Abstract
A symmetric coupling of methods of finite and boundary elements for numerical solution of transient eddy current problems is described. This is an essential step in modelling of electromagnetic forming of metalic sheets. The finite element method is employed in the conducting region of the metalic sheet. The boundary element method relies on the Stratton-Chu representation formula and it models the electromagnetic field in the air including its decay at infinity. We impose external currents by the Biot-Savart law.
Highlights
Eletromagnetic forming of metalic sheets relies on generating pulses of eddy currents, which are imposed by a surrounding coil
A symmetric coupling of methods of finite and boundary elements for numerical solution of transient eddy current problems is described. This is an essential step in modelling of electromagnetic forming of metalic sheets
The finite element method is employed in the conducting region of the metalic sheet
Summary
Eletromagnetic forming of metalic sheets relies on generating pulses of eddy currents, which are imposed by a surrounding coil. In order to analyze and later optimize this metalurgical process we shall model the transient eddy current problem and propose a numerical method that gives accurate enough results. This is the aim of the present respectively, that satisfy the low frequency case of Maxwell’s equations. There are potentialbased formulations [11] and [12], magnetic-field-based (H-based) formulations [6] and [15] and electric-fieldbased (E-based) formulations [1], [2], [3], [4], [5], [10] and [17] We prefer the latter approach, with which we are experienced [13] and [14]. We approximate Sobolev space H(curl; Ωint) using the lowest-order Nedelec-I finite elements [16].
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