Linear in the COMSOL Multiphysics Programming Reference Manual
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Number of iterations. The default is 2.
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Select a Multigrid cycle: V-cycle (the default), W-cycle, or F-cycle. For Multigrid cycle, the settings are the same as for the geometric multigrid (GMG) and algebraic multigrid (AMG) solvers.
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Enter the Number of multigrid levels to generate (the default is 1 for Geometric multigrid and 5 for Algebraic multigrid).
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Lower element order first (any). The default. Generates first a multigrid level by lowering the order (by one) of any of the used shape functions. If there are no shape functions that can be lowered, the mesh is coarsened.
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Coarsen mesh and lower order. Combines lowering of the used shape function order and a coarsening of the mesh.
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Lower element order first (all). Generates a multigrid level by lowering the order (by one) of all the used shape functions. If this is not possible, the mesh is coarsened.
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Coarsen mesh. Does not change the order.
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Lower element order and refine (all). Generates a multigrid level by lowering the order (by one) of all the used shape functions. If this is not possible, the mesh is refined a number of times. The mesh solved for can, with this method, be a finer one than the one selected under the study node.
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Lower element order and refine (any). Generates a multigrid level by lowering the order (by one) of any of the used shape functions. If there are no shape functions that can be lowered, the mesh is refined. The mesh solved for can, with this method, be a finer one than the one selected under the Study node.
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Refine mesh. Does not change the order.
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Manual. Use this setting to select a multigrid level from the existing ones. You then specify the multigrid level to use in the Use multigrid level list. Use the Move Up (), Move Down (), Delete (), and Add () buttons to configure the list of multigrid levels (see Multigrid Level). Use the Assemble on multigrid levels list to specify for which multigrid levels to assemble the discrete differential operators. See also The Geometric Multigrid Solver with Several Meshes.
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In the Use hierarchy in geometries list, select the geometries to apply the multigrid level to. Use the Move Up (), Move Down (), Delete (), and Add () buttons to configure the list of geometries.
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The Assemble on all levels check box is selected by default to assemble the discrete differential operators. Otherwise, these operators are formed using the restriction and prolongation operators. Click to clear the check box as needed.
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When Coarsen mesh and lower order, Lower element order first (all), Lower element order first (any), or Coarsen mesh are selected from the Coarse level generation method list, select the Keep generated multigrid levels check box to save the meshes for all levels under the mesh node.
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If None is selected, no coarse mesh is used in addition to the fine mesh. This can lead to severe reduction in convergence rate but saves memory.
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Enter a Maximum number of DOFs at coarsest level. The default is 5000. Coarse levels are added until the number of DOFs at the coarsest level is less than the max DOFs at coarsest level or until it has reached the number of multigrid levels. Also, you can specify the Maximum number of DOFs per thread on multigrid level for AMG on a parallel multithreaded system. The default is 5000.
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Choose a Coarsening method: Parallel modified independent set (the default) or Classical. The Parallel modified independent set method makes the algebraic multigrid solver more efficient in distributed computing using the method described in Ref. 13. The Classical method corresponds to the implementation of AMG in COMSOL versions before version 6.0 (that is, Ruge–Steuben coarsening). See below for the settings for each coarsening method.
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Enter a value for the Strength of connections is a positive number, typically between 0.25 and 0.75 (default value: 0.25). This is a strength threshold used to determine the relation of strong influence dependence between the points. There is some indication that you should use a lower number, such as 0.25, for problems with denser matrices, whereas for other problems with sparser matrices you should use larger values, such as 0.75.
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The Sparser prolongator check box is selected by default. When interpolating the value of the error in a specific fine point “i”, only the coarse points that strongly influencing “i” are used. If you clear the check box, all the coarse points that are influencing “i” are used.
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Use the Prolongator truncation factor (default: 0.1) to control the fill-in of the prolongator. Small elements from the prolongator are removed. More precisely, let P denote the prolongator and M the truncation factor, the element pij is removed if
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Enter a Maximum number of DOFs at coarsest level. The default is 5000. Coarse levels are added until the number of DOFs at the coarsest level is less than the max DOFs at coarsest level or until it has reached the number of multigrid levels.
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The aggregation algorithm is based on a connection criterion, which you specify as a coefficient in the Strength of connections field. A node j is connected to another node i, if where ε is the strength of connection coefficient, and Aij is the submatrix of the stiffness matrix defined by the degrees of freedoms on node i and j, respectively. Loosely speaking, the strength of connection value determines how strongly the aggregation should follow the direction of anisotropy in the problem. The default value is 0.01.
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From the Null-space vectors list, choose Constant (the default) or Rigid body modes. For linear elasticity problems, always select Rigid body modes because it enhances the convergence properties significantly.
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Select the Construct prolongators componentwise check box for CFD applications and other not strongly coupled physics. It is selected by default in predefined solver suggestions for CFD. This setting is only available when the Null-space vectors settings is set to Constant.
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Select the Compact aggregation check box to use an aggregation algorithm that forms, on average, smaller aggregates, which leads to a less rapid coarsening.
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By default, the Reuse prolongators check box is selected to avoid computing the prolongator matrix P when an old prolongator can be reused.
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Choose how to control the prolongator smoothing using the Smoothing list, which is active when the Prolongator smoothing check box (selected by default) is selected. The Auto option postpones the smoothing for sdim-1 levels, where sdim is the space dimension of the problem. If you choose Manual, enter the level to start smoothing at in the Start smoothing at multigrid level field.
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The final transfer operator, P, between the fine and coarse problems are smoothed by one application of Jacobi smoothing:
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By default, the Use filtering check box is selected. Filtering means that entries in the stiffness matrix have been dropped if they correspond to degrees of freedoms on a node that has no strong connections. Loosely speaking, filtering highlights anisotropy in the problem and results in a sparser coarse level problem.
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The Lower element order first (any) check box is selected by default. This setting provides the combination of GMG with lower order until order 1 is reached and then uses SAAMG to generate the coarser levels. The Assemble on the order-lowered levels check box, which is selected by default, then corresponds to the GMG option to assemble on all level. Using this setting is equivalent to using GMG with SAAMG as a coarse grid solver.
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The Physics from the list.
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Add a weak contribution method from the Add weak contribution list:
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Automatic: The code internally creates a weak contribution for the selected physics. Specify a Shift coefficient relaxation factor, which is a scalar value (default: 1). The shift coefficient multiplies the expression for the shifted Laplace contribution. You can think of it as the β coefficient in the Complex Shifted Laplacian for Large Helmholtz Problems section. It might be the case that you need more or less damping than what the original equation provides; you can then choose another value for this factor. The Automatic option is only supported for Helmholtz-type equations. In that case, the meaning of the shift coefficient is the factor α in the term −i α kru, where r is 1.5. Select the Keep generated weak contribution check box in order to keep the CSL weak contribution feature in the Physics node.
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