CEDRES++ swMATH ID: 18056 Software Authors: Holger Heumann, Jacques Blum, Cedric Boulbe, Blaise Faugeras, Gael Selig, P. Hertout, Eric Nardon, Jean-Marc Ané, Sylvain Brémond, Virginie Grandgirard Description: Quasi-static Free-Boundary Equilibrium of Toroidal Plasma with CEDRES++: Computational Methods and Applications. We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilib-ria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized non-linear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas. Homepage: https://hal.inria.fr/hal-01088772 Related Software: CREATE-NL+; CLISTE; Matlab; TOPICS; ECOM; XTOR; CHEASE; iFEM; Spinterp; Triangle; FRIDA; MAXFEA; GitHub; COMSOL; Maple; Gmsh; PETSc; PLCP; LIUQE; UMFPACK Cited in: 10 Publications all top 5 Cited by 22 Authors 5 Heumann, Holger 2 Faugeras, Blaise 2 Rapetti, Francesca 1 Abate, D. 1 Baelmans, Martine 1 Bettini, Paolo 1 Blommaert, Maarten 1 Blum, Jacques 1 Bonotto, M. 1 Elarif, Ali 1 Elman, Howard C. 1 Gauger, Nicolas R. 1 Koren, Barry 1 Liang, Jiaxing 1 Liu, Shuang 1 Nardon, Eric 1 Palha, Artur 1 Reiter, Detlev 1 Sánchez-Vizuet, Tonatiuh 1 Song, Xiao 1 Tang, Xian-Zhu 1 Villone, Fabio Cited in 4 Serials 7 Journal of Computational Physics 1 SIAM Journal on Scientific Computing 1 Communications in Computational Physics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys all top 5 Cited in 7 Fields 6 Numerical analysis (65-XX) 6 Fluid mechanics (76-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Partial differential equations (35-XX) 2 Approximations and expansions (41-XX) 2 Optics, electromagnetic theory (78-XX) 1 Calculus of variations and optimal control; optimization (49-XX) Citations by Year