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{{MODFLOW Links}}
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The Newton package (NWT) is one of the solvers available in MODFLOW-NWT. The NWT package is only used with the [[GMS:UPW Package|UPW Package]].  Using the NWT solver requires twice the memory of other MODFLOW solvers because using the Newton method results in an asymmetric matrix.  Because of the asymmetric matrix a different matrix solver must be used.  The NWT package provides an option to use one of two matrix solvers: a generalized-minimum-residual (GMRES) solver and an Orthomin/stabilized conjugate-gradient solver called ''x''MD (chi-MD).
[[File:NWTsolver.jpg|thumb|500 px|Example of the ''MODFLOW NWT Solver'' dialog.]]
The Newton package (NWT) is one of the solvers available in MODFLOW-NWT. The NWT package is only used with the [[GMS:UPW Package|UPW Package]].  Using the NWT solver requires twice the memory of other MODFLOW solvers because using the Newton method results in an asymmetric matrix.  Because of the asymmetric matrix a different matrix solver must be used.  The NWT package provides an option to use one of two matrix solvers: a generalized-minimum-residual (GMRES) solver and an Orthomin/stabilized conjugate-gradient solver called χMD (chi-MD). 
 
==General Options==
*''Comments (Text)'' – Allows up to 199 characters.
*''Max head change between outer iterations (L)(HEADTOL)'' – For solution of the nonlinear problem.
*''Max root-mean-squared flux difference between outer iterations (L^3/T) (FLUXTOL)'' – For solution of the nonlinear problem.
*''Max number of iterations allowed for outer problem (MAXITEROUT)'' – For solution of the nonlinear problem.
*''Portion of cell thickness used for adjusting coefficients to zero (THICKFACT)'' – The portion of the cell thickness (length) used for smoothly adjusting storage and conductance coefficients to zero.
*''Matrix solver to be used (LINMETH)'' – A flag that determines which matrix solver will be used.
<blockquote style="margin-top:0px; margin-bottom:0px;">
* (1) GMRES
* (2) &chi;MD
</blockquote>
*''Print additional info to listing file (IPRNWT)'' &ndash; A flag that indicates whether additional information about solver convergence will be printed to the main listing file
*''Correct head relative to cell-bottom if surrounded by dewatered cells (IBOTAV)'' &ndash; A flag that indicates whether corrections will be made to groundwater head relative to the cell-bottom altitude if the cell is surrounded by dewatered cells.
<blockquote style="margin-top:0px; margin-bottom:0px;">
* (0) Don't correct
* (1) Correct
</blockquote>
*''Options (OPTIONS)'' &ndash; Includes the following options:
<blockquote style="margin-top:0px; margin-bottom:0px;">
* SPECIFIED &ndash; Indicates that the optional solver input values will be entered by the user.
* SIMPLE &ndash; Indicates that default solver input values will be defined that work well for nearly linear models.
* MODERATE &ndash; Indicates that default solver input values will be defined that work well for moderately nonlinear models.
* COMPLEX &ndash; Indicates that default solver input values will be defined that work well for highly nonlinear models.
<!--* CONTINUE &ndash; Without this the model will stop after convergence failure.-->
</blockquote>
 
==General Specified Options==
*''Coefficient to reduce weight applied to head change (DBDTHETA)'' &ndash; Used to control oscillations in head. Values range between 0.0 and 1.0, and larger values increase the weight (decrease under-relaxation) applied to the head change.
*''Coefficient to increase weight applied to head change (DBDKAPPA)'' &ndash; Used to control oscillations in head. Values range between 0.0 and 1.0, and larger values increase the weight applied to the head change.
*''Factor used to weight the head change for iterations n&ndashl1 and n (DBGGAMMA)'' &ndash; Values range between 0.0 and 1.0, and greater values apply more weight to the head change calculated during iteration ''n''.
*''Momentum coefficient (MOMFACT)'' &ndash; Ranges between 0.0 and 1.0. Greater values apply more weight to the head change for iteration ''n''.
*''Use residual control (BACKFLAG)'' &ndash; Specify whether residual control will be used.
<blockquote style="margin-top:0px; margin-bottom:0px;">
* 1 = active
* 0 = inactive
</blockquote>
*''Max number of reductions (backtracks) in head change (MAXBACKITER)'' &ndash; A value between 10 and 50 works well. Only read if residual control is active.
*''Proportional decrease in root-mean-squared error (BACKTOL)'' &ndash; Only read if residual control is active.
*''Reduction factor for residual control that reduces head change (BACKREDUCE)'' &ndash; Values should be between 0.0 and 1.0, where smaller values result in smaller head-change values. Only read if residual control is active.
 
