC-137011
  • Grant Number: W-7405-Eng-48
  • Office of Scientific & Technical Information Report Number: 791027
  • Archival Resource Key: ark:/67531/metadc725434

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  • January 7, 2000

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  • Sept. 29, 2015, 5:31 a.m.

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  • May 6, 2016, 1:51 p.m.

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Woodward, C. & Jones, J. Preconditioning Newton-Krylor Methods for Variably Saturated Flow, article, January 7, 2000; California. (digital.library.unt.edu/ark:/67531/metadc725434/: accessed April 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.