Simplify/Fix Adaptivity for Small Errors or no CFL

CHANGELOG.md

@@ -27,6 +27,12 @@ Improved the efficiency of default ARKODE methods with the following changes:
 
 ### Bug Fixes
 
+Removed error floors from the `SUNAdaptController` implementations which could
+unnecessarily limit the time size growth, particularly after the first step.
+
+On the first two time steps, the Soderlind controller uses an I controller
+instead of omitting unavailable terms.
+
 Fixed bug in `ARKodeSetFixedStep` where it could return `ARK_SUCCESS` despite
 an error occurring.
 

doc/shared/RecentChanges.rst

@@ -37,6 +37,13 @@ Improved the efficiency of default ARKODE methods with the following changes:
 
 **Bug Fixes**
 
+Removed error floors from the :c:type:`SUNAdaptController` implementations
+which could unnecessarily limit the time size growth, particularly after the
+first step.
+
+On the first two time steps, the Soderlind controller uses an I controller
+instead of omitting unavailable terms.
+
 Fixed bug in :c:func:`ARKodeSetFixedStep` where it could return ``ARK_SUCCESS``
 despite an error occurring.
 

doc/shared/sunadaptcontroller/SUNAdaptController_ImExGus.rst

@@ -45,9 +45,7 @@ with the form
 
 In the above formulas, the default values of :math:`k_1^E`, :math:`k_2^E`,
 :math:`k_1^I`, and :math:`k_2^I` are 0.367, 0.268, 0.98, and 0.95, respectively,
-and :math:`p` is the global order of the time integration method.  In these
-estimates, a floor of :math:`\varepsilon_* > 10^{-10}` is enforced to avoid
-division-by-zero errors.
+and :math:`p` is the global order of the time integration method.
 
 The SUNAdaptController_ImExGus controller implements both formulas
 :eq:`expGusController` and :eq:`impGusController`, and sets its recommended step

doc/shared/sunadaptcontroller/SUNAdaptController_Soderlind.rst

@@ -27,11 +27,10 @@ and :cite:p:`Sod:06`.  This controller has the form
 
 with default parameter values :math:`k_1 = 1.25`, :math:`k_2 = 0.5`,
 :math:`k_3 = -0.75`, :math:`k_4 = 0.25`, and :math:`k_5 = 0.75`, where
-:math:`p` is the global order of the time integration method.  In this estimate,
-a floor of :math:`\varepsilon_* > 10^{-10}` is enforced to avoid division-by-zero
-errors.  During the first two steps (when :math:`\varepsilon_{n-2}`,
-:math:`\varepsilon_{n-1}`, :math:`h_{n-2}`, and :math:`h_{n-2}` may be unavailable),
-the corresponding terms are merely omitted during estimation of :math:`h'`.
+:math:`p` is the global order of the time integration method.  During the first
+two steps (when :math:`\varepsilon_{n-2}`, :math:`\varepsilon_{n-1}`,
+:math:`h_{n-2}`, and :math:`h_{n-2}` may be unavailable), the I controller
+:math:`h' = h_n \varepsilon_1^{-1/(p+1)}` is used.
 
 The SUNAdaptController_Soderlind controller is implemented as a derived
 SUNAdaptController class, and defines its *content* field as:

