COMSOL 6.4 - Matrix Diagonalization

) under > (if is active; otherwise, directly under ) to define variables representing the diagonalization of a symmetric 3-by-3 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 node has no selection. The eigenvalue and eigenvector variables are defined globally but the diagonalization is done locally, for each point where the variables 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 sections:

Enter the symmetric matrix elements for the 3-by-3 input matrix in the table. The matrix diagonalization is primarily intended for extracting principal components of 3D tensor quantities such as principal stresses and strains.

Select the checkbox to compute also the matrix eT, where T is the input matrix.

Select the checkbox (selected by default) to ignore any solution dependencies during the solution process.

The principal values become available as variables <name>.e, where <name> is the namespace set in the field, and is the principal component index, ordered from largest to smallest absolute value. Components of the corresponding principal vectors are called <name>.e<j>, where <j> are integer indices. If was selected, the result can be evaluated as a list of variables with names <name>.expT<j>. The input matrix with names <name>.T<j>, as well as its 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 complete vectors and matrices at once using a matrix evaluation node under . For example, to evaluate the first principal vector, select under > > > > if the node has been defined as with the name in .