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@Steven-Roberts
Steven-Roberts committed Oct 3, 2024
1 parent 89b8334 commit 7cd34e8
Showing 1 changed file with 73 additions and 111 deletions.
184 changes: 73 additions & 111 deletions doc/arkode/guide/source/Usage/SplittingStep/SplittingStepCoefficients.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -118,13 +118,9 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
see
:numref:`ARKODE.Usage.SplittingStep.SplittingStepCoefficients.Coefficients`.
**Arguments:**
* ``method`` -- the splitting coefficients identifier.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* A ``NULL`` pointer if *method* was invalid or an allocation error occurred.
:param method: the splitting coefficients identifier.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *method* was invalid or an allocation error occurred.
.. versionadded:: x.y.z
Expand All @@ -136,14 +132,9 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
current set of splitting coefficients and their corresponding name, see
:numref:`ARKODE.Usage.SplittingStep.SplittingStepCoefficients.Coefficients`.
**Arguments:**
* ``method`` -- the splitting coefficients identifier.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* A ``NULL`` pointer if *method* was invalid, *method* was
``"ARKODE_SPLITTING_NONE"``, or an allocation error occurred.
:param method: the splitting coefficients identifier.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *method* was invalid or an allocation error occurred.
.. note::
Expand All @@ -159,12 +150,9 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
their corresponding name, see
:numref:`ARKODE.Usage.SplittingStep.SplittingStepCoefficients.Coefficients`.
**Arguments:**
* *method* -- the splitting coefficients identifier.
**Return value:**
* The name associated with *method*.
* ``NULL`` pointer if *method* was invalid.
:param method: the splitting coefficients identifier.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *method* was invalid or an allocation error occurred.
.. versionadded:: x.y.z
Expand All @@ -177,12 +165,10 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
y_n = L_h(y_{n-1}) = \left( \phi^P_{h} \circ \phi^{P-1}_{h}
\circ \dots \circ \phi^1_{h} \right) (y_{n-1}).
**Arguments:**
* *partitions* -- The number :math:`P > 1` of partitions in the IVP.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* ``NULL`` if ``partitions`` was invalid or an allocation error occurred.
:param partitions: The number :math:`P > 1` of partitions in the IVP.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *partitions* was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -197,12 +183,10 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
where :math:`L_h` is the Lie-Trotter splitting and
:math:`L^*_h = L^{-1}_{-h}` is its adjoint.
**Arguments:**
* *partitions* -- The number :math:`P > 1` of partitions in the IVP.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* ``NULL`` if ``partitions`` was invalid or an allocation error occurred.
:param partitions: The number :math:`P > 1` of partitions in the IVP.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *partitions* was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -215,12 +199,10 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
y_n = \phi^1_h(y_{n-1}) + \phi^2_h(y_{n-1}) + \dots + \phi^P(y_{n-1}) +
(1 - p) y_{n-1}.
**Arguments:**
* *partitions* -- The number :math:`P > 1` of partitions in the IVP.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* ``NULL`` if ``partitions`` was invalid or an allocation error occurred.
:param partitions: The number :math:`P > 1` of partitions in the IVP.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *partitions* was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -235,13 +217,11 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
where :math:`L_h` is the Lie-Trotter splitting and
:math:`L^*_h = L^{-1}_{-h}` is its adjoint.
**Arguments:**
* *partitions* -- The number :math:`P > 1` of partitions in the IVP.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* ``NULL`` if ``partitions`` was invalid or an allocation error occurred.
:param partitions: The number :math:`P > 1` of partitions in the IVP.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *partitions* was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -257,13 +237,11 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
where :math:`L_h` is the Lie-Trotter splitting and
:math:`L^*_h = L^{-1}_{-h}` is its adjoint. The parameters
:math:`p_1, \dots, p_5` are selected to give third order.
**Arguments:**
* *partitions* -- The number :math:`P > 1` of partitions in the IVP.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* ``NULL`` if ``partitions`` was invalid or an allocation error occurred.
:param partitions: The number :math:`P > 1` of partitions in the IVP.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if *partitions* was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -283,15 +261,12 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
where :math:`S` is the Strang splitting and parameter :math:`\gamma_1` is
selected to increase the order by two each recursion.
**Arguments:**
* *partitions* -- The number :math:`P > 1` of partitions in the IVP.
* *order* -- A positive even number for the method order of accuracy.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* ``NULL`` if ``partitions`` or ``order`` was invalid or an allocation
error occurred.
:param partitions: The number :math:`P > 1` of partitions in the IVP.
