Civil Engineering Reference
In-Depth Information
Read data
Allocate arrays
For all elements
Calculate geometry and connectivity.
Compute element stiffness matrix and store.
Find preconditioner.
Invert the preconditioner.
For all pcg iterations
Gather.
Matrix*vector multiplication.
Scatter.
Complete pcg operations.
Check convergence.
For all elements
Find nodal coordinates and steering vector.
Retrieve element nodal coordinates.
Retrieve element nodal displacements.
For all integrating points
Compute shape functions and derivatives in
local coordinates.
Convert from local to global coordinates.
Form the [B] matrix.
Compute the strains and stresses.
Figure 5.35 Structure chart for pcg algorithm as used in Program 5.5. No global matrix
assembly
elements 2
) also builds the preconditioning matrix which is simply the inverse of the
diagonal terms in what would have been in the assembled global stiffness matrix. The pre-
conditioning matrix (stored as a vector) is called
diag
precon
. The section commented
“pcg equation solution” carries out the vector operations described in equations (3.22)
within the iterative loop labelled
pcg
. The matrix-vector multiply needed in the first of
(3.22) is done using (3.23). The steering vector
g
“gathers” the appropriate components of
p
, to be multiplied by the element stiffness matrix
km
retrieved from
storkm
. Similarly,
the vector
g
“scatters” the result of the matrix-vector multiply to appropriate locations in
u
. A tolerance
pcg tol
enables the iterations to be stopped when successive solutions
