Impact of element-level static condensation on iterative solver performance

Abstract

This paper provides theoretical estimates that quantify and clarify the savings associated to the use of element-level static condensation as a first step of an iterative solver. These estimates are verified numerically. The numerical evidence shows that static condensation at the element level is beneficial for higher-order methods. For lower-order methods or when the number of iterations required for convergence is low, the setup cost of the elimination as well as its implementation may offset the benefits obtained during the iteration process. However, as the iteration count (e.g., above 50) or the polynomial order (e.g., above cubics) grows, the benefits of element-level static condensation are significant.