Accurate derivative evaluation for any Grad–Shafranov solver
| Autor: | Manas Rachh, Lee Ricketson, J. P. Freidberg, Antoine J. Cerfon |
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| Rok vydání: | 2016 |
| Předmět: |
Dirichlet problem
Numerical Analysis Physics and Astronomy (miscellaneous) Applied Mathematics Numerical analysis Mathematical analysis 010103 numerical & computational mathematics Fredholm integral equation Solver 01 natural sciences Integral equation Finite element method 010305 fluids & plasmas Computer Science Applications Volume integral Computational Mathematics symbols.namesake Rate of convergence Modeling and Simulation 0103 physical sciences symbols 0101 mathematics Mathematics |
| Zdroj: | Journal of Computational Physics. 305:744-757 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2015.11.015 |
| Popis: | We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad-Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented. |
| Databáze: | OpenAIRE |
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