Sparse Matrix Aspects of the Finite Element Method

The application of the finite element method invariably involves the solution of large sparse systems of linear algebraic equations, and the solution of these systems often represents a significant or even dominant component of the total cost of applying the method. The object of this paper is to describe and relate various sparse matrix techniques which have been developed to make the solution of these equations more efficient.

[1]  O. Zienkiewicz.  The Finite Element Method In Engineering Science , 1971 .

[2]  Klaus-Jürgen Bathe,et al.  Direct solution of large systems of linear equations , 1974 .

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

[4]  Ian P. King,et al.  An automatic reordering scheme for simultaneous equations derived from network systems , 1970 .

[5]  A. George.  On Block Elimination for Sparse Linear Systems , 1974 .

[6]  Alston S. Householder,et al.  Handbook for Automatic Computation , 1960, Comput. J..

[7]  A. George.  Numerical Experiments Using Dissection Methods to Solve n by n Grid Problems , 1977 .

[8]  Carlos A. Felippa,et al.  Solution of linear equations with skyline-stored symmetric matrix , 1975 .

[9]  John Argyris,et al.  The natural factor formulation of the stiffness for the matrix displacement method , 1975 .

[10]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[11]  Christian Meyer.  Solution of Linear Equations—State-of-the-Art , 1973 .

[12]  F. W. Williams.  Comparison between sparse stiffness matrix and sub‐structure methods , 1973 .

[13]  E. Cuthill,et al.  Reducing the bandwidth of sparse symmetric matrices , 1969, ACM '69.

[14]  William G. Poole,et al.  An algorithm for reducing the bandwidth and profile of a sparse matrix , 1976 .

[15]  A. George.  Nested Dissection of a Regular Finite Element Mesh , 1973 .

[16]  Alan Jennings,et al.  A Compact Storage Scheme for the Solution of Symmetric Linear Simultaneous Equations , 1966, Comput. J..

[17]  A. George,et al.  A Note on Fill for Sparse Matrices , 1975 .

[18]  R. W. Thatcher,et al.  On the Construction and Use of Finite Elements , 1970 .

[19]  G. Fuchs,et al.  Hypermatrix solution of large sets of symmetric positive-definite linear equations , 1972 .

[20]  Gary D. Hachtel.  THE SPARSE TABLEAU APPROACH TO FINITE ELEMENT ASSEMBLY , 1976 .

[21]  R. J. Melosh,et al.  Efficient solution of load-deflection equations. , 1969 .