Systematic symbolic generation of additive and multiplicative discrete constituents

Abstract

The introduction of equality constraints in a finite element discretization is performed by matrix transformation methods on the clique format of sparse matrices. Topological ordering allows interdependent constraints to be applied without pre-assignment. Besides the standard finite element cliques, constraints generate pseudo-elements which are consequence of the second derivatives of the constraint functions. A partition by classes of constituents is achieved: elements, external loads, Lagrange multiplier-enforced constraints are additive constituents. Rigid body constraints, essential boundary conditions, symmetry relations, etc are multiplicative constituents. Decomposition order follows from an analysis of transformed cliques.