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Summary: Application of the operator splitting to the Maxwell equations
with the source term
M.A. Botchev¶
I. Farag´o
R. Horv´ath§
January 22, 2007
Abstract
Motivated by numerical solution of the time-dependent Maxwell equations, we consider
splitting methods for a linear system of differential equations w
(t) = Aw(t) + f(t), A
Rn×n
split into two subproblems w
1(t) = A1w1(t) + f1(t) and w
2(t) = A2w2(t) + f2(t),
A = A1 + A2, f = f1 + f2. First, expressions for the leading term of the local error
are derived for the Strang-Marchuk and the symmetrically weighted sequential splitting
methods. The analysis, done in assumption that the subproblems are solved exactly,
confirms the expected second order global accuracy of both schemes.
Second, several relevant numerical tests are performed for the Maxwell equations dis-
cretized in space either by finite differences or by finite elements. An interesting case
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