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

Figure 2.6: Fourth order nite dierence computational star. The symbol identies
those grid points coupled to the central grid point.
2.6 Operators and memory requirements
The memory requirement predictions in the previous section have assumed
that one can nd a two way dissector of size 2n on an n by n grid. This assumption
is valid provided second order nite dierence operators are used. If a fourth order
nite dierence operator is used, this involves coupling of grid points at distances
of 2 x and 2 z as shown on Figure 2.6. The minimal two way dissector size then
increases to 4n. At rst sight this does not look like a big increase. However the
memory requirements for nested dissection are highly dependent on the size of this
dissector.
If the dissector size is increased to 4n from 2n, how big will the impact be on
the required memory? Let us return to Figure 2.5. In this case n becomes 2n so:
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