==GMRES Specified Options==
*''Max number of iterations for the linear solution (MAXITINNER)'' &ndash; This value is the maximum number of iterations per call to the solver.
*''Method of incomplete factorization used as preconditioner (ILUMETHOD)'' &ndash; The index for selection of the method for incomplete factorization (ILU) used as a preconditioner.
<blockquote style="margin-top:0px; margin-bottom:0px;">
* (1) ILU with drop tolerance and fill limit
* (2) ILU(k), Order k incomplete LU factorization
</blockquote>
*''Fill limit for ILUMETHOD 1 or level of fill for ILUMETHOD 2 (LEVFILL)'' &ndash; Recommended values: 5&ndash;10 for method 1, 0&ndash;2 for method 2.
*''Tolerance for convergence of linear solver (STOPTOL)'' &ndash; This is the residual of the linear equations scaled by the norm of the root mean squared error.
*''Number of iterations between restarts of GMRES (MSDR)''
 
==&chi;MD Specified Options==
*''Acceleration method (IACL)'' &ndash; A flag for the acceleration method:
<blockquote style="margin-top:0px; margin-bottom:0px;">
* (0) conjugate gradient
* (1) ORTHOMIN
* (2) Bi-CGSTAB
</blockquote>
*''Scheme of ordering unknowns (NORDER)'' &ndash; A flag with the following options:
<blockquote style="margin-top:0px; margin-bottom:0px;">
* (0) original ordering
* (1) RCM ordering
* (2) Minimum Degree ordering
</blockquote>
*''Level of fill for incomplete LU factorization (LEVEL)''
*''Number of orthogonalization for the ORTHOMIN acceleration scheme (NORTH)'' &ndash; A number between 4 and 10 is appropriate. Small values require less storage but more iterations may be required. Should equal 2 for the other acceleration methods.
*''Reduced system preconditioning (IREDSYS)'' &ndash; A flag for reduced system preconditioning.
<blockquote style="margin-top:0px; margin-bottom:0px;">
* (0) do not apply
* (1) apply
</blockquote>
* ''Residual reduction-convergence criteria (RRCTOLS)''
*''Use drop tolerance in preconditioning (IDROPTOL)'' &ndash; A flag for using drop tolerance in the preconditioning.
<blockquote style="margin-top:0px; margin-bottom:0px;">
* 0 = don't use
* 1 = use
</blockquote>
*''Drop tolerance for preconditioning (EPSRN)''
*''Head closure criteria for inner (linear) iterations (HCLOSEXMD)''
*''Max number of iterations for linear solution (MXITERXMD)''
 
==References==
For more information on the NWT package see the USGS documentation at: [http://water.usgs.gov/nrp/gwsoftware/modflow2000/MFDOC/nwt_newton_solver.htm water.usgs.gov/nrp/gwsoftware/modflow2000/MFDOC/nwt_newton_solver.htm]


For more information on the NWT package see the USGS documentation here. [http://water.usgs.gov/nrp/gwsoftware/modflow2000/MFDOC/nwt_newton_solver.htm]


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Latest revision as of 19:39, 6 March 2023

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UZF1
v • e

Example of the MODFLOW NWT Solver dialog.

The Newton package (NWT) is one of the solvers available in MODFLOW-NWT. The NWT package is only used with the UPW Package. Using the NWT solver requires twice the memory of other MODFLOW solvers because using the Newton method results in an asymmetric matrix. Because of the asymmetric matrix a different matrix solver must be used. The NWT package provides an option to use one of two matrix solvers: a generalized-minimum-residual (GMRES) solver and an Orthomin/stabilized conjugate-gradient solver called χMD (chi-MD).

