COMSOL 6.4 - Matrix Inverse

) under > (if is active; otherwise, directly under ) to define a matrix of variables as the inverse of a square input matrix. You add it by right-clicking the node and choosing > or by right-clicking the node and choosing .

You can also add a global under > (if is active; otherwise, directly under ). In the global context, the has no selection. The matrix inverse component variables are defined globally but the inversion is done locally, for each point where the components are evaluated. The input matrix therefore does not have to depend only on constants and global variables. Its expressions will be evaluated at each evaluation point.

You can define a for the node, and a namespace for variables using the field. For the , see About Selecting Geometric Entities.

In addition, the window for a node contains the following section:

In this section, you define the input matrix to invert. Choose a : (the default), , or . For a symmetric or Hermitian matrix, you only enter the upper-triangular part of the matrix. A Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose. From the list, choose a matrix size from 1-by-1 to 9-by-9 or choose . The maximum size is 50. Then enter the matrix elements in the table below.

The resulting matrix inverse is available as a list of scalar variables with names <name>.invT<i><j>, where <name> is the namespace set in the field, and <i> and <j> are integer indices. The input matrix with names <name>.T<i><j>, as well as the matrix determinant <name>.detT are also made available. Note that the determinant is not computed for matrices of size 4-by-4 or larger; if required, use a node instead.

You can use individual components where variable expressions are allowed, but also evaluate all variables at once using a matrix evaluation node under For example, select under > > > > if it the node has been defined as with the name in .