Shape Synthesis Based on Topology Sensitivity

A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique, provide important advantages, one of them being impedance matrix inversion free evaluation of the sensitivity. The devised procedure utilizes port modes and their superposition which, together with only a single evaluation of all matrix operators, leads to a computationally effective procedure. The proposed method is approximately 100 times faster than the contemporary approaches, which allows the investigation of the sensitivity and the modification of shapes in real time. The method is compared with the known approaches and its validity and effectiveness are verified using a series of examples. The procedure can be implemented in up-to-date electromagnetic (EM) simulators in a straightforward manner. It is shown that the iterative repetition of the topology sensitivity evaluation can be used for gradient-based topology synthesis. This technique can also be employed as a local step in global optimizers.