examples/arkode/CXX_manyvector/ark_sod_lsrk.out

@@ -20,9 +20,9 @@ Problem parameters and options:
     t         ||rho||      ||mx||       ||my||       ||mz||       ||et||
  --------------------------------------------------------------------------
   0.00e+00  7.12610e-01  0.00000e+00  0.00000e+00  0.00000e+00  1.77658e+00
-  1.00e-02  7.09460e-01  5.28096e-02  0.00000e+00  0.00000e+00  1.76732e+00
-  2.00e-02  7.06459e-01  7.61804e-02  0.00000e+00  0.00000e+00  1.75863e+00
-  3.00e-02  7.03444e-01  9.39395e-02  0.00000e+00  0.00000e+00  1.74990e+00
+  1.00e-02  7.09460e-01  5.28085e-02  0.00000e+00  0.00000e+00  1.76732e+00
+  2.00e-02  7.06459e-01  7.61805e-02  0.00000e+00  0.00000e+00  1.75863e+00
+  3.00e-02  7.03444e-01  9.39390e-02  0.00000e+00  0.00000e+00  1.74990e+00
   4.00e-02  7.00418e-01  1.08850e-01  0.00000e+00  0.00000e+00  1.74113e+00
   5.00e-02  6.97379e-01  1.21955e-01  0.00000e+00  0.00000e+00  1.73232e+00
   6.00e-02  6.94326e-01  1.33784e-01  0.00000e+00  0.00000e+00  1.72346e+00
@@ -33,16 +33,16 @@ Problem parameters and options:
  --------------------------------------------------------------------------
 
 Final integrator statistics:
-Current time                 = 0.1
-Steps                        = 382
-Step attempts                = 397
-Stability limited steps      = 0
-Accuracy limited steps       = 397
-Error test fails             = 15
-NLS step fails               = 0
-Inequality constraint fails  = 0
-Initial step size            = 1.12228425974954e-14
-Last step size               = 0.000233441607859208
-Current step size            = 0.000233441607859208
-RHS fn evals                 = 3957
-Number of stages used        = 10
+Current time                  = 0.1
+Steps                         = 374
+Step attempts                 = 391
+Stability limited steps       = 0
+Accuracy limited steps        = 391
+Error test fails              = 17
+NLS step fails                = 0
+Inequality constraint fails   = 0
+Initial step size             = 1.12228425974954e-14
+Last step size                = 8.26420296853591e-05
+Current step size             = 8.26420296853591e-05
+RHS fn evals                  = 3895
+Number of stages used         = 10

examples/arkode/CXX_parallel/ark_brusselator1D_task_local_nls.USE_CUDA_NVEC_--monitor.out

@@ -25,49 +25,49 @@ Output directory: .
           t         ||u||_rms   ||v||_rms   ||w||_rms
    ----------------------------------------------------
        0.000000     1.060205     3.559930     3.059949
-       0.250000     1.134976     3.463307     3.499980
-       0.500000     1.251255     3.307480     3.499978
-       0.750000     1.421776     3.076173     3.499975
-       1.000000     1.617972     2.789695     3.499972
-       1.250000     1.738611     2.525641     3.499970
-       1.500000     1.724313     2.346645     3.499970
+       0.250000     1.134975     3.463308     3.499980
+       0.500000     1.251254     3.307483     3.499978
+       0.750000     1.421775     3.076175     3.499975
+       1.000000     1.617974     2.789694     3.499972
+       1.250000     1.738612     2.525640     3.499970
+       1.500000     1.724313     2.346644     3.499970
        1.750000     1.609332     2.267405     3.499972
-       2.000000     1.441938     2.284790     3.499975
