Auxiliary space preconditioners for virtual element methods on polytopal meshes
Provides efficient solvers for virtual element methods on polytopal meshes, addressing a computational bottleneck in numerical PDEs.
Developed auxiliary space preconditioners for virtual element methods on polytopal meshes for second-order elliptic equations, achieving uniformly bounded condition numbers independent of problem size and coefficient jumps.
In this paper, we develop the auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the second order elliptic equations. The preconditioners are constructed based on an auxiliary simplicial mesh. The condition numbers of the preconditioned systems are uniformly bounded, independent of the problem size and the jump in coefficients. Several numerical experiments are presented to demonstrate the performance of the preconditioners.