Parallel Algorithms And Parallel Implementation Of Meshless Numerical Simulation

Meshless numerical simulation (MNS) is computational method developed rapidly in recent decade. Based on domain geometry description and nodes, meshless numerical simulation can eliminate at least part of the difficulty of meshing. Due to the no meshing, high accuracy and high convergence speed, MNS is a novel and potential method for many engineering application.The computational effort in MNS is much larger than classical methods because a great lot of matrices need to be operated. Therefore, it is important to research parallel algorithms and parallel implementation for meshless numerical simulation.Seven aspects of parallel algorithms are studied for meshless numerical simulation:1. parallel nodes search. nodes search in MNS will cost much of computational effort if many nodes is used. To increase the nodes search efficiency, we can used parallel sequence search or parallel "bucket" search.2. parallel sample points search. To obtain accurate integration, large numbers of sample points are distributed in computational domain, which will cost much of sample points search time. Parallel sequence search or parallel geometry search can be used to do this task to reduce search time.3. parallel computation of meshless shape functions and their derivatives. A great lot of matrices operations are required to compute meshless shape functions and their derivatives. While a suitable load balance strategy is adopted, this task is automatically assigned to each processor, and it is not necessary to parallelize explicitly.4. parallel computation of numerical quadrature. Numerical quadrature is a important portion for MNS, and is very difficult to get high accuracy. Partition of unity quadrature is a good choice for numerical quadrature in MNS.5. parallel enforcement of essential boundary condition. Enforcement of essential boundary condition is also difficult in MNS. We studied some methods to deal with essential boundary condition, and analyzed the parallel processing of boundary condition. Modified variational principle, penalty function method and collocation method based on D'Alembert's principle are can employed to enforce essential boundary condition in MNS.6. parallel solving of the system of equations. Parallel Gaussian elimination or parallel preconditioned conjugate gradient method are available to solve the system of equations.