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Speaker: Prof. Jingmei Qiu
Mathematical and Computer Science, Colorado School of
Mines
Title: Higher order dimensional splitting with integral
deferred corrections with applications in Vlasov equation
Time: Thursday June 23, 16:00 pm - 17:00pm
Venue: B703
Abstract:
We apply the very high order Strang split semi-Lagrangian WENO
algorithm for kinetic equations. The spatial accuracy of the
current Strang split finite difference WENO algorithm is very high
(as high as ninth order), however the temporal error is dominated
by the dimensional splitting, which is only second order accurate.
It is therefore very important to overcome this splitting error, in
order to have a consistently high order numerical algorithm. We are
currently working on using the IDC framework to overcome the `at
best' second order Strang splitting error. Specifically, the
dimensional splitting error is overcomed by iteratively correcting
the numerical solution via the error function, which is solved by
approximating the error equation. We will show numerically that if
one embeds a low order dimensional splitting algorithm into the IDC
framework, there will be order increase when one applies a
correction loop in IDC algorithm with care. Applications to the
Vlasov-Poisson system will be demonstrated.