A BLOCK PRECONDITIONING METHOD FOR HIGHER-ORDER FINITE ELEMENT DISCRETIZATIONS OF LINEAR ELASTICITY EQUATIONS IN THREE DIMENSIONS

The higher-order finite elements have been often used in practical computations in that they are superior and necessary under certain conditions over the commonly used low-order ones, for example, they can overcome the Poisson’s ratio locking in linear elasticity. However, they have much higher computational complexity than the low-order elements. A block preconditioned conjugate gradient (BPCG) algorithm with a block diagonal preconditioner is proposed for solving the linear systems derived from higher-order finite element discretizations of linear elasticity equations in three dimensions. In the BPCG method, an algebraic multigrid (AMG) V-cycle, firstly introduced for high-order discretizations of the scalar elliptic problems, is employed for computing approximately the action of the inverse of each diagonal block. The results of various numerical experiments show that the resulting BPCG method based on AMG V-cycle (AMG-BPCG) is more robust and efficient than the usual ILU-type PCG methods.