Electrical–Thermal Cosimulation With Nonconformal Domain Decomposition Method for Multiscale 3-D Integrated Systems

Abstract

Because of the multiple scales in 3-D integrated systems, numerical simulation methods that are able to handle multiscale problems efficiently are strongly required. In this paper, electrical-thermal cosimulation of multiscale integrated systems using Mortar finite element-based domain decomposition method is proposed. Using the nonconformal domain decomposition approach, integrated systems can be divided into separate subdomains. Individual subdomains can be discretized independently based on its detailed feature size and formulated using the finite element method with associated boundary conditions. The coupling between domains is captured using Lagrange multipliers. For large multiscale 3-D problems, the cascadic multigrid method combined with the subspace confined preconditioned conjugate gradient method is used to accelerate the convergence of the solution with hierarchical meshing grids. Several examples are simulated and the results validate the accuracy and efficiency of the electrical-thermal cosimulation using nonconformal domain decomposition.