Auxiliary space preconditioners for linear elasticity based on generalized finite element methods
This work provides a novel preconditioning technique for linear elasticity problems, which is important for computational mechanics and engineering simulations.
The authors develop a preconditioner for linear elasticity discretized by linear finite elements, using an auxiliary space method based on a scalar elliptic equation solved with Generalized Finite Element Methods. The preconditioner is shown to be robust and efficient, with numerical results demonstrating improved convergence rates.
We construct and analyze a preconditioner of the linear elastiity system discretized by conforming linear finite elements in the framework of the auxiliary space method. The auxiliary space preconditioner is based on discretization of a scalar elliptic equation with Generalized Finite Element Method.