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Electromagnetics is a very important area in science and engineering, especially when the electromagnetic effects are coupled with mechanical and fluid flow systems. There are many important applications: electric motors, heating of furnaces/ovens, medical procedures, electromagnetic switches, electromagnetic pumps or brakes, wave guides, antennas, transmission lines, electromagnetic casting, non-destructive testing of metals, and so on. All these electromagnetic phenomena and applications are uniformly governed by the general Maxwell's equations. For our multiphysics applications, we have therefore worked for some time to develop in the ADINA system a new modeling capability — the program ADINA-EM — to solve the general Maxwell's equations with different loading and boundary conditions. With the exciting new features provided by ADINA-EM, the ADINA users can now solve the general Maxwell’s equations for many different problems and also couple the electromagnetic effects with fluid flows. Fundamentally, the original first-order Maxwell’s equations governing electromagnetics for the electric field intensity and the magnetic field intensity are, see Ref. [1], with Also, the Maxwell’s equations in the frequency domain (for harmonic analysis) are where In these equations, the electromagnetic material is characterized by , that is, the electric permittivity, magnetic permeability, and electric conductivity, respectively. The source terms are the two densities and , and the electric charge density . Together with appropriate boundary conditions, Maxwell's equations uniquely determine and in the problem domain. In ADINA-EM, two distinctly different formulations, namely a novel formulation and an formulation are used, where in the formulation as usual we use For both formulations we utilize the finite element method. For efficiency and accuracy, instead of solving the first-order Maxwell's equations, given above, we have reformulated these equations to second-order relations, but without adding additional equations, see Ref. [2]. It is important to note that we offer in ADINA-EM the two distinct formulations, that is, the formulation and the formulation. The reason is that the formulation is familiar to engineers and scientists and can therefore directly be used — but has the well-known disadvantages. The formulation is novel, it uses the physical variables as unknowns, is more direct and these variables can directly be coupled to the actions of fluids and solids. We should note as well that we do not use edge-type elements (with degrees of freedom at the element edges) but we use a more powerful formulation where — also — the finite element degrees of freedom directly couple to the usual fluid and solid elements used. The details of the formulation are presented in Ref. [2]. ADINA-EM can solve:
Of course, the pre- and post-processing for the ADINA-EM models and solutions are performed using the ADINA User Interface.
Below we show the solutions of three example problems solved using ADINA-EM: · Sharp material interface in harmonic analysis · Electromagnetically induced mixing of glass melt in a pipe · Eddy current in a torus with cracks, induced by time-harmonic magnetic field
References 1. C. A. Balanis, Advanced Engineering Electromagnetics, John Wiley & Sons, New York, 1989. 2. K. J. Bathe et al., The Direct Solution of Maxwell’s Equations in Multiphysics, in preparation |