:param order: A positive even number for the method order of accuracy.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if an argument was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -312,15 +287,12 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
where :math:`S` is the Strang splitting and parameter :math:`\gamma_1` is
selected to increase the order by two each recursion.
**Arguments:**
* *partitions* -- The number :math:`P > 1` of partitions in the IVP.
* *order* -- A positive even number for the method order of accuracy.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* ``NULL`` if ``partitions`` or ``order`` was invalid or an allocation
error occurred.
:param partitions: The number :math:`P > 1` of partitions in the IVP.
:param order: A positive even number for the method order of accuracy.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if an argument was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -329,16 +301,13 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
Allocates an empty SplittingStepCoefficients.
**Arguments:**
* *sequential_methods* -- The number :math:`r` of sequential methods
combined to produce the overall operator splitting solution.
* *stages* -- The number :math:`s` of stages.
* *partitions* -- The number :math:`P` of partitions in the IVP.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* A ``NULL`` pointer if *sequential_methods*, *stages* or *partitions* was
invalid or an allocation error occurred.
:param sequential_methods: The number :math:`r` of sequential methods
combined to produce the overall operator splitting solution.
:param stages: The number :math:`s` of stages.
:param partitions: The number :math:`P` of partitions in the IVP.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if an argument was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -347,26 +316,24 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
Allocates a SplittingStepCoefficients and fills it with the given values.
**Arguments:**
* *sequential_methods* -- The number :math:`r` of sequential methods
combined to produce the overall operator splitting solution.
* *stages* -- The number :math:`s` of stages.
* *partitions* -- The number :math:`P` of partitions in the IVP.
* *order* -- The method order of accuracy.
* *alpha* -- An array of length ``sequential_methods`` containing the
weight of each sequential method used to produce the overall operator
splitting solution.
* *beta* -- An array of length
``sequential_methods * (stages+1) * partitions`` containing the time nodes
of the inner integrations in the order
.. math::
\beta_{1,0,1}, \dots, \beta_{1,0,P}, \beta_{1,1,1}, \dots, \beta_{1,1,P}, \dots, \beta_{2,0,1}, \dots, \beta_{r,s,P}.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* A ``NULL`` pointer if an argument was invalid or an allocation error
occurred.
:param sequential_methods: The number :math:`r` of sequential methods
combined to produce the overall operator splitting solution.
:param stages: The number :math:`s` of stages.
:param partitions: The number :math:`P` of partitions in the IVP.
:param order: The method order of accuracy.
:param alpha: An array of length ``sequential_methods`` containing the
weight of each sequential method used to produce the overall operator
splitting solution.
:param beta: An array of length
``sequential_methods * (stages+1) * partitions`` containing the time nodes
of the inner integrations in the order
.. math::
\beta_{1,0,1}, \dots, \beta_{1,0,P}, \beta_{1,1,1}, \dots, \beta_{1,1,P}, \dots, \beta_{2,0,1}, \dots, \beta_{r,s,P}.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if an argument was invalid or an allocation error
occurred.
.. versionadded:: x.y.z
Expand All @@ -375,12 +342,9 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
Creates copy of the given splitting coefficients.
**Arguments:**
* ``coefficients`` -- The splitting coefficients to copy.
**Return value:**
* A :c:type:`SplittingStepCoefficients` structure if successful.
* A ``NULL`` pointer if an allocation error occurred.
:param coefficients: The splitting coefficients to copy.
:return: A :c:type:`SplittingStepCoefficients` structure if successful or a
``NULL`` pointer if an allocation error occurred.
.. versionadded:: x.y.z
Expand All @@ -389,8 +353,7 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
Deallocate the splitting coefficients memory.
**Arguments:**
* ``coefficients`` -- The splitting coefficients.
:param coefficients: The splitting coefficients.
.. versionadded:: x.y.z
Expand All @@ -399,9 +362,8 @@ integer constants are defined ``arkode/arkode_splittingstep.h``.
Write the splitting coefficients to the provided file pointer.
**Arguments:**
* ``coefficients`` -- The splitting coefficients.
* ``outfile`` -- Pointer to use for printing the splitting coefficients.
:param coefficients: The splitting coefficients.
:param outfile: Pointer to use for printing the splitting coefficients.
.. note::
Expand All @@ -422,7 +384,7 @@ references for each in the table below. We use the naming convention
.. code-block:: text
<name>_<stages>_<order>_<partitions>
ARKODE_SPLITTING_<name>_<stages>_<order>_<partitions>
Each of the splitting coefficients that are packaged with SplittingStep are
specified by a unique ID having type:
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