[Carpet] Tapered grids

[Erik Schnetter]

On May 5, 2006, at 08:17:36, Ian Hawke wrote:

> Dear all,
>
> For those that like playing with totally untested patches, I attach  
> the
> following (darcs DEV version). As the description says, it _should_ do
> the tapered grid approach, but you'll need to specify the number of
> buffer zones by hand. I haven't tested much (except to check that the
> default behaviour of Carpet is unchanged).

If you want to use tapered grids to avoid the storage for past time  
levels, consider the following:

Assume that you have 30 evolved grid functions, 8 levels, and each  
level has 50^3 grid points.  Assume also that you use RK4 as time  
integrator and a 4th order centred method, requiring 2 ghost zones.   
This requires 4 x 2 = 8(4 integrator substeps, 2 stencil size) buffer  
+ ghost zones for Carpet's current approach, and 2 x 8 = 16 buffer +  
ghost zones for a fully tapered approach.  Currently, you need 3 time  
levels plus the RHS, with a fully tapered approach you need only 2  
time levels plus the RHS.

The total amount of storage for both cases is then:

current Carpet:
	30 x 4 x (50 + 2x8)^3 x 8 = 275,996,160 Bytes
tapered:
	30 x 3 x (50 + 2x16)^3 x 8 = 396,984,960 Bytes

That is, you will need more memory, not less.  The ratio changes in  
favour of a fully tapered approach if you use larger grids or lower  
order methods.  The break even occurs e.g. approximately for 100^3  
grids (which are very large) and an RK3 integrator instead of RK4.   
Note that many people use a stencil size of 3 instead of 2 (which I  
assumed), which makes things worse again.

-erik

-- 
Erik Schnetter <schnetter at cct.lsu.edu>

My email is as private as my paper mail.  I therefore support encrypting
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