SIMD implementation of a non-linear transient shell program with partially structured meshes

The implementation of an explicit transient program for the three-dimensional non-linear finite element analysis of shells on a massively parallel SIMD computer, the CONNECTION Machine, is described. Particular emphasis is placed on interprocessor communication using router and NEWS schemes. A hybrid communication scheme, where NEWS is used within structured subdomains and the router is used to exchange nodal forces between subdomains, is examined. It is shown that the ‘mesh-structure index’ of most large meshes is sufficient to make hybrid schemes effective and this is verified by computer runs. Some benchmark non-linear calculations with 8K to 32K elements are also presented.

[1]  S. Lennart Johnsson,et al.  Data structures and algorithms for the finite element method on a data parallel supercomputer , 1990 .

[2]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[3]  Ted Belytschko,et al.  Eigenvalues and Stable Time Steps for the Uniform Strain Hexahedron and Quadrilateral , 1984 .

[4]  T. Belytschko,et al.  Efficient large scale non‐linear transient analysis by finite elements , 1976 .

[5]  J. M. Kennedy,et al.  Hourglass control in linear and nonlinear problems , 1983 .

[6]  Jerry I. Lin,et al.  Explicit algorithms for the nonlinear dynamics of shells , 1984 .

[7]  K. Park,et al.  Solving structural mechanics problems on the CalTech Hypercube machine , 1987 .

[8]  N. Salvesen,et al.  Technology and design for stars & stripes , 1988 .

[9]  Ted Belytschko,et al.  Recent developments in explicit finite element techniques and their application to reactor structures , 1986 .

[10]  Noboru Kikuchi,et al.  Adaptive finite element methods for shape optimization of linearly elastic structures , 1986 .

[11]  L. Morino,et al.  An Improved Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells: Part 2—Evaluation and Applications , 1971 .

[12]  Y. Yamada,et al.  Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method , 1968 .

[13]  Belytschko Fission-fusion adaptivity in finite elements for nonlinear dynamics of shells. Annual technical report, 1 October 1987-30 September 1988 , 1988 .

[14]  Charbel Farhat On the mapping of massively parallel processors onto finite element graphs , 1989 .

[15]  B. J. Hsieh,et al.  Non-Linear Transient Finite Element Analysis with Convected Co--ordinates , 1973 .

[16]  Michael J. Flynn,et al.  Some Computer Organizations and Their Effectiveness , 1972, IEEE Transactions on Computers.

[17]  Ted Belytschko,et al.  Finite element analysis on the connection machine , 1990 .

[18]  Ted Belytschko,et al.  Eigenvalues and stable time steps for the bilinear Mindlin plate element , 1985 .

[19]  Charbel Farhat,et al.  A general approach to nonlinear FE computations on shared-memory multiprocessors , 1989 .