Iterative solvers for elliptic problems with arbitrary anisotropy strengths

In this paper new asymptotic-preserving schemes are introduced for the iterative resolution of anisotropic elliptic equations arising in magnetized plasma simulations. These methods overcome the resolution of the saddle point problems systematically implemented in precedent real- izations. This allows us to easily derive iterative solvers for these asymptotic-preserving schemes. It brings a leap forward in the computational efficiency of the method for three-dimensional problems. This is conclusively outlined thanks to three-dimensional serial computations carrying out tens of millions of unknowns. The gains are substantial in terms of memory as well as computational require- ments compared to sparse direct solvers, which represent the only alternative successfully operated so far.