Parallel Algorithms For A Class Of Peridynamic Problem

The destruction of the solid material and structure problem is a classic problem in mechanics, is also a difficult problem. It has extensive engineering background, it is in civil engineering and water conservancy, equipment man-ufacturing, aerospace and other fields related to common problems.Becuase of the discontinuity in damage and destruction, classical continuum theory cannot be directly applied to the damage problem. To solve these problems, Silling puts forward the peridynamics theory, the theory by adopting the idea of nonlocal effects describe the reaction between the material point, makes the fracture and failure problems can be described.In many science and engineering calculation in solving discontinuous problems such as fracture, crack, damage has unique advantages. Thus, it is significance for research the peridynamics algorithm.However,the operators in the peridynamic models are nonlocal,so the re-sulting numerical methods generate dense stiffness matrices.Gaussian types of direct solvers were traditionally used solve these problems,which requires O(N3) of operations and O(N2) of memory where N is the number of s-patial nodes.So look for can reduce the amount of calculation and memory requirements, reduce the computing time, improve the computational efficien-cy of numerical, algorithm is our purpose.Predecessors have proposed a fast algorithm, by studying the coefficient matrix, and found that the coefficient matrix from left to right every diagonals except tridiagonal values are constan-t, can be divided into three diagonal matrix and Toplize matrix, and Toplize matrix can be expanded for cyclic matrix, cyclic matrix has relationship with the FFT matrix,so reduces the computational from O(N3) to O(N logN) and memory requirement from O(N2) to O(N).In succession on the basis of pre-vious work, we aimed at FFT computation structure itself can parallelism, using the popular MPI parallel technology, we study the parallel algorithm of peridynamic.The core of the problem of parallel algorithm is the of the FFT parallel algorithm, we are going to have to specific operation is FFT transfor-m vector block storage to each processor, according to the characteristics of the calculation, for data exchange between the processor, make each processor can FFT computation inside, then integrating the data of each processor to calculate. Finally,give a numerical example, and test the parallel efficiency of parallel algorithm.This paper structure is as follows:The first chapter, introduction part, mainly introduces the background and related research progress.The second chapter introduce parallel algorithm for FFT and parallel Ef-ficiency Analysis.The third chapter, introduce peridynamics model and the related theory.The fourth chapter,parallel algorithm is given for a class of near field dynamics problem, expand Toplize matrix for cyclic matrix, then use FFT parallel algorithm, simplify the coefficient matrix, finally, solve it by the conju-gate gradient method.Then give a numerical example, and analysis the parallel efficiency...