Adaptive Mesh Refinement
The Adaptive Mesh Refinement node () is a solver attribute that handles adaptive mesh refinement together with a Stationary Solver, an Eigenvalue Solver, or a Time-Dependent Solver. The adaptive mesh refinement creates multiple meshes for segments of a time-dependent simulation. Also see The Adaptive Mesh Refinement Solver.
For stationary and eigenvalue solvers, the Adaptive Mesh Refinement node cannot be added manually but is instead added by the solvers to indicate that they run an adaptive mesh refinement. The Adaptive Mesh Refinement node then only includes an Output section with information about the adaptation solutions and meshes.
General
The software performs adaptive mesh refinement in one geometry only. Use the Adaptation in geometry list to specify that geometry.
Use the Maximum number of elements field to specify the maximum number of elements in the refined mesh. If the number of elements exceeds this number, the solver stops even if has not reached the number specified in the Maximum number of refinements field.
The following properties appear under Time interval control:
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The Time interval length can be controlled manually or automatically. Select Manual (default) or Automatic.
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The value in the Interval reduction factor field (default value: 0.5) determines how the solver reduces the time interval length. A value of 0.5 makes the interval length half of the previous interval length when reduced.
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By default, the solver determines the Interval length (unit: s) automatically (only available when Time interval length is Manual) using an interval length that gives a total of 10 intervals. The length of the time interval is the simulation time before a refinement of the mesh takes place. Click the check box to specify a user-defined time interval length in the field (default value: 0.1 s).
If the number of intervals (that is, the simulation time divided by the interval length) exceeds 100, the interval length specified here may not be respected. You can enforce such a large number of intervals by prescribing a minimal interval length in the Minimal interval length field (see below).
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The value in the Interval growth factor (only available when Time-interval length is Automatic) text field (default value: 2.0) determines how the solver increases the time interval length. A value of 2.0 makes the interval length twice as large as the previous interval length when increased.
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By default, the solver determines the Initial interval length (unit: s) automatically (only available when Time-interval length is Automatic). The length of the initial time interval is the simulation time before the first refinement of the mesh takes place. Select the check box to specify a user-defined time interval length in the field (default value: 0.1 s).
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By default, the solver also determines the Minimal interval length (unit: s) automatically. The minimal length of the time interval is the shortest possible simulation time without performing a mesh refinement. Click to select the check box to specify a user-defined minimal interval length in the field (default value: 0.01 s). The interval length is reduced according to the Interval reduction factor if the solver fails to converge with the current interval length, in which case the minimal interval length setting can be useful.
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If Time interval length is Automatic, the algorithm strives to assume the given value of Fraction of maximum refinement (default value: 0.2) by controlling the size of the time interval. A value of zero means no refinement of the base mesh and a value of one means refinement everywhere using Maximum element refinements. The shortening and lengthening of the interval is determined by the interval reduction and growth factors described below.
For the properties under Mesh element control; see Mesh Refinement below. Also, select or clear the Convert to simplex mesh check box (the default is to use this conversion). Mesh refinement is only possible for simplex meshes. If the original mesh is not a simplex mesh, it can be converted to a simplex mesh by this selection.
Error Estimation
Use the Error estimate list to control how the error estimate is computed.
For time-dependent adaptive mesh refinement you need to specify a user-defined Error indicator. Use the text field to give the error indicator function used for the adaptive mesh refinement. For background information to help with this section, see The Adaptive Mesh Refinement Solver.
Mesh Refinement
Use the Refinement method list to control how to refine mesh elements. Select one of the following methods:
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Longest, to make the solver refine only the longest edge of an element by recursively bisecting the longest edge of edge elements that need refinement. This method is less suitable for models with nonsimplex elements. This is the default method.
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Regular, to make the solver refine elements in a regular pattern by bisecting all edges of an element that needs refinement.
Use the Element selection list to specify how the solver should select which elements to refine. Select:
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Rough global minimum to minimize the L2 norm of the error by refining a fraction of the elements with the largest error in such a way that the total number of elements increases roughly by the factor specified in the accompanying Element count growth factor field. The default value is 1.7, which means that the number of elements increases by roughly 70%.
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Fraction of worst error to refine elements whose local error indicator is larger than a given fraction of the largest local error indicator. Use the accompanying Element fraction field to specify the fraction. The default value is 0.5, which means that the fraction contains the elements with more than 50% of the largest local error.
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Fraction of elements to refine a given fraction of the elements. Use the accompanying Element fraction field to specify the fraction. The default value is 0.5, which means that the solver refines about 50% of the elements with the largest local error indicator.
For time-dependent adaptive mesh refinement, you can specify the maximum number of refinements of the mesh elements (default: 2) in the Maximum element refinements field.
Restart
After each mesh adaptation, the time integration is restarted and you can control the following time-stepping properties:
By default the solver chooses an initial step automatically. Select the Initial step check box for manual specification of an initial step.
Use the Consistent initialization list to control how the solver performs consistent initialization of differential-algebraic systems by selecting Off (the default), On, or Backward Euler.
Output
This section contains information about the solution and mesh that contain the results from the adaptive mesh refinement.
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The Adaptive Mesh Refinement Solver
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Adaptive Mesh Refinement (Utility Node)
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The Log Window
Implementing a Point Source: Application Library path COMSOL_Multiphysics/Equation_Based/point_source.