constrained problem

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Author Message   Archie Campbell (amc1) Member Username: amc1 Post Number: 4 Registered: 03-2008 Posted on Thursday, May 22, 2008 - 02:55 pm:    I am having a problem using ‘constraints’ in what appears to be quite a simple application. I want to find the field distribution in an air-cored magnet where the vector potential of the conducting material obeys the relation div(grad(A))=L*A. L is a material constant. It is essentially the eddy current equation for a harmonic current, but without the imaginary part so only real fields are involved. L is the effective conductivity. The conductors are long wires normal to the paper so that it should be a 2D problem. It is similar to the magnetic problem in Backstrom Books, with the difference that there the current density is defined. I thought I could do this by defining the integral of B round the wire as a constraint (‘twowiresI.pde’ attached). However although a solution is obtained, it is not realistic and there is a large discontinuity in the field at the surface, although this is not physical. I thought I had avoided over-specifying the problem by using only differential boundary conditions but perhaps not. A similar problem arises if I apply an external field to the wires instead of a current. In ‘twowiresB1.pde’ the constraints are removed and I get a sensible solution , but not the one I want. This solution is for the case where the wires are coupled electrically by the medium between them (or the ends) so that a circulating current is induced. Although the medium between the wires has zero resistance, it is of infinite extent, which probably explains why I get this solution. In the case I want the wires are isolated from each other and I tried to ensure this by a constraint of zero current in each (‘twowiresB2.pde’). Again I get a discontinuity at the surface (or at the integral surface if I put this outside the wire). If I plot the tangential component of B round the wire I get a symmetric result with zero integral as required. However this is inconsistent with the plot of By across the wire which gives a similar asymmetry to the previous solution. It may not be possible to do this in 2D but if there is a way I would be very pleased to learn it. two wires with current twowiresI.pde (1.8 k) two wires in field twowiresB1.pde (1.8 k) in field constrained twowiresB2.pde (1.8 k)