Frequency domain seismic forward modelling: A tool for waveform ...

U 11
0
U 15
L 11
U 55
U 22
U 25
L 22
L 33
L 44
U 33
0
U 35
U 44
L 15 L 25 L 35 L 45
L 55
U 45
Figure 2.3: Two way dissected matrix S ~
= L ~
U ~
. During LU decomposition the
values for L i;j and U i;j are lled in at the corresponding locations used by S i;j . L i;j
and U i;j denotes possible non-zero elements in matrices L ~
and U ~
respectively after
LU decomposition while 0 denotes zero elements.
the amounts necessary to perform LU decomposition on the n 2
by n 2 grids (L i;i), plus
L 5;i which comes from the coupling between the elements within each subgrid and
the elements within the dissector. In the rst dissection one can write the memory
requirements as:
S(n; 0) = 4S(n=2; 2) + D(n; 0) (2.9)
where S(i; j) represents memory requirement for the subgrid of size i bordered by
n
n
n
n
n
n
S(n,2) S(n,3) S(n,4)
Figure 2.4: All possible subgrid (S(n; 2);S(n; 3) and S(n; 4)) situations arising during
nested dissection. The thick black borders represent neighbouring dissectors
from previous dissections in the recursion.
45