Numerical Simulation for Blood Flow - Microsurgery: Advances, Simulations, and Applications - page 180

AQ

G

(5.61)

ȭ (

ȭ 6

$ 6 ȭ 3

ȭ 1

$ : $ 3 $ 1 $ ( 4 3

ȭ :

Figure 5.11 Structure of matrix.

where A is the square sparse coeficient matrix, G is a vector (or
column matrix) containing the variable values at the grid nodes, and
Q is the vector containing the terms on the right-hand side of Eq.
(5.60).
The structure of matrix A depends on the ordering of variable
in the vector G . For structured grids, if the variables are labeled
starting at a corner and traversing line after line in a regular manner
(lexicographic ordering), the matrix has a poly-diagonal structure.
For the case of a ive-point computational molecule, all the non-
zero coeficients lie on the main diagonal, the two neighboring
diagonals, and two other diagonals removed by N positions from the
main diagonal, where N is the number of nodes in one direction. All
other coeficients are zero. This structure allows the use of eficient
iterative solvers.
Throughout this topic we shall, for the sake of deiniteness,
order the entries in vector G starting at the southwest corner of
the domain, proceeding northwards along each grid line and then
eastward across the domain (in three-dimensional cases we shall