[cig-commits] r14710 - doc/CitcomS/manual
tan2 at geodynamics.org
tan2 at geodynamics.org
Tue Apr 14 18:31:05 PDT 2009
Author: tan2
Date: 2009-04-14 18:31:04 -0700 (Tue, 14 Apr 2009)
New Revision: 14710
Modified:
doc/CitcomS/manual/citcoms.lyx
Log:
Update to Cookbook 6-9
Modified: doc/CitcomS/manual/citcoms.lyx
===================================================================
--- doc/CitcomS/manual/citcoms.lyx 2009-04-15 00:53:20 UTC (rev 14709)
+++ doc/CitcomS/manual/citcoms.lyx 2009-04-15 01:31:04 UTC (rev 14710)
@@ -9127,8 +9127,14 @@
\end_layout
\begin_layout LyX-Code
+[CitcomS.solver.bc]
+\newline
topvbc = 1
\newline
+
+\newline
+[CitcomS.solver.param]
+\newline
file_vbcs = on
\end_layout
@@ -9201,14 +9207,20 @@
\end_layout
\begin_layout LyX-Code
+[CitcomS.solver]
+\newline
datadir_old = ./ic
\newline
datafile_old = cookbook5
\newline
-tic_method = -1
+
\newline
-solution_cycles_init
- = 0
+[CitcomS.solver.ic]
+\newline
+tic_met
+hod = -1
+\newline
+solution_cycles_init = 0
\end_layout
\begin_layout Standard
@@ -9222,6 +9234,8 @@
\end_layout
\begin_layout LyX-Code
+[CitcomS.solver.tsolver]
+\newline
finetunedt = 0.75
\newline
monitor_max_T = on
@@ -9360,23 +9374,12 @@
\newline
nodez = 33
\newline
-theta_min = 1.47
-\newline
-theta_m
-ax = 1.67
-\newline
-fi_min = 0
-\newline
-fi_max = 0.5
-\newline
-radius_inner = 0.7
-\newline
\newline
[CitcomS.solver.tsolver]
\newline
-finetunedt
- = 0.75
+
+finetunedt = 0.75
\newline
monitor_max_T = on
\newline
@@ -9386,21 +9389,21 @@
\newline
num_mat = 4
\newline
-visc0 = 100,0.003,1,2
+visc0 =
+ 100,0.003,1,2
\newline
-TDEPV
- = on
+TDEPV = on
\newline
viscE = 24,24,24,24
\newline
viscT = 0.182,0.182,0.182,0.182
\newline
-VMIN = on
+VMIN
+ = on
\newline
visc_min = 0.01
\newline
-VMAX
- = on
+VMAX = on
\newline
visc_max = 100.0
\end_layout
@@ -9508,7 +9511,13 @@
\begin_layout Enumerate
Calculate the normal traction on the top surface based on the accumulated
topography up to the current time step, and add it to the forcing term
- in the matrix version of the momentum equation.
+ in Equation
+\begin_inset LatexCommand ref
+reference "eq:discrete momentum eqn"
+
+\end_inset
+
+.
\end_layout
@@ -9569,7 +9578,11 @@
\begin_inset Formula $\times$
\end_inset
- 25 with mesh refinement (coord.dat)
+ 25 nodes with mesh refinement (
+\family typewriter
+coor=1
+\family default
+)
\end_layout
\begin_layout Itemize
@@ -9586,23 +9599,31 @@
\end_layout
\begin_layout Standard
-Specific options:
+The pseudo-free-surface boundary condition is enabled by:
\end_layout
-\begin_layout Itemize
-
-\family typewriter
-solver.tsolver.fixed_timestep = 7.770000e-10
-\family default
- (= ~1000 yrs)
+\begin_layout LyX-Code
+[CitcomS.solver.bc]
+\newline
+topvbc = 2
+\newline
+pseudo_free_surf = on
\end_layout
-\begin_layout Itemize
+\begin_layout Standard
+The time step size is fixed to
+\begin_inset Formula $7.77\times10^{-10}$
+\end_inset
-\family typewriter
-solver.bc.pseudo_free_surf = on
+ (about 1000 yrs), instead of determined dynamically by the velocity solution.
\end_layout
+\begin_layout LyX-Code
+[CitcomS.solver.tsolver]
+\newline
+fixed_timestep = 7.77e-10
+\end_layout
+
\begin_layout Subsection
Discussion
\end_layout
@@ -9865,8 +9886,13 @@
\end_inset
.
