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