135 research outputs found
Generating Equidistributed Meshes in 2D via Domain Decomposition
In this paper we consider Schwarz domain decomposition applied to the
generation of 2D spatial meshes by a local equidistribution principle. We
briefly review the derivation of the local equidistribution principle and the
appropriate choice of boundary conditions. We then introduce classical and
optimized Schwarz domain decomposition methods to solve the resulting system of
nonlinear equations. The implementation of these iterations are discussed, and
we conclude with numerical examples to illustrate the performance of the
approach
A Schwarz Method for the Magnetotelluric Approximation of Maxwell's equations
The magnetotelluric approximation of the Maxwell's equations is used to model
the propagation of low frequency electro-magnetic waves in the Earth's
subsurface, with the purpose of reconstructing the presence of mineral or oil
deposits. We propose a classical Schwarz method for solving this
magnetotelluric approximation of the Maxwell equations, and prove its
convergence using maximum principle techniques. This is not trivial, since
solutions are complex valued, and we need a new result that the magnetotelluric
approximations satisfy a maximum modulus principle for our proof. We illustrate
our analysis with numerical experiments.Comment: 9 pages, 3 figure
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