The presented method was suitable for 3-D elasto-plastic frictional contact Fast Multipole Boundary Element Method(FM-BEM),which was much efficient for the elasto-plastic complicated iteration and time-consuming problems.

The presented method is well suitable for 3D elasto-plastic frictional contact Fast Multipole Boundary Element Method(FM-BEM),which is much efficient for the elasto-plastic complicated iteration and time-consuming problems.

The three-dimensional elastic contact multipole-BEM and the corresponding program are successfully used in solving the distributions of traction in the press down screw-pairs of 3500 heavy plate mill, which is a large scale computing subject.

Methods Fast Multipole Boundary Element Method,the method of solving the singularity,and the method of Laplace Transformation.

In this paper, we study 3D fast multipole boundary element method (FM-BEM) for potential problems and 3D FM-BEM for elastic problems, prove the existence and uniqueness of 3D FM-BEM for potential problems, the singular integrals in 3D Fast Multipole BEM for potential problems can be dealt with, also, the FMM expansion of the kernels for 3D elastic problems can be derived.

In this paper, we study parallel of generalized minimal residual algorithm (GMRES) in fast multipole boundary element method (FM-BEM), present the discretization of the boundary integral equation and numerical application of parallel algorithm, then improve on the conventional QR decomposition in order to reduce the problem solution process seriously.

We study the Designing Parallel Algorithms for GMRES(m) in the FM-BEM in this paper, and bring forward Householder Reduction Methods of QR decomposition,and give designing the parallel algorithm at computer’s system .