Abstract: A computer aided design can be decomposed into multiple domains or regions in a domain decomposition method, and then one or more finite element method boundary conditions at an interface between the domains can be imprinted on the faces of the domains at the interface, and then mesh generation can be performed independently on the domains. Thus, nonconformal domain decomposition can use the imprinting of the boundary conditions to improve the results of the independent mesh generation.

Abstract: A computer aided design can be decomposed into multiple domains or regions in a domain decomposition method, and then one or more finite element method boundary conditions at an interface between the domains can be imprinted on the faces of the domains at the interface, and then mesh generation can be performed independently on the domains. Thus, nonconformal domain decomposition can use the imprinting of the boundary conditions to improve the results of the independent mesh generation.

Abstract: Systems and methods are provided for analyzing an electromagnetic field in an original domain. An original domain is decomposed into one or more finite-element-boundary-integral (FEBI) regions and one or more integral-equation (IE) regions. A model is determined for an electromagnetic field in the one or more FEBI regions and the one or more IE regions. An initial block system matrix for the original domain is generated based at least in part on the model. The initial block system matrix includes a first diagonal block corresponding to the one or more FEBI regions and a second diagonal block corresponding to the one or more IE regions. A replacement matrix is generated based at least in part on a physical optics (PO) method. A final block system matrix is generated by replacing the second diagonal block in the initial block system matrix with the replacement matrix.

Abstract: In a system for simulations of fields related to physical objects by iteratively solving a system matrix equation, the system matrix is preconditioned using a modified Gauss-Seidel preconditioner so as to eliminate or reduce a sequential nature of the iterations, thus facilitating parallel solution of the conditioned system matrix.

Abstract: Physical systems modeled by matrix equations may simultaneously be simulated for multiple excitations using, for example, an adaptive Krylov iterative recycling method.

Abstract: Disclosed are domain-decomposition approaches to simulations of electromagnetic fields may that, in various embodiments, use second-order Robin transmission conditions at subdomain boundaries.