Measured Equation of Invariance : A New Concept in Field Computations

Numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations. The new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions. The postulated equations are local and invariant to excitation. It is shown how the equations can be determined by a sequence of “measures.” The measured equations are particularly useful at the mesh boundary, where the finite difference methods fail. The measured equations do not assume the physical condition of absorption, so they are also applicable to concave boundaries. Using the measured equations, we can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions. It will definitely make a great impact on the way we apply finite difference and finite element methods in many problems. Computational results using the measured equations of invariance in two and three dimensions are presented.