+       2.000000     1.441938     2.284789     3.499975
        2.250000     1.254548     2.387110     3.499978
        2.500000     1.067861     2.552978     3.499982
        2.750000     0.894914     2.755797     3.499985
-       3.000000     0.742698     2.972707     3.499988
-       3.250000     0.614424     3.189681     3.499990
-       3.500000     0.511703     3.400292     3.499992
-       3.750000     0.435022     3.602349     3.499993
-       4.000000     0.382884     3.795611     3.499993
+       3.000000     0.742698     2.972706     3.499988
+       3.250000     0.614424     3.189680     3.499990
+       3.500000     0.511703     3.400291     3.499992
+       3.750000     0.435022     3.602348     3.499993
+       4.000000     0.382885     3.795610     3.499993
        4.250000     0.351268     3.980789     3.499994
-       4.500000     0.334675     4.159066     3.499994
-       4.750000     0.327999     4.331676     3.499994
+       4.500000     0.334675     4.159065     3.499994
+       4.750000     0.327999     4.331675     3.499994
        5.000000     0.327576     4.499585     3.499994
        5.250000     0.331182     4.663357     3.499994
-       5.500000     0.337619     4.823164     3.499994
-       5.750000     0.346346     4.978846     3.499994
-       6.000000     0.357245     5.129937     3.499994
+       5.500000     0.337620     4.823164     3.499994
+       5.750000     0.346346     4.978845     3.499994
+       6.000000     0.357244     5.129937     3.499994
        6.250000     0.370526     5.275660     3.499994
-       6.500000     0.386740     5.414810     3.499993
-       6.750000     0.406897     5.545549     3.499993
-       7.000000     0.432797     5.664942     3.499992
-       7.250000     0.467856     5.767888     3.499992
-       7.500000     0.519324     5.844481     3.499991
-       7.750000     0.605996     5.871569     3.499989
-       8.000000     0.797170     5.775343     3.499986
-       8.250000     1.629022     5.135025     3.499974
-       8.500000     3.774898     3.499505     3.499941
-       8.750000     4.025788     2.194933     3.499932
-       9.000000     3.877379     0.967603     3.499933
-       9.250000     3.148899     1.087229     3.499946
-       9.500000     2.471560     1.322866     3.499958
-       9.750000     1.912340     1.594916     3.499967
-      10.000000     1.450253     1.896162     3.499975
+       6.500000     0.386741     5.414808     3.499993
+       6.750000     0.406897     5.545550     3.499993
+       7.000000     0.432798     5.664941     3.499992
+       7.250000     0.467855     5.767889     3.499992
+       7.500000     0.519325     5.844479     3.499991
+       7.750000     0.605996     5.871568     3.499989
+       8.000000     0.797169     5.775343     3.499986
+       8.250000     1.629015     5.135030     3.499974
+       8.500000     3.774895     3.499509     3.499941
+       8.750000     4.025789     2.194934     3.499932
+       9.000000     3.877381     0.967603     3.499933
+       9.250000     3.148900     1.087229     3.499946
+       9.500000     2.471561     1.322865     3.499958
+       9.750000     1.912340     1.594915     3.499967
+      10.000000     1.450254     1.896163     3.499975
 
