Efficient parallel implementations of finite element methods based on the conjugate gradient method

摘要

In this paper, we introduce a special way to store only the nonzero elements of the stiffness matrix to obtain an efficient parallel algorithm to solve partial differential equations with finite element method. This storage method is obtained by considering the structure of the mesh and the form of the stiffness matrix. The size of the matrix is “the number of unknowns” by “a constant” instead of “the number of unknowns” by “the number of unknowns”. Our method and algorithm are efficient in both time and memory. Experimental results are presented.