Error tracking in boundary element formulations

Error bounding has been a subject of keen interest for field theoreticians over the last decade. This paper details the technique for not only specifying and indexing field uncertainty at any given point, but force and torque errors as well. The technique allows one to specify the force or torque on an object to a given value plus or minus another value. With single-layer or boundary formulations, continuity of the normal B field is implicitly insured; the discontinuity in tangential H is shown to imply an error in surface current which can be linked directly to the calculation of the uncertainty of forces and torques. With nonlinear problems additional errors result from internal magnetization current which is used to handle internal saturation. The theoretical formulations predicting errors with three cases are presented: static-linear, static- and nonlinear, and time harmonic. Any error predictions in the field and global quantities such as force, torque, or inductance result from equivalent surface and volume currents.