 Final Solver Statistics (for processor 0):
-   Internal solver steps = 482 (attempted = 482)
-   Total RHS evals:  Fe = 1931,  Fi = 5936
-   Total number of error test failures = 0
+   Internal solver steps = 481 (attempted = 483)
+   Total RHS evals:  Fe = 1933,  Fi = 5951
+   Total number of error test failures = 2
    Total number of nonlinear solver convergence failures = 0

examples/arkode/CXX_parallel/ark_brusselator1D_task_local_nls.USE_CUDA_NVEC_--monitor_--global-nls.out

@@ -25,52 +25,52 @@ Output directory: .
           t         ||u||_rms   ||v||_rms   ||w||_rms
    ----------------------------------------------------
        0.000000     1.060205     3.559930     3.059949
-       0.250000     1.134976     3.463307     3.499980
-       0.500000     1.251255     3.307480     3.499978
-       0.750000     1.421776     3.076173     3.499975
-       1.000000     1.617972     2.789695     3.499972
-       1.250000     1.738611     2.525641     3.499970
-       1.500000     1.724313     2.346645     3.499970
+       0.250000     1.134975     3.463308     3.499980
+       0.500000     1.251254     3.307483     3.499978
+       0.750000     1.421775     3.076175     3.499975
+       1.000000     1.617974     2.789694     3.499972
+       1.250000     1.738612     2.525640     3.499970
+       1.500000     1.724313     2.346644     3.499970
        1.750000     1.609332     2.267405     3.499972
-       2.000000     1.441938     2.284790     3.499975
+       2.000000     1.441938     2.284789     3.499975
        2.250000     1.254548     2.387110     3.499978
        2.500000     1.067861     2.552978     3.499982
        2.750000     0.894914     2.755797     3.499985
-       3.000000     0.742698     2.972707     3.499988
-       3.250000     0.614424     3.189681     3.499990
-       3.500000     0.511703     3.400292     3.499992
-       3.750000     0.435022     3.602349     3.499993
-       4.000000     0.382884     3.795611     3.499993
+       3.000000     0.742698     2.972706     3.499988
+       3.250000     0.614424     3.189680     3.499990
+       3.500000     0.511703     3.400291     3.499992
+       3.750000     0.435022     3.602348     3.499993
+       4.000000     0.382885     3.795610     3.499993
        4.250000     0.351268     3.980789     3.499994
-       4.500000     0.334675     4.159066     3.499994
-       4.750000     0.327999     4.331676     3.499994
+       4.500000     0.334675     4.159065     3.499994
+       4.750000     0.327999     4.331675     3.499994
        5.000000     0.327576     4.499585     3.499994
        5.250000     0.331182     4.663357     3.499994
-       5.500000     0.337619     4.823164     3.499994
-       5.750000     0.346346     4.978846     3.499994
-       6.000000     0.357245     5.129937     3.499994
+       5.500000     0.337620     4.823164     3.499994
+       5.750000     0.346346     4.978845     3.499994
+       6.000000     0.357244     5.129937     3.499994
        6.250000     0.370526     5.275660     3.499994
-       6.500000     0.386740     5.414810     3.499993
-       6.750000     0.406897     5.545549     3.499993
-       7.000000     0.432797     5.664942     3.499992
-       7.250000     0.467856     5.767888     3.499992
-       7.500000     0.519324     5.844481     3.499991
-       7.750000     0.605996     5.871569     3.499989
-       8.000000     0.797170     5.775343     3.499986
-       8.250000     1.629022     5.135025     3.499974
-       8.500000     3.774898     3.499505     3.499941
-       8.750000     4.025788     2.194933     3.499932
-       9.000000     3.877379     0.967603     3.499933
-       9.250000     3.148899     1.087229     3.499946
-       9.500000     2.471560     1.322866     3.499958
-       9.750000     1.912340     1.594916     3.499967
-      10.000000     1.450253     1.896162     3.499975
+       6.500000     0.386741     5.414808     3.499993
+       6.750000     0.406897     5.545550     3.499993
+       7.000000     0.432798     5.664941     3.499992
+       7.250000     0.467855     5.767889     3.499992
+       7.500000     0.519325     5.844479     3.499991
+       7.750000     0.605996     5.871568     3.499989
+       8.000000     0.797169     5.775343     3.499986
+       8.250000     1.629015     5.135030     3.499974
+       8.500000     3.774895     3.499509     3.499941
+       8.750000     4.025789     2.194934     3.499932
+       9.000000     3.877381     0.967603     3.499933
+       9.250000     3.148900     1.087229     3.499946
+       9.500000     2.471561     1.322865     3.499958
+       9.750000     1.912340     1.594915     3.499967
+      10.000000     1.450254     1.896163     3.499975
 
 Final Solver Statistics (for processor 0):
-   Internal solver steps = 482 (attempted = 482)
-   Total RHS evals:  Fe = 1931,  Fi = 6084
-   Total number of error test failures = 0
+   Internal solver steps = 481 (attempted = 483)
+   Total RHS evals:  Fe = 1933,  Fi = 6088
+   Total number of error test failures = 2
    Total number of nonlinear solver convergence failures = 0
-   Total number of nonlinear iterations = 4153
-   Total number of linear iterations = 2912
-   Total number of preconditioner solves = 5690
+   Total number of nonlinear iterations = 4155
+   Total number of linear iterations = 2913
+   Total number of preconditioner solves = 5688

examples/arkode/CXX_parallel/ark_brusselator1D_task_local_nls.USE_SERIAL_NVEC_--monitor.out

