FWF - Gebietsdekomositionsmethoden - Boundary and Finite Element Domain Decomposition Methods

Project: Research project

Description

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.
StatusFinished
Effective start/end date1/05/0730/04/12