In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of ${\mathbb{R}}^{n}$. The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.

In this paper, we propose a new numerical method for solving
elliptic equations in unbounded regions of ${\mathbb{R}}^{n}$. The
method is based on the mapping of a part of the domain into a
bounded region. An appropriate family of weighted spaces is used
for describing the growth or the decay of functions at large distances. After
exposing the main ideas of the method, we analyse
carefully its convergence. Some 3D computational results are displayed
to demonstrate its efficiency and its high performance.

Linear Force-free (or Beltrami) fields are three-components
divergence-free fields solutions of the equation =
,
where is a real number.
Such fields appear in many branches of physics like astrophysics,
fluid mechanics, electromagnetics and plasma physics. In this paper,
we deal with some related boundary value problems
in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.

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