Method and apparatus for simulating physical fields

Abstract

In order to design on-chip interconnect structures in a flexible way, a CAD approach is advocated in three dimensions, describing high frequency effects such as current redistribution due to the skin-effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by a scalar electric potential and a magnetic vector potential. These potentials are not uniquely defined, and in order to obtain a consistent discretization scheme, a gauge-transformation field is introduced. The displacement current is taken into account to describe current redistribution and a small-signal analysis solution scheme is proposed based upon existing techniques for static fields in semiconductors. In addition methods and apparatus for refining the mesh used for numerical analysis is described.

1 . A method of numerical analysis of a simulation of a physical system, the physical system being describable by field equations in which a parameter is identifiable as a one-form and solving for a field equation corresponding to the parameter results in a singular differential operation, the method comprising: 
 directly solving the field equations modified by addition of a dummy field by numerical analysis, and    outputting at least one parameter relating to a physical property of the system.