Emerging technologies present existing modelling methods with unmet requirements. The complexity of electronic components, circuits and systems is ever increasing. In addition, novel manufacturing techniques such as 3D integrated circuits and 3D packaging are required to deliver high data rate, low latency designs with minimal power consumption. Multi-scale and multi-physics sources for THz radiation require the integrated design and full-wave modelling of these system.

In the last decades, important advances in simulation techniques have been introduced. Multi-trace methods are powerful domain-decomposition techniques that allow for simulation speed-up by preconditioning. Multi-screen methods achieve similar results when metallic junctions are present.

I will respond to these urgent modelling requirements by designing a unified method for the modelling of electronic devices across the frequency band. The method will be based on the boundary integral equation for the electromagnetic vector potential. By leveraging state-of-the-art multi-trace and multi-screen methods this will enable the modelling of systems that contain multiple domains, occupied by uniform or non-uniform materials arranged in entirely general geometric configurations. I will develop powerful preconditioning strategies that reduce modelling times by a factor of ten and more. I will design time domain integral equation methods that are suited to model non-linear, multi-physics systems.