# Hierarchical Electromagnetics

### Fast electromagnetic designs and accurate full wave modelizations

## The Hierarchical Elctromagnetic Modeler

The * Hierarchical Electromagnetic Modeler * exploits a new numerical method which
allows the generation of an equivalent circuit that represents the electrical response of a
generic electromagnetic problem (microwave, optical ..).

The circuit is generated in a direct path without going trough an electromagnetic simulation and a subsequent circuit
extraction process as it happens with the macro-modeling techniques based on the zero-pole
fitting of response curves.

The new method is more robust than the zero-pole fitting which
does not scale well when the number of ports becomes large. The new method can in fact
handle very large electromagnetic structures excited by a large number of input ports.

The generated circuit may be exported in the standard Spice format assuring the interoperability
with most circuit simulators. It preserves the fundamental properties (such as
passivity, causality, reciprocity..) of the actual device so that it can be exploited for reliable
and stable time domain simulations.

The * Hierarchical Electromagnetic Modeler * is designed to achieve the maximum
efficiency when executed in a distributed environment and to exploit the full power offered
by the modern cloud computing architectures. In this way it is able to tackle the complex
electromagnetic problems which arise in the design flow of modern microwave/electronic
industry and to overcome the constraints imposed by limited local resources.

Because of the steady increase of system performance, operating frequencies and miniaturization,
the need of accurate modeling of electromagnetic interactions occurring inside the electronic
circuits is becoming always more important. With higher frequencies and smaller spaces
the electromagnetic interactions are intensified causing a degradation of the quality of electrical
signals (noise effects, crosstalk..).

These adverse effects need to be properly simulated at system level in order to appreciate their
global effect on the system performances. The * Hierarchical Electromagnetic Modeler *
responds to these needs trough the generation of circuit models that capture
all the relevant electromagnetic effects and are well suited to be exploited in any kind of
simulation in the time or in the frequency domain..

The generated model can be included in a complex system (which may include non linear devices)
providing a better interoperability than the simulated responses generated by traditional Electromagnetic Solvers.
These responses are indeed typically given in the frequency domain and their utilization in the time
domain requires the application of heavy numerical algorithms (domain transforms and convolutions).

The most distinguishing property which puts the * Hierarchical Electromagnetic Modeler * aside of
competition is nevertheless given by the adoption of a very efficient domain decomposition strategy.
This technique allows to overcome the fundamental drawback of all other current
general purpose full-wave simulators which, by going against the hierarchical (top-down) design methodologies that
the electronics industry is accustomed to, treat the electromagnetic device as an unstructured black box.

The * Hierarchical Electromagnetic Modeler * decomposes the device in its constituent parts (sub-domains)
which are subjected to independent modelizations. As a result there is a one to one relationship between the
hierarchical structure of the electromagnetic problem and the hierarchical structure of the circuital model.
This property allows a dramatic improvement in the computational speed of the repetitive tasks which are
typically required in the design/optimization phase. In fact a local change in the geometrical or physical parameters of a given subcomponent affects only
the related subcircuit and there is no need to recompute the circuital models of the other (unchanged) parts.