- The density anomaly of the anomalous chemical composition is 0.5.
+ The density anomaly of the anomalous chemical composition is defined by
+\begin_inset Formula $B=\Delta\rho_{ch}/\left(\rho_{0}\alpha_{0}\Delta T\right)$
+\end_inset
+
+, the buoyancy ratio.
+
\end_layout
\begin_layout LyX-Code
@@ -9921,16 +9947,6 @@
cookbook7.tracer_log.*
\family default
) for error messages.
- Note that this code does not work if
-\family typewriter
-nprocx
-\family default
- or
-\family typewriter
-nprocy
-\family default
- is greater than 1 in the full spherical version.
- The regional spherical version does not have this constraint.
\end_layout
\begin_layout Standard
@@ -9939,7 +9955,11 @@
\begin_inset Formula $\mathbf{A}x=b$
\end_inset
- for x.
+ for
+\begin_inset Formula $x$
+\end_inset
+
+.
The conjugate gradient solver is more efficient than the multigrid solver
(
\family typewriter
@@ -9963,25 +9983,14 @@
vlowstep
\family default
.
- For the Uzawa algorithm, the desired accuracy for the continuity equation
- (Equation
-\begin_inset LatexCommand ref
-reference "eq:discrete continuite eqn"
-
-\end_inset
-
-) and maximum iterations are set by
+ For the Uzawa algorithm, the maximum iterations are set by
\family typewriter
-tole_compressibility
-\family default
- and
-\family typewriter
piterations
\family default
.
\family typewriter
-vlowstep
+Both vlowstep
\family default
and
\family typewriter
@@ -9999,14 +10008,11 @@
\begin_layout LyX-Code
Solver = cgrad
\newline
-accuracy = 1e-06
+accuracy = 1e-03
\newline
vlowstep = 1000
\newline
-tole_compressibility = 1e-07
-\newline
-piterat
-ions = 1000
+piterations = 1000
\end_layout
\begin_layout Subsubsection
@@ -10024,8 +10030,6 @@
\newline
\newline
-
-\newline
[CitcomS.c
ontroller]
\newline
@@ -10033,8 +10037,6 @@
\newline
\newline
-
-\newline
[CitcomS.solv
er]
\newline
@@ -10047,8 +10049,6 @@
\newline
\newline
-
-\newline
[CitcomS.solver.ic]
\newline
num_perturbati
@@ -10064,8 +10064,6 @@
\newline
\newline
-
-\newline
[CitcomS.solver.out
put]
\newline
@@ -10073,8 +10071,6 @@
\newline
\newline
-
-\newline
[CitcomS.solver.tracer]
\newline
tracer = on
@@ -10112,49 +10108,49 @@
\newline
\newline
-
-\newline
[Citcom
S.solver.vsolver]
\newline
Solver = cgrad
\newline
-accuracy = 1e-06
+accuracy = 1e-04
\newline
vlowstep = 1000
\newline
-tole_compressibility
- = 1e-07
+piterations
+ = 1000
\newline
-piterations = 1000
-\newline
\newline
-
-\newline
# Assign the viscosities.
\newline
[CitcomS.solver.visc]
\newline
-VISC_UPDATE
- = on
+VISC_UPDATE = on
\newline
-num_mat = 4
+num_mat
+ = 4
\newline
visc0 = 1,1,1,1
\newline
TDEPV = on
\newline
+rheol = 4
+\newline
viscE = 0.2,0.2,0.2,0.2
\newline
viscT = 0,0,0,0
\newline
-VMIN
- = on
+viscZ
+ = 0,0,0,0
\newline
+VMIN = on
+\newline
visc_min = 1.0
\newline
VMAX = on
+\newline
+visc_max = 100.0
\end_layout
\begin_layout Standard
@@ -10208,6 +10204,178 @@
\end_layout
\begin_layout Standard
+When the model is running, it will output the progress of the run to the
+ screen.
