IMPOSING LINEAR CONSTRAINTS IN FINITE-ELEMENT ANALYSIS

It is often necessary to impose linear constraints on solutions obtained with the finite-element method. This can be done by the penalty method or by eliminating dependent variables. The penalty method requires the careful selection of a penalty parameter and may lead to an inexact imposition of the constraints. Elimination is preferable because it is exact. The zero rows that elimination generates in the coefficient matrix can be removed by reducing the order of the matrix, or by adding back the constraints. The latter approach has the advantage of keeping the imposition of constraints separate from matrix assembly. However, straightforward addition of multi-point constraint equations destroys the symmetry of the matrix. A new method of adding the constraints preserves matrix symmetry.