Parallel Computation Of 3D Elastic Problems With BEM And Its Engineering Application

Boundary Element Method (BEM), as an effective numerical analysis method of scientific and engineering problems developed following Finite Element Method (FEM), has many advantages such as easier simulating complex boundary shape, high accuracy and dimension reduction. It has been turned into the most important supplement to FEM in the field of solid mechanics. But the scale of the problem that can be solved by BEM is greatly limited, because the matrix of the system equations generated by BEM is fully populated and unsymmetrical. Therefore it is difficult to solve practical complex engineering and scientific problems using BEM, especially in the PC computing environment widely applied in our country. As an important developing direction of large-scale engineering computation, parallel computing has been paid more and more attention in our country and in the world. The combination of BEM and parallel computing can be used to enlarge the problem scale solved by BEM, and to promote the application of BEM in many engineering practical aspects in our country.The author firstly set up a low-cost high-performance PC cluster based on current computational condition of our lab. The basic parallel message-passing platform together with some monitor and control software are installed. The whole system is carefully tuned and then tested by using standard benchmark.Then the intrinsic parallelism of each steps of BEM is studied, and according to the characteristics of computational steps and the data transfer between steps, the parallel storage and load-balancing pattern for the whole algorithm are designed. The parallel in-core and out-of-core version of solvers are given. In order to take the advantage of BEM in surface meshing, a improved scheme of equal accuracy Gaussian quadrature is developed so that the surface weakly singular integral can be well calculated even if the element is extremely narrow. Loop-unrolling technique is implemented to fully utilize the capacity of computer.Multi-domain approach of BEM is frequently used in order to solve large-scale BEM problems. In this paper, the parallel computation of BEM is combined with themulti-domain approach. According to the block structure of system matrix of multi-domain BEM, a frontal like algorithm is designed. The degrees of freedom related to external surface nodes are eliminated during the system integration of each domain, so the storage complexity of program can be decreased. The algorithms presented above are coded under the PC cluster environment. Some numerical examples with practical engineering background are calculated. The results compared with the FEM results given by MSC/NASTRAN show that the PC cluster set up in this paper is reliable and the algorithms presented are efficient, and the solution of stresses is more accurate tan FEM. Parallel computing can be served as a powerful tool in expanding the application of BEM and will accelerate the development of BEM in certain extent. The largest scale of numerical example carried out in this PC cluster is about 50,000 degrees of freedom.Finally, a formulation of frictional contact problem in BEM and parametric linear complementary form is presented.