Simulation of Laser Propagation With a Frequency Maxwell Equation
Remi Sentis (CEA/Bruyeres)Sylvian S.\ Desroziers (CEA/Bruyeres)
Frederic Nataf (University Paris VI)
Abstract:
The aim of this work is to perform numerical simulations of the propagation
of a laser beam in a plasma. At each time step, one has to solve a Helmholtz
equation with variable coefficients in a domain which may contain more than
hundred millions of cells.
One uses an iterative method of Krylov type to deal with this system. At
each inner iteration, the preconditioning amounts essentially to solve a
linear system which corresponds to the same five-diagonal symmetric
non-hermitian matrix. If $n_{x}$ and $n_{y}$ denote the number of
discretization points in each spatial direction, this matrix is block
tri-diagonal and the diagonal blocks are equal to a square matrix $A$ of
dimension $n_{x}$ which corresponds to the
discretization form of a one-dimension wave operator. The
corresponding linear system is solved by a block cyclic reduction method.
The crucial point is the product of a full square matrix $Q$ of dimension $%
n_{x}$ by a set of $n_{y}$ vectors where $Q$ corresponds to the basis of the
$n_{x}$ eigenvectors of the tri-diagonal symmetric matrix $A$. We show some
results which are obtained on a parallel architecture. Simulations with 200
millions of cells have run on 200 processors and the results are presented.
Keywords:
Numerical Methods (Linear algebra)
