FWF - Gebietsdekomositionsmethoden - Boundary and Finite Element Domain Decomposition Methods

Domain Decomposition (DD) methods are nowadays not only used for constructing parallel solvers for Partial Differential Equations (PDE), but also for coupling different physical fields and different discretization techniques. For example, Finite Element Methods (FEM) and Boundary Element Methods (BEM) exhibit certain complementary properties. Therefore, it is not astonishing that the coupling of FEM and BEM within a DD framework has successfully been used in many practical applications. Among the DD methods, the so-called Finite Element Tearing and Interconnecting (FETI) methods are probably the most successful ones, at least, for largescale parallel computations. Recently, the applicants have introduced data-sparse Boundary Element Tearing and Interconnecting (BETI) methods as boundary element counterparts of the well-established FETI methods as well as coupled BETI-FETI methods for some model problems such as the potential equation and the linear elasticity system. In this project, we propose to construct and analyze new DD solvers for large-scale FEM, BEM and coupled FEMBEM DD equations derived from linear and non-linear magnetostatic problems as well as from linear and nonlinear eddy current problems in the time and in the frequency domain. The numerical treatment of non-linear eddy current problems in the frequency domain is not straightforward. The multiharmonic approach that is based on Fourier series is one possible technique to treat such problems. The construction of fast solvers, in particular, efficient DD solvers for the resulting large-scale system of non-linear equations is challenging. The new algorithms to be developed in this project will essentially contribute to a new software generation in Computational Electromagnetics.