69 research outputs found
Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
This paper introduces a new sweeping preconditioner for the iterative
solution of the variable coefficient Helmholtz equation in two and three
dimensions. The algorithms follow the general structure of constructing an
approximate factorization by eliminating the unknowns layer by layer
starting from an absorbing layer or boundary condition. The central idea of
this paper is to approximate the Schur complement matrices of the factorization
using moving perfectly matched layers (PMLs) introduced in the interior of the
domain. Applying each Schur complement matrix is equivalent to solving a
quasi-1D problem with a banded LU factorization in the 2D case and to solving a
quasi-2D problem with a multifrontal method in the 3D case. The resulting
preconditioner has linear application cost and the preconditioned iterative
solver converges in a number of iterations that is essentially indefinite of
the number of unknowns or the frequency. Numerical results are presented in
both two and three dimensions to demonstrate the efficiency of this new
preconditioner.Comment: 25 page
Absorbing boundary conditions for wave-equation migration
The standard boundary conditions used at the sides of a seismic section in wave-equation migration generate
artificial reflections. These reflections from the edges of the computational grid appear as artifacts in the final
section. Padding the section with zero traces on either side adds to the cost of migration and simply delays the
inevitable reflections.
We develop stable absorbing boundary conditions that annihilate almost all of the artificial reflections. This
is demonstrated analytically and with synthetic examples. The absorbing boundary conditions presented can
be used with any of the different types of finite-difference wave-equation migration, at essentially no extra cost
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