The remaining Schur complement system on the unknowns associated with subdomain interfaces is solved by the conjugate gradient method.
The Schur complement method proceeds by noting that we can find the values on the interface by solving the smaller system for the interface values UΓ, where we define the Schur complement matrix The important thing to note is that the computation of any quantities involving
The multiplication of a vector by the Schur complement is a discrete version of the Poincaré–Steklov operator, also called the Dirichlet to Neumann mapping.
For second-order problems, such as the Laplace equation or linear elasticity, the matrix of the system has condition number of the order 1/h2, where h is the characteristic element size.
When a fast function is utilized, especially in low cost parallel computers, the Schur complement method is relatively efficient.