Finite Element Problem For Parallel Processing

Finite element method is an efficient method in solving the large project. The parallel finite element is becoming much more important as a result of the larger scale. The existing ways are: in hardware, using the common or the special machine that was designed, for example: every kind of vector machines and machines only for solving finite element; in algorithm: many scholars keep developing the parallel algorithms. These algorithms including parallel equation solving machine and the parallel algorithm based on the area splitting, two-stage computing technology or the element by element method, and every kinds of methods and technology in every stage during the analysis of the finite element.This paper is focus on the followed questions:1 Put forward a special splitting way of the solving area on the MIMP parallelcomputing system——splitting in order. This special way can make use of the everyexiting mesh generation when it was made in the parallel computing system and we don't make the communication between the processes. A special node numberingmethod——numbering in order is designed based on the splitting in order. Thesystemic equation formed by this numbering method has a very special structure. It guarantees the sameness of the node number between the adjacent area. When the mesh is generating we do not make the communication of the data, when systemic equation is solving we needn't to form the stiffness matrix. This method can make the adaptive finite element computing.2 We give the parallel multisplitting method in solving the systemic equation formed in 1; make the classic conjugate gradient method become a parallel method; form the precondition matrix of the precondition conjugate gradient method by using the splitting format of multisplitting, achieve the parallelization of the precondition conjugate gradient method.3 We solved two partial differential equations by the methods given in 2 and compared with the serial methods. Then we make the test and analysis the parallel capability. At last we applied the methods in electromagnetic field and elasticity and showed the efficiency and practicability of the methods.