Lumped Step

The node (

) is available when using the Segregated attribute node. This step is intended for speeding up and regularizing the computation of any L2-projection stemming from a FEM formulation; for example, where a dependent variable field u is updated or computed from some source field uSrc:

test(u)*(u-uSrc)

Using the lumped step approximates the Jacobian matrix resulting from finite element discretization when solving the linear system for the unknown field variables. The approximation consists of replacing the Jacobian by a diagonal matrix with row sums. In doing so, take care to ensure that the resulting approximate Jacobian is invertible (nonsingular).

General

Use the list to specify variables to be solved for in this step.

By default, all field or state components are included. Select from the list to specify which fields or states to include.

The variables are the ones that appear under the node, and the components are the components listed by each of these (for instance, u is the variable and u, v, and w are the components for a Solid Mechanics model); see also the Field and State nodes.

Jacobian matrices requested by the lumped solver during solution can be stored in a sparse or a filled format, which you choose as or , respectively, from the list. The default setting is . In this case, the setting from the node is used.

In addition, you can choose a matrix-free format, which you choose as . Since the Lumped solver does not benefit from matrix-free evaluation of matrix-vector products, a warning will be issued. COMSOL Multiphysics then assembles the matrix when needed but does not store it between repeated requests from the segregated solver. This may reduce peak memory usage at the cost of multiple assembly calls.