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Modeling Variably Saturated Flow Problems Using Newton-Type Linearization Methods
Abstract Numerical procedures to solve the nonlinear equation governing flow in variably saturated porous media commonly involve Newton or Picard iteration. The former scheme is stable and quadratically convergent in a local sense, but costly and algebraically complex. The latter scheme is simple and cheap, but slower converging and not as robust. We present a common framework for comparing these two methods, and introduce other approaches that range from simplifications of the Picard scheme to approximations of Newton’s method. These other approaches include explicit discretizations, first and second order accurate linearizations, and quasi-Newton schemes. Relaxation and line search algorithms to accelerate convergence of the Picard, Newton, and quasi-Newton methods will also be considered. The effectiveness of these various iterative and noniterative methods will be assessed according to criteria of efficiency and robustness.
Modeling Variably Saturated Flow Problems Using Newton-Type Linearization Methods
Abstract Numerical procedures to solve the nonlinear equation governing flow in variably saturated porous media commonly involve Newton or Picard iteration. The former scheme is stable and quadratically convergent in a local sense, but costly and algebraically complex. The latter scheme is simple and cheap, but slower converging and not as robust. We present a common framework for comparing these two methods, and introduce other approaches that range from simplifications of the Picard scheme to approximations of Newton’s method. These other approaches include explicit discretizations, first and second order accurate linearizations, and quasi-Newton schemes. Relaxation and line search algorithms to accelerate convergence of the Picard, Newton, and quasi-Newton methods will also be considered. The effectiveness of these various iterative and noniterative methods will be assessed according to criteria of efficiency and robustness.
Modeling Variably Saturated Flow Problems Using Newton-Type Linearization Methods
Paniconi, C. (author) / Putti, M. (author)
1995-01-01
20 pages
Article/Chapter (Book)
Electronic Resource
English
Newton Method , Line Search , Pressure Head , Time Step Size , Saturated Flow Engineering , Geoengineering, Foundations, Hydraulics , Waste Management/Waste Technology , Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution , Atmospheric Protection/Air Quality Control/Air Pollution , Soil Science & Conservation , Noise Control
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