Adaptive Mesh Refinement

The 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.

The software performs adaptive mesh refinement in one geometry only. Use the list to specify that geometry. If you have specified the geometry in the time-dependent study step, this list is not available.

The following properties appear under :

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The can be controlled manually or automatically. Select (default) or . If is ,the algorithm strives to assume the given value for the 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 the maximum element refinements. The shortening and lengthening of the interval is determined by the interval reduction and growth factors described below.

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The value in the 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 (unit: s) automatically (only available when is ) 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. Select 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 (only available when is ) 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 (unit: s) automatically (only available when is ). 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 (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 if the solver fails to converge with the current interval length, in which case the minimal interval length setting can be useful.

For the properties under ; see Mesh Refinement below.

Use the list to control how the error estimate is computed.

For time-dependent adaptive mesh refinement you need to specify a user-defined . Use the text field to give the error indicator function used for the adaptive mesh refinement. You can also specify a range of sample points as an array of real numbers between 0 and 1 for the error estimation in the field. This array controls where to check the error in the next subinterval. For background information to help with this section, see The Adaptive Mesh Refinement Solver.

Use the list to control how to adaptively refine mesh elements. Select one of these methods:

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, 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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, to use the current mesh as a starting point and modify it by refinements, coarsening, topology modification, and point smoothing. Use the check box (selected by default) to control if mesh coarsening is used. If the mesh contains anisotropic elements (for example, a boundary layer mesh), it is best to disable mesh coarsening to preserve the anisotropic structure. If mesh coarsening is allowed, enter a (default: 5) if needed.

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, to set up a size expression describing the error and rebuild the meshing sequence using the size expression as input. Note that structured meshes, such as mapped and swept meshes, in general are not appropriately refined. This method is not supported on imported meshes. The size of the refined mesh is the minimum of the size of the original mesh (previous refined mesh) and the size defined by the refinement. Specify the (a value of 3 by default) to scale the refined mesh size in the regions where refinement is not needed.

For the and adaptive mesh refinement methods, you can specify the maximum number of refinements of the mesh elements (default: 2) in the field. If the is set to , you can also specify a value between 0 and 1 in the field (default value: 0.2) for these adaptation methods. A value of zero means no refinement of the base mesh and a value of one means refinement everywhere using the specified value for the . Also for these adaptation methods, select or clear the check box (the default is to not 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.

Use the list to specify how the solver should select which elements to refine. Select:

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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 field. The default value is 1.7, which means that the number of elements increases by roughly 70%.

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to refine elements whose local error indicator is larger than a given fraction of the largest local error indicator. Use the accompanying 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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to refine a given fraction of the elements. Use the accompanying 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.

Select the check box if you want to save the solution for all new adaptively refined meshes. If cleared, the adaptive mesh refinement solver will only store solutions and meshes for adaptation time intervals that contain requested output times. This option is useful if you have many time adaptation intervals but are only interested in a few output times.

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 check box for manual specification of an initial step.

Use the list to control how the solver performs consistent initialization of differential-algebraic systems by selecting (the default), , or .