Domain Decomposition Solvers for Electro-Magnetic and Multi-Physics Problems
In this talk, we will discuss the development of robust and efficient
solvers for the Time-Harmonic Maxwell’s (THM) equations and
Fluid-Structure interaction (FSI) problems. A particular focus is on
algorithmic concepts and sustainable software development to ensure ease
of use. To achieve this, a deal.II-FROSch interface was developed, which
is based on the newly developed Tpetra-based interface to Trilinos, that
was added to deal.II. This combines the ease-of-use from deal.II with
the power of algebraic preconditioners available through FROSch.
First, the long-standing sign conflict problem in the presence of
hanging nodes for Nédélec elements is addressed, and the solution is
presented along with pseudo-code examples and an actual implementation
in deal.II. The support for hanging nodes enables adaptive grid
refinement, which allows the solution of even larger problems.
Second, to test the deal.II-FROSch interface, the FSI problem is
considered on a series of benchmark problems. For the description of the
FSI problem, we consider a monolithic formulation, and to solve the
linear equation system that arises from the finite element
discretization, after linearization and time discretization, a GMRES
solver along with a two-level restricted additive Schwarz preconditioner
is employed.
Third, for solving THM equations, the deal.II-FROSch interface is
extended by the implementation of an optimized restricted additive
Schwarz (ORAS) preconditioner. A benchmark problem for the THM equations
is proposed to validate the ORAS preconditioner, where the numerical
methods are validated against analytical solutions obtained from Mie’s
scattering theory.
