Signal Integrity Analysis of Integrated Circuits by Using Embedded Domain Decomposition Method

In integrated circuit designs, adjustments and replacements of components are frequently required for analyzing or improving signal integrity. However, the modifications of geometry will cause remeshings and resimulations in the full-wave analysis. Consequently, the design efficiency can be impaired due to repeated discretizations. In this paper, we introduce an embedded domain decomposition approach to address such repetitive simulations. A problem is first decomposed into a simpler background subdomain and multiple embedded subdomains. The geometrical details of interest can be placed into the embedded subdomains while the background subdomain covers the rest. Afterward, the communications between the subdomains are built by imposing coupling sources that represent field continuities, material polarizations, and surface currents on perfect electric conductor and port. The meshes between the subdomains are completely nonconformal, and the modification of an embedded subdomain will not affect the geometries and discretizations in the other subdomains. Such flexibility can be exploited in simulating complicated 3-D printed circuit board structures or investigating different components in an electronic system, as illustrated in the numerical examples.