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Limitations and Requirements
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.. \index{Coarse Mesh!for Explicit Control Modes}
.. \index{Reference Mesh!for Explicit Control Modes}

In explicit dynamic calculations, the Explicit Control Modes method uses a coarse mesh overlaying the actual problem mesh (called the reference or fine mesh) to increase the critical time step. The name *control mode* comes from the implicit multigrid solution algorithm in Adagio. The Explicit Control Modes algorithm is discussed in the Sierra/SM Theory manual and [:footcite:`spencer`].

.. warning::

   Explicit Control Modes is an experimental analysis technique. It has been shown to be an extremely useful technique on specific problems. However, it does not interoperate with some features, such as rigid bodies. Contact the Sierra/SM development team for more information on the features that do cooperate with Explicit Control Modes.

.. admonition:: Known Issue
   :class: admonition warning

   When using Explicit Control Modes, the Lanczos and Power Method time step estimators cannot yet be used with problems that have contact, rigid bodies, blocks in the fine mesh that are not controlled by the coarse mesh, or coarse elements that contain no fine nodes.

In explicit dynamics, nodal accelerations are computed by dividing the residual (external minus internal) force by the nodal mass. In the Explicit Control Modes algorithm, the reference mesh residual is mapped to the coarse mesh, and accelerations are computed on the coarse mesh.  These accelerations are then interpolated back to the reference mesh.  The portion of the residual with higher frequency content (i.e., that which is not representable by the basis functions of the coarse mesh) determines a fine mesh acceleration that is added to the acceleration interpolated from the coarse mesh.

By computing the acceleration on the coarse mesh, the Explicit Control Modes algorithm allows for the critical time step to be computed based on the size of the coarse mesh rather than the size of the reference mesh. A critical time step is estimated based on the coarse mesh.  Mass scaling is applied to the high frequency component of the acceleration (computed on the reference mesh to increase the time step to the coarse mesh critical time step). Mass scaling introduces error, but the error only occurs in the high frequency part of the response. In contrast, traditional mass scaling affects the full spectrum of structural response. Explicit Control Modes is effective in problems in which the coarse grid represents the frequency range of interest and is significantly coarser than the reference mesh to maximize the critical time step.

The choice of the degree of refinement in the coarse and reference meshes has a large influence on the effectiveness of the Explicit Control Modes algorithm. The reference mesh should be created to give a discretization that is appropriate to capture the geometry of the problem with sufficient refinement to adequately represent gradients in the discretized solution. The coarse mesh should completely overlay the reference mesh, and it should be coarser than the reference mesh at every location in the model. All coarse elements need not contain elements in the reference mesh; it is possible to use a coarse mesh that extends significantly beyond the domain of the reference mesh.

The user has the freedom to create a coarse mesh that gives an acceptable critical time step without using an excessively crude discretization.  Remember that the reference mesh controls the spatial discretization, while the coarse mesh controls the temporal discretization of the model.

To use Explicit Control Modes, the user should set up the reference mesh file and the input file as usual, except that the following additional items must be provided:

- A coarse mesh must be generated, as discussed above. The coarse mesh must be in a separate file from the reference mesh, which is the real model.
- A second ``FINITE ELEMENT MODEL`` command block must be provided in addition to the standard definition for the reference finite element model in the input file.  This command block is set up exactly like the first ``FINITE ELEMENT MODEL`` command block (described in the Sierra/SM User Manual) except that the mesh file referenced is the coarse mesh instead of the reference mesh.  Even though the coarse mesh uses no material models, each block in the coarse mesh must be assigned a material model.
- A ``CONTROL MODES REGION`` command block must appear alongside the standard ``PRESTO REGION`` command block within the ``PRESTO PROCEDURE`` command block.  The presence of the ``CONTROL MODES REGION`` command block instructs Presto to use the Explicit Control Modes algorithm. The ``CONTROL MODES REGION`` command block is documented in :numref:`ecm-region`. It contains the same commands used within the standard ``PRESTO REGION`` command block, except that the commands in the ``CONTROL MODES REGION`` command block are used to control the control modes algorithm and the boundary conditions on the coarse mesh.

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