In this paper,we develop subspace correction preconditioners for discontinuous Galerkin(DG)discretizations of elliptic problems with hp-refnement.These preconditioners are based on the decomposition of the DG fnite el...In this paper,we develop subspace correction preconditioners for discontinuous Galerkin(DG)discretizations of elliptic problems with hp-refnement.These preconditioners are based on the decomposition of the DG fnite element space into a conforming subspace,and a set of small nonconforming edge spaces.The conforming subspace is preconditioned using a matrix-free low-order refned technique,which in this work,we extend to the hprefnement context using a variational restriction approach.The condition number of the resulting linear system is independent of the granularity of the mesh h,and the degree of the polynomial approximation p.The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees.Numerical examples are shown on several test cases involving adaptively and randomly refned meshes,using both the symmetric interior penalty method and the second method of Bassi and Rebay(BR2).展开更多
基金This work was performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and was partially supported by the LLNL-LDRD Program under Project No.20-ERD-002(LLNL-JRNL-814157).
文摘In this paper,we develop subspace correction preconditioners for discontinuous Galerkin(DG)discretizations of elliptic problems with hp-refnement.These preconditioners are based on the decomposition of the DG fnite element space into a conforming subspace,and a set of small nonconforming edge spaces.The conforming subspace is preconditioned using a matrix-free low-order refned technique,which in this work,we extend to the hprefnement context using a variational restriction approach.The condition number of the resulting linear system is independent of the granularity of the mesh h,and the degree of the polynomial approximation p.The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees.Numerical examples are shown on several test cases involving adaptively and randomly refned meshes,using both the symmetric interior penalty method and the second method of Bassi and Rebay(BR2).
