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The interaction of intense, short pulse lasers with atoms and molecules
is best treated by propagating an initial state forward in time using
the time dependent Schrodinger equation. In order to accomplish this it
is essential to ﬁnd computationally efficient techniques to discretize
the spatial coordinates as well as to propagate the typically very large
set of algebraic equations that results from the discretization
procedure. The authors have developed a computational approach using a
Finite Element Discrete Variable Method which scales linearly with the
size of the basis set and can propagate the wavefunction in O(N)
operations. In addition, the method only requires that basis functions
or grid points at the boundaries of the elements communicate at each
timestep. This allows us to parallelize the method using standard
message passing techniques with high efficiency. The result is a
numerical approach which scales linearly with the number of processors.
I will describe the methodology in some detail and demonstrate the
efficacy of the approach on a number of problems using up to 1000
processors. To date, we have observed linear scaling with both the
number of processors as well as the number of ﬁnite elements in a
variety of problems including the interaction of a circularly polarized
laser pulse with atomic hydrogen.
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