Abstract Much of the computational effort of the finite element process involves the solution of a system of linear equations. The coefficient matrix of this system, known as the global stiffness matrix, is symmetric, positive definite, and generally sparse. An important technique for reducing the time required to solve this system is substructuring or matrix partitioning. Substructuring is based on the idea of dividing a structure into pieces, each of which can then be analyzed relatively independently. As a result of this division, each point in the finite element discretization is either interior to a substructure or on a boundary between substructures. Contributions to the global stiffness matrix from connections between boundary points form the Kbb matrix. This paper focuses on the triangularization of a general Kbb matrix on a parallel machine.
[1]
Robert E. Fulton,et al.
Substructuring techniques—status and projections
,
1978
.
[2]
J. Pasciak,et al.
Computer solution of large sparse positive definite systems
,
1982
.
[3]
G. Strang,et al.
An Analysis of the Finite Element Method
,
1974
.
[4]
R. G. Voigt,et al.
A methodology for exploiting parallelism in the finite element process
,
1983
.
[5]
J. A. George.
Computer implementation of the finite element method
,
1971
.
[6]
E. Cuthill,et al.
Reducing the bandwidth of sparse symmetric matrices
,
1969,
ACM '69.