Computations of electromagnetic fields are based either on differential equations or on integral equations. The differential equation approach using finite difference or finite element methods results in sparse matrices, which is an advantage, but has 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. It is noted that 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 is a new concept in field computation capable of approaching this ideal situation. The mathematics and reasonings to reach a novel computational method based on this concept are presented. It is shown that the method is robust for both convex and concave objects, is much faster than the MOM, and uses a fraction of the memory.

Peer Reviewed