+ This line has information about the grid:
+\end_layout
+
+\begin_layout LyX-Code
+Problem has 9 x 9 x 9 nodes per cap, 6930 nodes and 6144 elements in total
+\end_layout
+
+\begin_layout Standard
+The following lines give the radial coordinate and reference density of
+ each nodes and their viscosity layer:
+\end_layout
+
+\begin_layout LyX-Code
+ nz radius depth rho layer
+\newline
+ 1 0.550000
+ 0.450000 1.000000e+00 4
+\newline
+ 2 0.606250 0.393750 1.000000e+00
+ 4
+\newline
+ 3 0.662500 0.337500 1.000000e+00 4
+\newline
+ 4 0.718750
+ 0.281250 1.000000e+00 4
+\newline
+ 5 0.775000 0.225000 1.000000e+00
+ 4
+\newline
+ 6 0.831250 0.168750 1.000000e+00 4
+\newline
+ 7 0.887500
+ 0.112500 1.000000e+00 4
+\newline
+ 8 0.943750 0.056250 1.000000e+00
+ 2
+\newline
+ 9 1.000000 0.000000 1.000000e+00 1
+\end_layout
+
+\begin_layout Standard
+This line gives the perturbation parameters used to construct the initial
+ temperature:
+\end_layout
+
+\begin_layout LyX-Code
+Initial temperature perturbation: layer=5 mag=0.05 l=3 m=2
+\end_layout
+
+\begin_layout Standard
+This line gives the magnitude the right-hand side vector in Equation
+\begin_inset LatexCommand ref
+reference "eq:discrete momentum eqn"
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout LyX-Code
+Momentum equation force 2.207120371e+03
+\end_layout
+
+\begin_layout Standard
+The following lines give the convergence progress of the Stokes solver,
+ where
+\family typewriter
+v
+\family default
+ is the volume averaged norm of velocity,
+\family typewriter
+p
+\family default
+ is the volume averaged norm of pressure,
+\family typewriter
+div/v
+\family default
+ is the volume averaged norm of
+\begin_inset Formula $\nabla\cdot(\bar{\rho}v)$
+\end_inset
+
+ divided by
+\family typewriter
+v
+\family default
+,
+\family typewriter
+dv/v
+\family default
+ is the volume averaged norm of velocity change divided by
+\family typewriter
+v
+\family default
+, and
+\family typewriter
+dp/p
+\family default
+ is the volume averaged norm of pressure change divided by
+\family typewriter
+p
+\family default
+.
+\end_layout
+
+\begin_layout LyX-Code
+(000) 7.0 s v=1.470010e+02 p=0.000000e+00 div/v=5.37e+00 dv/v=1.00e+00 dp/p=1.00e+00
+ step 0
+\newline
+
+\begin_inset Formula $\vdots$
+\end_inset
+
+
+\newline
+(090) 151.3 s v=1.012752e+02 p=1.304499e+04 div/v=5.54e-04 dv/v=1.84e-05 dp/p=9.20e-05
+ step 0
+\newline
+(091) 151.8 s v=1.012752e+02 p=1.304512e+04 div/v=5.66e-04 dv/v=2.07e-05
+ dp/p=7.45e-05 step 0
+\end_layout
+
+\begin_layout Standard
+This line gives the rotation angle and the angular coordinates of rotation
+ pole of the removed net angular momentum:
+\end_layout
+
+\begin_layout LyX-Code
+Angular momentum: rot=9.917258e-02 tr=8.924735e+01 fr=1.083630e+02
+\end_layout
+
+\begin_layout Standard
+These lines give the heat flux across the top and bottom surfaces:
+\end_layout
+
+\begin_layout LyX-Code
+surface heat flux= 2.227892
+\newline
+bottom heat flux= 2.216542
+\end_layout
+
+\begin_layout Standard
+The surface heat flux
+\family typewriter
+
+\begin_inset Formula $H_{surf}$
+\end_inset
+
+
+\family default
+ can be converted to the Nusselt number
+\family typewriter
+
+\begin_inset Formula $Nu_{surf}$
+\end_inset
+
+
+\family default
+ by:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+Nu_{surf}=H_{surf}\times\frac{r_{outer}^{3}}{r_{outer}-r_{inner}}\label{eq:Nusselt number}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
The results for this problem are presented in Figure
\begin_inset LatexCommand ref
reference "fig:Cookbook-7:-The"
@@ -10307,8 +10475,12 @@
\begin_layout Standard
A compressible convection model has four dimensionless numbers: the Rayleigh
- number, the dissipation number, the Gruneisen parameter, and the non-dimensiona
-lized absolute surface temperature, which are defined in Section
+ number, the dissipation number, the Gruneisen parameter
+\begin_inset Formula $\gamma=\alpha_{0}K_{S0}/\rho_{0}c_{P0}$
+\end_inset
+
+, and the non-dimensionalized absolute surface temperature, which are defined
+ in Section
\begin_inset LatexCommand ref
reference "sec:Governing-Equations"
@@ -10326,10 +10498,67 @@
\end_inset
).