@@ -25,49 +25,49 @@ Output directory: .
           t         ||u||_rms   ||v||_rms   ||w||_rms
    ----------------------------------------------------
        0.000000     1.060205     3.559930     3.059949
-       0.250000     1.134976     3.463307     3.499980
-       0.500000     1.251255     3.307480     3.499978
-       0.750000     1.421776     3.076173     3.499975
-       1.000000     1.617972     2.789695     3.499972
-       1.250000     1.738611     2.525641     3.499970
-       1.500000     1.724313     2.346645     3.499970
+       0.250000     1.134975     3.463308     3.499980
+       0.500000     1.251254     3.307483     3.499978
+       0.750000     1.421775     3.076175     3.499975
+       1.000000     1.617974     2.789694     3.499972
+       1.250000     1.738612     2.525640     3.499970
+       1.500000     1.724313     2.346644     3.499970
        1.750000     1.609332     2.267405     3.499972
-       2.000000     1.441938     2.284790     3.499975
+       2.000000     1.441938     2.284789     3.499975
        2.250000     1.254548     2.387110     3.499978
        2.500000     1.067861     2.552978     3.499982
        2.750000     0.894914     2.755797     3.499985
-       3.000000     0.742698     2.972707     3.499988
-       3.250000     0.614424     3.189681     3.499990
-       3.500000     0.511703     3.400292     3.499992
-       3.750000     0.435022     3.602349     3.499993
-       4.000000     0.382884     3.795611     3.499993
+       3.000000     0.742698     2.972706     3.499988
+       3.250000     0.614424     3.189680     3.499990
+       3.500000     0.511703     3.400291     3.499992
+       3.750000     0.435022     3.602348     3.499993
+       4.000000     0.382885     3.795610     3.499993
        4.250000     0.351268     3.980789     3.499994
-       4.500000     0.334675     4.159066     3.499994
-       4.750000     0.327999     4.331676     3.499994
+       4.500000     0.334675     4.159065     3.499994
+       4.750000     0.327999     4.331675     3.499994
        5.000000     0.327576     4.499585     3.499994
        5.250000     0.331182     4.663357     3.499994
-       5.500000     0.337619     4.823164     3.499994
-       5.750000     0.346346     4.978846     3.499994
-       6.000000     0.357245     5.129937     3.499994
+       5.500000     0.337620     4.823164     3.499994
+       5.750000     0.346346     4.978845     3.499994
+       6.000000     0.357244     5.129937     3.499994
        6.250000     0.370526     5.275660     3.499994
-       6.500000     0.386740     5.414810     3.499993
-       6.750000     0.406897     5.545549     3.499993
-       7.000000     0.432797     5.664942     3.499992
-       7.250000     0.467856     5.767888     3.499992
-       7.500000     0.519324     5.844481     3.499991
-       7.750000     0.605996     5.871569     3.499989
-       8.000000     0.797170     5.775343     3.499986
-       8.250000     1.629022     5.135025     3.499974
-       8.500000     3.774898     3.499505     3.499941
-       8.750000     4.025788     2.194933     3.499932
-       9.000000     3.877379     0.967603     3.499933
-       9.250000     3.148899     1.087229     3.499946
-       9.500000     2.471560     1.322866     3.499958
-       9.750000     1.912340     1.594916     3.499967
-      10.000000     1.450253     1.896162     3.499975
+       6.500000     0.386741     5.414808     3.499993
+       6.750000     0.406897     5.545550     3.499993
+       7.000000     0.432798     5.664941     3.499992
+       7.250000     0.467855     5.767889     3.499992
+       7.500000     0.519325     5.844479     3.499991
+       7.750000     0.605996     5.871568     3.499989
+       8.000000     0.797169     5.775343     3.499986
+       8.250000     1.629015     5.135030     3.499974
+       8.500000     3.774895     3.499509     3.499941
+       8.750000     4.025789     2.194934     3.499932
+       9.000000     3.877381     0.967603     3.499933
+       9.250000     3.148900     1.087229     3.499946
+       9.500000     2.471561     1.322865     3.499958
+       9.750000     1.912340     1.594915     3.499967
+      10.000000     1.450254     1.896163     3.499975
 
 Final Solver Statistics (for processor 0):
-   Internal solver steps = 482 (attempted = 482)
-   Total RHS evals:  Fe = 1931,  Fi = 5936
-   Total number of error test failures = 0
+   Internal solver steps = 481 (attempted = 483)
+   Total RHS evals:  Fe = 1933,  Fi = 5951
+   Total number of error test failures = 2
    Total number of nonlinear solver convergence failures = 0