Some quantitative evaluations on finite difference local and global results

Open access


Refined Schwarz-Christoffel (SC) conformal transformations allow us to perform reliable quantitative evaluation of the accuracy of local computation of electric and magnetic fields with limited effort, which can be useful to complement well known comparisons of global results. In this paper some examples are presented for mesh point potentials obtained by means of finite difference (FD) methods, but it is possible that similar considerations will be useful in the case of finite element methods (FEM) or meshless computations too.

[1] Driscoll T.A., Trefethen L.N., Schwarz-Christoffel Mapping, Cambridge University Press, 9-30 and 70-74 (2002).

[2] Costamagna E., Di Barba P., Mognaschi M.E., Savini A., Fast algorithms for the design of complexshape devices in electromechanics, Computational Methods for the Innovative Design of Electrical Devices, Springer, pp. 61-65 (2010).

[3] Costamagna E., A new approach to standard Schwarz-Christoffel formula calculations, Microwave and Optical Technology Letters 32(3): 196-199 (2002).

[4] Costamagna E., Di Barba P., Savini A., A kinematic approach to the optimal shape synthesis of electric fields, Electrical Review, ISSN 0033-2097, 88(7b): 90-93 (2012).

[5] Alfonzetti S., Costamagna E., Fanni A., Computing capacitances of vias in multilayered boards, IEEE Transactions on Magnetics 37(5): 3186-3189 (2001).

[6] Costamagna E., A simple procedure to optimize small radius rounded corners obtained from Schwarz-Christoffel conformal transformations, IEEE Transactions on Magnetics 51(3): 3186-3189 (2015).

[7] Costamagna E., Di Barba P., Palka R., Field models of high-temperature superconductor devices for magnetic levitation, Engineering Computations 29(6): 605-616 (2012).

[8] Van Bladel J., Singular Electromagnetic Fields and Sources, Clarendon Press, Oxford, Chapt. 4 (1991).

[9] Van Bladel J., How electrically sharp is a needle?, IEEE Antennas and Propagation Magazine, 45(5): 118-122 (2003).

[10] Costamagna E., Conformal mapping and field singularities in perfectly conducting wedge and rotational symmetry structures, Microwave and Optical Technology Letters 24(3):191-195 (2000).

Archives of Electrical Engineering

The Journal of Polish Academy of Sciences

Journal Information

CiteScore 2016: 0.71

SCImago Journal Rank (SJR) 2016: 0.238
Source Normalized Impact per Paper (SNIP) 2016: 0.535


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 149 147 13
PDF Downloads 45 44 4