+ Similarily, the effective dissipation number is 0.275 (
+\begin_inset Formula $=0.5\times(r_{outer}-r_{inner})$
+\end_inset
+
+).
Under these non-dimensional numbers, the convection is of low vigor and
low compressibility.
- If
+\end_layout
+
+\begin_layout LyX-Code
+rayleigh = 7.68175583e4
+\newline
+dissipation_number = 0.5
+\newline
+gruneisen = 1.25
+\newline
+surfaceT = 0.1
+\end_layout
+
+\begin_layout Standard
+Since we are going to use the multigrid solver, the grid size is specified
+ by:
+\end_layout
+
+\begin_layout LyX-Code
+nodex = 33
+\newline
+nodey = 33
+\newline
+nodez = 33
+\newline
+levels = 5
+\end_layout
+
+\begin_layout Standard
+The additional parameter
\family typewriter
+levels
+\family default
+ specifies the nested levels of multigrid units and is subjected to the
+ following constraint:
+\begin_inset Formula \begin{equation}
+\mathrm{nodex}=1+\mathrm{nprocx}\times\mathrm{mgunitx}\times2^{levels-1}\label{eq:mgunit}\end{equation}
+
+\end_inset
+
+where
+\family typewriter
+mgunitx
+\family default
+ must be an integer.
+ In the pure C version,
+\family typewriter
+mgunitx
+\family default
+ is an input parameter.
+\end_layout
+
+\begin_layout Standard
+If
+\family typewriter
reference_state=0
\family default
, then constant gravity, heat capacity, thermal expansivity, and
@@ -10408,13 +10637,20 @@
\begin_layout Standard
You will need the output of dynamic topography and the geoid.
+ The dynamics topography will be computed by the Consistent Boundary Flux
+ (CBF) method, and the effect of self-gravitation is included in the geoid.
The maximum spherical harmonics degree for the geoid is 20.
\end_layout
\begin_layout LyX-Code
output_optional = geoid,surf,botm
\newline
-output_ll_max = 20
+use_cbf_topo = on
+\newline
+self_gravitation = on
+\newline
+output_ll
+_max = 20
\end_layout
\begin_layout Standard
@@ -10434,13 +10670,17 @@
\begin_inset Formula $\mathbf{A}x=b$
\end_inset
- for x.
+ for
+\begin_inset Formula $x$
+\end_inset
+
+.
The multigrid solver is more efficient than the conjugate gradient solver
(
\family typewriter
Solver=cgrad
\family default
-) for bigger problems (e.g., more than 17
+) for larger problems (e.g., more than 17
\begin_inset Formula $\times$
\end_inset
@@ -10453,15 +10693,19 @@
\family typewriter
mg_cycle=1
\family default
- for the V cycle and 2 for the W cycle;
+ for the V cycle and
\family typewriter
+2
+\family default
+ for the W cycle;
+\family typewriter
down_heavy
\family default
and
\family typewriter
up_heavy
\family default
- are the number of smoothing cycles for downward/upward smoothing; and
+ are the number of smoothing cycles for downward/upward smoothing;
\family typewriter
vlowstep
\family default
@@ -10469,7 +10713,11 @@
\family typewriter
vhighstep
\family default
- are the number of smoothing passes at lowest/highest levels.
+ are the number of smoothing passes at lowest/highest levels; and
+\family typewriter
+max_mg_cycles
+\family default
+ is the maximum number of multigrid cycles per solve.
All these parameters should be small integers.
\end_layout
@@ -10486,18 +10734,17 @@
\newline
vhighstep
= 2
+\newline
+max_mg_cycles = 50
\end_layout
\begin_layout Standard
-The following parameters turn on the pre-conditioner and specify the desired
- accuracy for the matrix equation solver (either multigrid or conjugate
- gradient).
+The following parameter turn on the pre-conditioner for the matrix equation
+ solver (either multigrid or conjugate gradient).
\end_layout
\begin_layout LyX-Code
precond = on
-\newline
-accuracy = 0.001
\end_layout
\begin_layout Standard
@@ -10536,31 +10783,28 @@
and velocity solutions.
Three variations of the Uzawa algorithm are used in CitcomS, one for the
incompressible case, and the other two for the compressible case.
- Two parameters are common to the three variations.
