An Integral Formulation for an Array of Wires in a 3-D Magneto-Quasi-Static Field

There are many applications in which it is required to compute quasi-stationary magnetic fields and related quantities in possibly large regions containing many magnetic and/or conductive thin wires. When analyzing these problems by the finite-element method, one has to discretize the wires into fine elements in order to resolve the skin effect and the space separating the wires. Heavy computational burden is, therefore, needed to solve the resulting equations. To overcome such limitations, we propose a magnetic field integral formulation in the magneto-quasi-static regime that is suitable for computing the magnetic field in a 3-D domain in the presence of thin wires. To reduce the computational complexity, the wires are treated as 1-D manifolds embedded in the surrounding 3-D space. To validate the proposed methodology, we compare the cost and accuracy of our approach to full scale finite-element simulations of an array of wires in a 3-D external magneto-quasi-static field.