Aslan,
I can see that there is an implementation of IRK method in deal.ii. If you do
not mind, may I ask what was the reason that that particular method was chosen
in your software? I am aware that IRK and BDF schemes have overall similar
efficiency, so that might have been just some personal preference of the
developer(s).
That would be a question for Bruno and Damien. I don't know.
> I am wondering how deal.ii solves the issue when the dimension
of the problem is large and then it is impossible to store the matrix
(I-tau*AxJ)^(-1) of the simplified Newton iteration in IRK (where x is the
Kronecker product; from Hairer & Wanner). I believe you use some modification
that leads to the use of simply (I-tau*J)^(-1) as it is seen from the name
/id_minus_tau_J_inverse/ of one of the variables in the code. Is it recomputed
for each Newton iteration?
You never store this matrix. What you need to provide to the integrators is a
function that multiplies a vector with this matrix. In practice, that always
means that you solve a linear system with (I - tau J) and the given vector as
the right hand side.
Take a look at the tutorial program that demonstrates the use of these time
integrators to see an example of how this is implemented in practice.
Best
W.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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