HEUMANN , Holger

We present a new approach to the optimization of plasma scenarios in tokamaks. We formulate this task as an optimal control problem and use numerical methods for optimization problems with partial differential equation (PDE) constraints. The latter are discretized by linear finite elements and implicit Euler time stepping. Due to the...

International audience

International audience

International audience

Incorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing. The combination of finite element methods (FEM) and boundary element methods (BEM) is the obvious instrument, and we adapt here for the first time the two standard FEM-BEM coupling approaches...

Incorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing. The combination of finite element methods (FEM) and boundary element methods (BEM) is the obvious instrument, and we adapt here for the first time the two standard FEM-BEM coupling approaches...

International audience

International audience

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard {lowest order} continuous finite elements with discontinuous gradients. \hh{As a consequence,} the location of critical points of the poloidal flux, that are of paramount...

Taking the cue from stabilized Galerkin methods for scalar advection problems, we adapt the technique to boundary value problems modeling the advection of magnetic fields. We provide rigorous a priori error estimates for both fully discontinuous piecewise polynomial trial functions and H (curl, Ω)-conforming finite elements.

We present a new approach to the optimization of plasma scenarios in tokamaks. We formulate this task as an optimal control problem and use numerical methods for optimization problems with partial differential equation (PDE) constraints. The latter are discretized by linear finite elements and implicit Euler time stepping. Due to the...

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in...

International audience

International audience

We deal with the discretization of generalized transient advection problems for differential forms on bounded spatial domains. We pursue an Eulerian method of lines approach with explicit timestepping. Concerning spatial discretization we extend the jump stabilized Galerkin discretization proposed in [ H. HEUMANN and R.HIPTMAIR, Stabilized...

International audience

We rely on a combination of different finite element methods on composite meshes, for the simulation of axisymmetric plasma equilibria in tokamaks. One mesh with Cartesian quadrilaterals covers the burning chamber and one mesh with triangles discretizes the region outsidethe chamber. The two meshes overlap in a narrow region around the...

We introduce a novel method to compute approximations of integrals over implicitly defined hyper-surfaces. The new method is based on a weak formulation in L 2 (0, 1), that uses the coarea formula to circumvent an explicit integration over the hypersurfaces. As such it is possible to use standard quadrature rules in the spirit of hp/spectral...

We rely on a combination of different finite element methods on composite meshes, for the simulation of axisymmetric plasma equilibria in tokamaks.One mesh with Cartesian quadrilaterals covers the vacuum chamber and one mesh with triangles discretizes the region outside the chamber. The two meshes overlap in a narrow region around the chamber....

We introduce a novel method to compute approximations of contour integrals.The new method is based on the coarea formula in combination with a Galerkin projection.As such it fits seamlessly into the spirit of hp/spectral finite element methods and circumvents the expensive and technical computation of contours.We provide convergence estimates...

In order to identify the plasma equilibrium operating space for future tokamaks, a new objective function is introduced in the inverse static free-boundary equilibrium code FEEQS.M. This function comprises terms which penalize the violation of the central solenoid and poloidal field coils limitations (currents and forces). The penalization...