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SimulationRuntime/IntegrationAlgorithms/IntegrationAlgorithms.tex
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interop_c_python | ||
ompython | ||
scripting_api | ||
simulationflags | ||
faq | ||
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.. toctree:: | ||
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Small Overview of Simulation Flags | ||
================================== | ||
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This chapter contains a :ref:`short overview of simulation flags <cruntime-simflags>` | ||
as well as additional details of the :ref:`numerical integration methods <cruntime-integration-methods>`. | ||
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.. _cruntime-simflags : | ||
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OpenModelica (C-runtime) Simulation Flags | ||
----------------------------------------- | ||
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.. include :: simoptions.inc | ||
.. _cruntime-integration-methods : | ||
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Integration Methods | ||
------------------- | ||
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This section contains additional information about the different | ||
integration methods in OpenModelica, selected by the method flag | ||
of the :ref:`simulate` command or the :ref:`-s simflag <simflag-s>`. | ||
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dassl | ||
~~~~~ | ||
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Default integration method in OpenModelica. | ||
Adams Moulton; the default uses a colored numerical Jacobian and interval root finding. | ||
To change settings, use simulation flags such as | ||
:ref:`dasslJacobian <simflag-dassljacobian>`, | ||
:ref:`dasslNoRootFinding <simflag-dasslnorootfinding>`, | ||
:ref:`dasslNoRestart <simflag-dasslnorestart>`, | ||
:ref:`initialStepSize <simflag-initialstepsize>`, | ||
:ref:`maxStepSize <simflag-maxstepsize>`, | ||
:ref:`maxIntegrationOrder <simflag-maxintegrationorder>`, | ||
:ref:`noEquidistantTimeGrid <simflag-noequidistanttimegrid>`. | ||
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+----------------------+-----------------------------+ | ||
| Order: | 1-5 | | ||
+----------------------+-----------------------------+ | ||
| Step Size Control: | true | | ||
+----------------------+-----------------------------+ | ||
| Order Control: | true | | ||
+----------------------+-----------------------------+ | ||
| Stability Region: | variable; depend from order | | ||
+----------------------+-----------------------------+ | ||
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euler | ||
~~~~~ | ||
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Explicit Euler. | ||
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+----------------------+---------------------+ | ||
| Order: | 1 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(1,0) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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rungekutta | ||
~~~~~~~~~~ | ||
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Classical Runge-Kutta method. | ||
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+----------------------+---------------------+ | ||
| Order: | 4 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(4,0) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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radau1 | ||
~~~~~~ | ||
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Radau IIA with one point. | ||
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+----------------------+---------------------+ | ||
| Order: | 1 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(0,1) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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radau3 | ||
~~~~~~ | ||
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Radau IIA with two points. | ||
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+----------------------+---------------------+ | ||
| Order: | 3 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(1,2) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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radau5 | ||
~~~~~~ | ||
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Radau IIA with three points. | ||
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+----------------------+---------------------+ | ||
| Order: | 5 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(2,3) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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lobatto2 | ||
~~~~~~~~ | ||
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Lobatto IIIA with two points. | ||
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+----------------------+---------------------+ | ||
| Order: | 2 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(2,2) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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lobatto4 | ||
~~~~~~~~ | ||
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Lobatto IIIA with three points. | ||
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+----------------------+---------------------+ | ||
| Order: | 4 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(3,3) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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lobatto6 | ||
~~~~~~~~ | ||
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Lobatto IIIA with four points. | ||
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+----------------------+---------------------+ | ||
| Order: | 6 | | ||
+----------------------+---------------------+ | ||
| Step Size Control: | false | | ||
+----------------------+---------------------+ | ||
| Order Control: | false | | ||
+----------------------+---------------------+ | ||
| Stability Region: | \|(4,4) Padé \| ≤ 1 | | ||
+----------------------+---------------------+ | ||
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Notes | ||
~~~~~ | ||
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Simulation flags | ||
:ref:`maxStepSize <simflag-maxstepsize>` and | ||
:ref:`maxIntegrationOrder <simflag-maxintegrationorder>` | ||
specifiy maximum absolute step size and maximum integration order used by | ||
the dassl solver. | ||
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General step size without control :math:`\approx \cfrac{\mbox{stopTime} - \mbox{startTime}}{\mbox{numberOfIntervals}}`. | ||
Events change the step size (see `Modelica spec 3.3 p. 88 <https://www.modelica.org/documents/ModelicaSpec33.pdf>`__). | ||
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For (a,b) Padé see `wikipedia <http://en.wikipedia.org/wiki/Pad%C3%A9_table>`__. |