Nested Iteration, Algebraic Multigrid, and First-Order Least Squares System Finite-Element Method for Magnetohydrodynamics

James Adler

Mathematics, Tufts University


Complex fluid problems, such as magnetohydrodynamics (MHD), involve multi-physics and multi-scale phenomena that require advanced techniques in scientific computing in order to be solved efficiently. The MHD systems yield time-dependent nonlinear systems of partial differential equations that couple a fluid with other internal properties (magnetic field in MHD). In this talk, I will discuss the application of a first order least squares finite-element discretization method and multilevel solvers to solve such systems of equations. The goal is to solve the systems as efficiently as possible, while approximating the physical properties of the system accurately. To accomplish this, tools such as nested iteration and adaptive refinement are used. In addition, the energetics of the system are considered in order to develop a more physically-tractable scheme. Finally, examples of solving various MHD test problems and, if time, multiphase flow problems will be given.

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