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Abstract:
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We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed
to improve the performance and reduce the execution time of parallel node-based finite-element solvers
for three-dimensional electromagnetic numerical modelling in exploration geophysics. This new preconditioner
is based on algebraic multigrid that uses different basic relaxation methods, such as Jacobi,
symmetric successive over-relaxation and Gauss-Seidel, as smoothers and the wave-front algorithm to
create groups, which are used for a coarse-level generation. We have implemented and tested this new
preconditioner within our parallel nodal finite-element solver for three-dimensional forward problems
in electromagnetic induction geophysics. We have performed series of experiments for several models
with different conductivity structures and characteristics to test the performance of our algebraic multigrid
preconditioning technique when combined with biconjugate gradient stabilised method. The results
have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between
the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner.
Compared to other preconditioning schemes, such as diagonal, symmetric successive over-relaxation and
truncated approximate inverse, the algebraic multigrid preconditioner greatly improves the convergence
of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners
succeed to converge to a desired precision, algebraic multigrid is able to considerably reduce the total
execution time of the forward-problem code -up to an order of magnitude. Furthermore, the tests have
confirmed that our algebraic multigrid scheme ensures grid-independent rate of convergence, as well as
improvement in convergence regardless of how big local mesh refinements are. In addition, algebraic
multigrid is designed to be a black-box preconditioner, which makes it easy to use and combine with
different iterative methods. Finally, it has proved to be very practical and eficient in the parallel context. |
