Architecture and operation of a systolic engine for finite element computations

Abstract Finite element analysis requires the solution of very large and sparse systems of linear equations. This paper presents the architecture and operation of a linear systolic engine designed specifically for sparse matrix operations. Examples of various sparse matrix and vector operations are given. Applications of the systolic engine for the preconditioned conjugate gradient methods and the element by element solution methods are presented.

[1]  E. L. Poole,et al.  Multicolor ICCG methods for vector computers , 1987 .

[2]  R. Schreiber Solving Eigenvalue and Singular Value Problems on an Undersized Systolic Array , 1986 .

[3]  T. Hughes,et al.  An element-by-element solution algorithm for problems of structural and solid mechanics , 1983 .

[4]  Beresford N. Parlett,et al.  Element Preconditioning Using Splitting Techniques , 1985 .

[5]  E. L. Stanton,et al.  Developments in structural analysis by direct energy minimization. , 1968 .

[6]  Robert J. Dunki-Jacobs,et al.  Architecture and Operation of a Systolic Sparse Matrix Engine , 1987, PPSC.

[7]  H. T. Kung,et al.  A systolic array computer , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[8]  H. T. Kung,et al.  Systolic Arrays for (VLSI). , 1978 .

[9]  H. T. Kung,et al.  Warp architecture: From prototype to production , 1899 .

[10]  S. Eisenstat Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods , 1981 .

[11]  H. T. Kung Why systolic architectures? , 1982, Computer.

[12]  I. Fried,et al.  More on gradient iterative methods in finite- element analysis. , 1969 .

[13]  Kincho H. Law,et al.  Systolic arrays for finite element analysis , 1985 .

[14]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[15]  Bruce M. Irons,et al.  A frontal solution program for finite element analysis , 1970 .

[16]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[17]  Linda J. Hayes,et al.  A vectorized version of a sparse matrix‐vector multiply , 1986 .

[18]  T. Manteuffel An incomplete factorization technique for positive definite linear systems , 1980 .

[19]  Rami Melhem On the Design of a Pipelined/Systolic Finite Element System. , 1985 .

[20]  Lennart Johnsson Computational Arrays for Band Matrix Equations , 1981 .

[21]  Ilse C. F. Ipsen,et al.  Systolic Networks for Orthogonal Decompositions , 1983 .

[22]  Gene H. Golub,et al.  Matrix computations , 1983 .

[23]  I. Gustafsson,et al.  A preconditioning technique based on element matrix factorizations , 1986 .