A Parallel DDM Preconditioner For Solving Elasticity Problem Based On Laplace Operator

Linear elasticity problem has widely practical application. Finite element method is one of the most efficient discrete methods for the problems. But we face many challenges for solving this kind of problem, such as large-scale and high efficiency. Therefore how to design efficient and fast algorithm for it is particularly important.In this paper, we study efficient parallel solvers for the three-dimensional linear elastic problems. First,we propose an additive preconditioner +Δand a multiplicative preconditioner ×Δ, which based on Laplace operator with simple coarse spaces by use of the spectrum equivalence of elastic operator and Laplace operator. They are constructed by three kinds of subsystems with lower complexity operator. Then based on Open MP and MPI parallel programming environment, combining algebraic freedom multicolor group, we design parallel algorithms and the corresponding parallel program module for the +Δand ×Δrespectively. Because complexity of the Laplace operator is lower than the elastic operator, these subsystems above mentioned are natural parallelism, the internal of the second and the third class subsystems are also the same,so the new preconditioner +Δhas low algorithm complexity and good parallel scalability. Further,×Δimprove the convergence speed but increase the communication overhead according to the additive one. Numerical experiments show that they have obvious advantage on efficiency and scalability in solving these problems. In particular, when the size of problem is = 8, = 16,the newly designed additive preconditioner is 3.56 times and 2.48 times faster than the existing one in single process and 8 process respectively.