Local Finite Element Method Based On The Node Parallel Mechanism

Aiming at breaking through the serial connect characteristic in the global solving domain of FEM that mesh generation parallel process first, structure analysis parallel process as the second step, a natural idea is that as soon as the local mesh of a node is generated independently, a corresponding row of the global stiffness matrix will be built. Thereby, Node-based Parallel Design Concept (shorted for NPDC) comes into being.Based on NPDC, the parallel scheme of NLFEM (Node based Local Finite Element Method) as well as its 3 specific parallel solutions: dynamic allocation, static allocation and self-adapting allocation was proposed in Chapter 2, which achieved the highly efficient parallel seamless connection between the FEM mesh generation process and structure analysis process. Both theoretical analysis and parallel numerical experiments showed that the scheme has good extensibility and upper parallel efficiency. Dynamic allocation can naturally achieve the real load balance that each processor almost finishes the computation simultaneously, satisfy characteristic of good fault-tolerance and have very limited communication amount; Static solution achieves non-communication needing and the load balance of node number among the processors; adaptive allocation which is a compromise between dynamic solution and static solution can reach good load balance, have limited communication amount and some fault-tolerance, so that it has better adaptability than the other two solutions.NPDC of NLFEM parallel scheme rests with NLMG (Node-based Local Mesh Generation) algorithm. Different from conventional mesh generation algorithm, the NLMG is node-based, independent and parallel and for each node, once its local mesh is generated, the corresponding row of global stiffness matrix will be built. Via introducing domain partitioning algorithm based on CDP (Constrained Delaunay Path), a NLMG parallel algorithm is presented in Chapter 3. The algorithm use CDP to partition arbitrary planar domain. The generation of the sub-domain mesh and the CDP in each processor is also node-based, independent and parallel. Because sub-domain interface mesh generation need not be taken into account, there is no communication among processors. Parallel numerical experiments show that the algorithm is efficient and extensible.