General Options

  • Comments (Text) – Allows up to 199 characters.
  • Max head change between outer iterations (L)(HEADTOL) – For solution of the nonlinear problem.
  • Max root-mean-squared flux difference between outer iterations (L^3/T) (FLUXTOL) – For solution of the nonlinear problem.
  • Max number of iterations allowed for outer problem (MAXITEROUT) – For solution of the nonlinear problem.
  • Portion of cell thickness used for adjusting coefficients to zero (THICKFACT) – The portion of the cell thickness (length) used for smoothly adjusting storage and conductance coefficients to zero.
  • Matrix solver to be used (LINMETH) – A flag that determines which matrix solver will be used.
  • (1) GMRES
  • (2) χMD
  • Print additional info to listing file (IPRNWT) – A flag that indicates whether additional information about solver convergence will be printed to the main listing file
  • Correct head relative to cell-bottom if surrounded by dewatered cells (IBOTAV) – A flag that indicates whether corrections will be made to groundwater head relative to the cell-bottom altitude if the cell is surrounded by dewatered cells.
  • (0) Don't correct
  • (1) Correct
  • Options (OPTIONS) – Includes the following options:
  • SPECIFIED – Indicates that the optional solver input values will be entered by the user.
  • SIMPLE – Indicates that default solver input values will be defined that work well for nearly linear models.
  • MODERATE – Indicates that default solver input values will be defined that work well for moderately nonlinear models.
  • COMPLEX – Indicates that default solver input values will be defined that work well for highly nonlinear models.

General Specified Options

  • Coefficient to reduce weight applied to head change (DBDTHETA) – Used to control oscillations in head. Values range between 0.0 and 1.0, and larger values increase the weight (decrease under-relaxation) applied to the head change.
  • Coefficient to increase weight applied to head change (DBDKAPPA) – Used to control oscillations in head. Values range between 0.0 and 1.0, and larger values increase the weight applied to the head change.
  • Factor used to weight the head change for iterations n&ndashl1 and n (DBGGAMMA) – Values range between 0.0 and 1.0, and greater values apply more weight to the head change calculated during iteration n.
  • Momentum coefficient (MOMFACT) – Ranges between 0.0 and 1.0. Greater values apply more weight to the head change for iteration n.
  • Use residual control (BACKFLAG) – Specify whether residual control will be used.
  • 1 = active
  • 0 = inactive
  • Max number of reductions (backtracks) in head change (MAXBACKITER) – A value between 10 and 50 works well. Only read if residual control is active.
  • Proportional decrease in root-mean-squared error (BACKTOL) – Only read if residual control is active.
  • Reduction factor for residual control that reduces head change (BACKREDUCE) – Values should be between 0.0 and 1.0, where smaller values result in smaller head-change values. Only read if residual control is active.

GMRES Specified Options

  • Max number of iterations for the linear solution (MAXITINNER) – This value is the maximum number of iterations per call to the solver.
  • Method of incomplete factorization used as preconditioner (ILUMETHOD) – The index for selection of the method for incomplete factorization (ILU) used as a preconditioner.
  • (1) ILU with drop tolerance and fill limit
  • (2) ILU(k), Order k incomplete LU factorization
  • Fill limit for ILUMETHOD 1 or level of fill for ILUMETHOD 2 (LEVFILL) – Recommended values: 5–10 for method 1, 0–2 for method 2.
  • Tolerance for convergence of linear solver (STOPTOL) – This is the residual of the linear equations scaled by the norm of the root mean squared error.
  • Number of iterations between restarts of GMRES (MSDR)

χMD Specified Options

  • Acceleration method (IACL) – A flag for the acceleration method:
  • (0) conjugate gradient
  • (1) ORTHOMIN
  • (2) Bi-CGSTAB
  • Scheme of ordering unknowns (NORDER) – A flag with the following options:
  • (0) original ordering
  • (1) RCM ordering
  • (2) Minimum Degree ordering
  • Level of fill for incomplete LU factorization (LEVEL)
  • Number of orthogonalization for the ORTHOMIN acceleration scheme (NORTH) – A number between 4 and 10 is appropriate. Small values require less storage but more iterations may be required. Should equal 2 for the other acceleration methods.
  • Reduced system preconditioning (IREDSYS) – A flag for reduced system preconditioning.
  • (0) do not apply
  • (1) apply
  • Residual reduction-convergence criteria (RRCTOLS)
  • Use drop tolerance in preconditioning (IDROPTOL) – A flag for using drop tolerance in the preconditioning.
  • 0 = don't use
  • 1 = use
  • Drop tolerance for preconditioning (EPSRN)
  • Head closure criteria for inner (linear) iterations (HCLOSEXMD)
  • Max number of iterations for linear solution (MXITERXMD)

References

For more information on the NWT package see the USGS documentation at: water.usgs.gov/nrp/gwsoftware/modflow2000/MFDOC/nwt_newton_solver.htm


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