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Computations of electromagnetic fields are based either on differential equations or on integral equations. The differential equation approach using finite difference (FD) or finite element (FE) methods result in sparse matrices, which is an advantage, but have to cover large volumes, which is a disadvantage. The integral equation approach using the method of moments (MOM) limits the mesh to the surface of the object, which is an advantage, but results in full matrices, which is a disadvantage. The ideal case would be to reduce the finite difference type equations close to the object surface and still preserve the sparsity of the matrices. The measured equation of invariance (MEI) is a new concept in field computation capable of approaching this ideal situation. The mathematics and reasonings to reach a new computational method based on this new concept will be presented. It is shown that the method is robust for both convex and concave objects, much faster than the MOM, and uses a fraction of the memory.The radiation conditions, or absorbing boundary conditions, are physical conditions imposed on the outer mesh boundaries of finite difference or finite element meshes in lieu of the differential equations in order to terminate the mesh [l], [2]. Since memory and computation time both grow very fast with the mesh volume, there have been efforts to bring the absorbing boundary close to the object boundary [3], [4]. But, those close-tothe-object-surface absorbing boundary conditions give mixed results, and in general are not robust.

Absfraci-The feasibility of direct numerical calculations of anrenna integral equations is investigated. It is shown that integral equation of Hallen's type is the most adequate for such applications.The extension of Hallen's integral equation to describe thin wire antennas of arbitrary geometry is accomplished, and results are presented for dipole, circular loops, and equiangular spiral antennas.

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