Towards robust 3D \(Z\)-pinch simulations: Discretization and fast solvers for magnetic diffusion in heterogeneous conductors. (English) Zbl 1201.76041
Summary: The mathematical model of the \(Z\)-pinch is comprised of many interacting components. One of
these components is magnetic diffusion in highly heterogeneous media. In this paper we discuss finite element
approximations and fast solution algorithms for this component, as represented by the eddy current equations. Our
emphasis is on discretizations that match the physics of the magnetic diffusion process in heterogeneous media in
order to enable reliable and robust simulations for even relatively coarse grids. We present an approach based on
the use of exact sequences of finite element spaces defined with respect to unstructured hexahedral grids. This leads
to algorithms that effectively capture the physics of magnetic diffusion. For the efficient solution of the ensuing
linear systems, we consider an algebraic multigrid method that appropriately handles the nullspace structure of the
discretization matrices.
MSC:
76D05 | Navier-Stokes equations for incompressible viscous fluids |
76D07 | Stokes and related (Oseen, etc.) flows |
65F10 | Iterative numerical methods for linear systems |
65F30 | Other matrix algorithms (MSC2010) |