Numerical Approximation of the Magnetoquasistatic Model with by Ulrich Römer
By Ulrich Römer
This e-book offers a complete mathematical technique for fixing stochastic magnetic box difficulties. It discusses variability in fabric houses and geometry, with an emphasis at the renovation of structural actual and mathematical houses. It specifically addresses uncertainties within the computing device simulation of magnetic fields originating from the producing strategy. Uncertainties are quantified by means of approximating a stochastic reformulation of the governing partial differential equation, demonstrating how facts of actual amounts of curiosity, reminiscent of Fourier harmonics in accelerator magnets, can be utilized to accomplish powerful designs. The booklet covers a couple of key equipment and effects akin to: a stochastic version of the geometry and fabric houses of magnetic units in keeping with size information; an in depth description of numerical algorithms in accordance with sensitivities or on a higher-order collocation; an research of convergence and potency; and the applying of the built version and algorithms to uncertainty quantification within the complicated magnet platforms utilized in particle accelerators.
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Additional info for Numerical Approximation of the Magnetoquasistatic Model with Uncertainties: Applications in Magnet Design
Sc. thesis, Johannes Kepler Universität Linz, Austria (2004) 12. : Optimal control of quasilinear H (curl)-elliptic partial differential equations in magnetostatic field problems. SIAM J. Control Optim. 51(5), 3624–3651 (2013) 13. : Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies. Proc. Inst. Electr. Eng. 124(11), 1026–1034 (1977) 14. : Eddy Current Approximation of Maxwell Equations: Theory, Algorithms and Applications, vol.
2. The respective commuting diagrams have been established in [20, 25]. Concerning the Poincaré-Friedrichs inequality we refer to [29, p. 58] for the Whitney finite element method. Based on the same techniques the result holds true for the spline complex as well, by referring to the gap property, see again . , . The next step is a nonlinear version of Céa’s Lemma. 3 hold true and let J be weak divergence free in D, then A − vh H(curl,D) . 42) A − Ah H(curl,D) ≤ C inf vh ∈Wst,h (D) Proof Using the continuous and discrete saddle point formulation with test function vh ∈ Hh (curl, D) we obtain a(A; vh ) − a(Ah ; vh ) = (vh , grad(λh − λ)) D , ∀vh ∈ Hh (curl, D).
193(36), 4057–4066 (2004) 23. : A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing. Comput. Methods Appl. Mech. Eng. 200(25), 2131–2144 (2011) 24. : Guide for verification and validation in computational solid mechanics. Am. Soc. Mech. Eng. (2006) 25. : Mathematical representation of uncertainty. In: AIAA Non-Deterministic Approaches, Forum, pp. 16–19 (2001) 26. : Uncertain Input Data Problems and the Worst Scenario Method. Elsevier (2004) 27.