- These parameters specify the maximum number of iterations and the desired
- residual level for the continuity equation
+ One parameter,
+\family typewriter
+piterations,
+\family default
+ common to the three variations, specifies the maximum number of iterations
+ and the desired residual level for the continuity equation
\begin_inset LatexCommand ref
reference "eq:discrete continuite eqn"
\end_inset
.
- Sometimes, larger values of
+ Sometimes, larger value of
\family typewriter
piterations
\family default
- and
-\family typewriter
-tole_compressibility
-\family default
- are required for convergence if complicated velocity boundary conditions
+ is required for convergence if complicated velocity boundary conditions
are used.
\end_layout
\begin_layout LyX-Code
piterations = 375
-\newline
-tole_compressibility = 1e-08
\end_layout
\begin_layout Standard
@@ -10576,9 +10820,19 @@
\end_inset
is used.
- In this case, two additional parameters control the maximum number and
- the desired accuracy of outer iterations.
- If
+ In this case, an additional parameter controls the maximum number of outer
+ iterations.
+
+\end_layout
+
+\begin_layout LyX-Code
+uzawa = cg
+\newline
+compress_iter_maxstep = 100
+\end_layout
+
+\begin_layout Standard
+If
\family typewriter
uzawa=bicg
\family default
@@ -10588,27 +10842,53 @@
\end_inset
- is used.
+ is used, and no additional parameter is needed.
\end_layout
+\begin_layout Standard
+The overall accuracy of the velocity solver is controlled by a single parameter.
+ The solver is converged if the residuals of Equation
+\begin_inset LatexCommand ref
+reference "eq:discrete continuite eqn"
+
+\end_inset
+
+ and
+\begin_inset LatexCommand ref
+reference "eq:discrete momentum eqn"
+
+\end_inset
+
+ both are smaller than
+\family typewriter
+accuracy
+\family default
+, or if the changes in the velocity and pressure both are smaller than
+\family typewriter
+accuracy
+\family default
+ for the last two iterations.
+\end_layout
+
\begin_layout LyX-Code
-uzawa = cg
-\newline
-compress_iter_maxstep = 100
-\newline
-relative_err_accuracy = 0.001
+accuracy = 0.001
\end_layout
\begin_layout Standard
-Finally, the rigid body rotation component of the velocity solution is removed.
- The mode of rigid body rotation is unconstrained by the Stokes equation,
- if free-slip boundary conditions are used for the top and bottom boundaries
- in a full spherical model.
+Finally, the net angular momentum of the velocity solution is removed.
+ For incompressible case, the reference density does not change with the
+ radius, and the net angular momentum would be equivalent to the rigid body
+ rotation.
+ The net angular momentum and the mode of rigid body rotation are unconstrained
+ by the Stokes equation, if free-slip boundary conditions are used for the
+ top and bottom boundaries in a full spherical model.
\end_layout
\begin_layout LyX-Code
-remove_rigid_rotation = on
+remove_rigid_rotation = off
+\newline
+remove_angular_momentum = on
\end_layout
\begin_layout Standard
@@ -10617,6 +10897,10 @@
\family typewriter
remove_rigid_rotation
\family default
+ and
+\family typewriter
+remove_angular_momentum
+\family default
.
