Network Parallel Computation Based On The Large Increment Method

The Large Increment Method (LIM) is a new method presented by Prof. Xila Liu's group in recent years, which is based on the force method and the generalized inverse matrix (GIM) theory for material nonlinearity problems. The whole theory system and the deduction of LIM are presented and discussed in detail. And the formulations of LIM are given. After the comparison between LIM and LATIN ( Large Time Increment Method presented by Ladeveze from Paris ), a conclusion is made that LIM and LATIN are basically two different iteration method in both mechanical concept and mathematical background. The mathematical proof of LIM is also given for the unique of the solution, the astringency of the solution and the stability of iteration, which means that LIM is self-contained in mathematics. Furthermore, the chosen of sample points in LIM shows more optional without break the stability of iteration according to the step by step method. This is also an advantage of LIM. In a word, LIM brings the force method a new light in the computer calculation field. The parallel computation of structural mechanics is a hot research field in western counties, while in China what has been done is far from enough. LIM has some natural parallel-calculating characteristics which are different with the classical sub-structural algorithm. These characteristics are discussed detailedly. LIM can be executed parallel in time field and space field. The calculation of matrix and vector in LIM can also be parallelized. A master-slave parallel model based on the distributed memory is given. Taking the plane stress problem for example, two parallel schemes are given, based on the broadcast and noblocking communication respectively. The parallel environment used by LIM is a cluster system installed with LINUX and MPI, which belongs to the Computation Science Department of Tsinghua University. The two given parallel schemes are tested and evaluated in this environment. Then the optimized program is given and shows a good efficiency with an approximate accelerated ratio of 8 and an occupancy of calculation joint up to 95%. While the ratio between the calculation and the communication is the key for a cluster system using massage passing mode. In order to get higher efficiency, one must pay more attention to it. Besides, the load-balancing is another important factor in parallel computation. The parallelization of LIM can bring some fresh air into the parallel computation field of structural mechanics.