\end_layout
@@ -10638,8 +10922,6 @@
\newline
\newline
-
-\newline
[CitcomS.controller]
\newline
monitoringFrequency = 1000
@@ -10649,8 +10931,6 @@
\newline
\newline
-
-\newline
[CitcomS.solver]
\newline
datadir = output
@@ -10675,8 +10955,6 @@
\newline
\newline
-
-\newline
[CitcomS.solver.mesher]
\newline
nodex = 33
@@ -10696,8 +10974,6 @@
\newline
\newline
-
-\newline
[CitcomS.solver.param]
\newline
reference
@@ -10707,31 +10983,32 @@
\newline
\newline
-
-\newline
[CitcomS.solver.output]
\newline
output_optional = geoid,sur
f,botm
\newline
+use_cbf_topo = on
+\newline
+self_gravitation = on
+\newline
output_ll_max = 20
\newline
\newline
-
-\newline
[CitcomS.solver.ic]
\newline
-tic_method = 3
+t
+ic_method = 3
\newline
-num_perturbations
- = 1
+num_perturbations = 1
\newline
perturbl = 3
\newline
perturbm = 2
\newline
-perturblayer = 17
+perturblayer =
+ 17
\newline
perturbmag = 0.01
\newline
@@ -10739,19 +11016,16 @@
\newline
restart = off
\newline
-soluti
-on_cycles_init = 9000
+solution_cycles_init = 9000
\newline
\newline
-
-\newline
[CitcomS.solver.visc]
\newline
-VISC_UPDATE = on
+VI
+SC_UPDATE = on
\newline
-visc_smooth_method
- = 1
+visc_smooth_method = 1
\newline
\newline
@@ -10761,10 +11035,10 @@
\newline
num_mat = 4
\newline
-viscE = 2.99573,2.99573,2.99573,2.99573
+viscE
+ = 2.99573,2.99573,2.99573,2.99573
\newline
-viscT
- = 0.5,0.5,0.5,0.5
+viscT = 0.5,0.5,0.5,0.5
\newline
visc0 = 1,1,1,1
\newline
@@ -10772,68 +11046,64 @@
\newline
VMIN = on
\newline
-visc_min = 0.001
+visc_mi
+n = 0.001
\newline
VMAX = on
\newline
-visc_max =
- 1e+06
+visc_max = 1e+06
\newline
\newline
-
-\newline
[CitcomS.solver.tsolver]
\newline
finetunedt = 0.75
\newline
\newline
-
+[CitcomS.s
+olver.vsolver]
\newline
-[CitcomS.solver.vsolver]
+uzawa = cg
\newline
-uzawa
- = cg
-\newline
Solver = multigrid
\newline
mg_cycle = 1
\newline
down_heavy = 2
\newline
-up_heavy = 2
+up_heavy
+ = 2
\newline
-vlowstep =
- 20
+vlowstep = 20
\newline
vhighstep = 2
\newline
+max_mg_cycles = 50
+\newline
\newline
aug_lagr = on
\newline
-aug_number = 2.0e3
+aug_number
+ = 2.0e3
\newline
precond = on
\newline
\newline
-piterations =
- 375
+piterations = 375
\newline
accuracy = 0.001
\newline
-tole_compressibility = 1e-08
+compress_iter_maxstep
+ = 100
\newline
-compress_iter_maxstep = 100
+
\newline
-relati
-ve_err_accuracy = 0.001
+remove_rigid_rotation = off
\newline
-
-\newline
-remove_rigid_rotation = on
+remove_angular_momentum = on
\end_layout
\begin_layout Subsection
@@ -10850,19 +11120,26 @@
.
A tetrahedral symmetric pattern is developed for the convection.
The surface heatflux
-\begin_inset Formula $Q_{surf}$
+\begin_inset Formula $H_{surf}$
\end_inset
at the steady state is 3.892, and the bottom heatflux
-\begin_inset Formula $Q_{botm}$
+\begin_inset Formula $H_{botm}$
\end_inset
is 12.817.
The heatflux imbalance (
-\begin_inset Formula $Q_{botm}r_{inner}^{2}/Q_{surf}r_{outer}^{2}-1$
+\begin_inset Formula $H_{botm}r_{inner}^{2}/H_{surf}r_{outer}^{2}-1$
\end_inset
) is -0.38%.
+ The Nussult number, converted from Equation
+\begin_inset LatexCommand ref
+reference "eq:Nusselt number"
+
+\end_inset
+
+, is 3.182.
The total viscous heating is 7.68991, and the totoal adiabatic cooling is
7.71719.
Under a steady state, these two terms should be exactly balanced.
@@ -12650,30 +12927,16 @@
These specify the nested level of multigrid units.
Used by multigrid solver only.
These parameters are not completely independent to each other.
- The following constraints must be satisfied:
-\newline
+ The constraint of Equation
+\begin_inset LatexCommand ref
+reference "eq:mgunit"
-\newline
-
-\begin_inset Formula $\mathrm{nodex}=1+\mathrm{nprocx}\times\mathrm{mgunitx}\times2^{levels-1}$
\end_inset
-
+ must be satisfied.
\newline
-\begin_inset Formula $\mathrm{nodey}=1+\mathrm{nprocy}\times\mathrm{mgunity}\times2^{levels-1}$
-\end_inset
-
-
\newline
-
-\begin_inset Formula $\mathrm{nodez}=1+\mathrm{nprocz}\times\mathrm{mgunitz}\times2^{levels-1}$
-\end_inset
-
-
-\newline
-
-\newline
For a full spherical model,
\family typewriter
mgunitx
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