arXiv subjects

Sebastian Kinnewig

Publications and source records attributed to Sebastian Kinnewig.

3 recordsLinked to original sources

arXiv2024

Coupling deal.II and FROSch: A Sustainable and Accessible (O)RAS Preconditioner

In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and FROSch is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to FROSch. The FROSch-deal.II interface works for both Lagrange-based and N\'ed\'elec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell's equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the FROSch-deal.II interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.

math.NA↗

arXiv2023

Algorithmic realization of the solution to the sign conflict problem for hanging nodes on hp-hexahedral N\'ed\'elec elements

In this work, N\'ed\'elec elements on locally refined meshes with hanging nodes are considered. A crucial aspect is the orientation of the hanging edges and faces. For non-orientable meshes, no solution or implementation has been available to date. The problem statement and corresponding algorithms are described in great detail. As a model problem, the time-harmonic Maxwell's equations are adopted because N\'ed\'elec elements constitute their natural discretization. The algorithms and implementation are demonstrated through two numerical examples on different uniformly and adaptively refined meshes. The implementation is performed within the finite element library deal.II.

math.NA↗

arXiv2021

Parallel domain decomposition solvers for the time harmonic Maxwell equations

The time harmonic Maxwell equations are of current interest in computational science and applied mathematics with many applications in modern physics. In this work, we present parallel finite element solver for the time harmonic Maxwell equations and compare different preconditioners. We show numerically that standard preconditioners like incomplete LU and the additive Schwarz method lead to slow convergence for iterative solvers like generalized minimal residuals, especially for high wave numbers. Even more we show that also more specialized methods like the Schur complement method also yield slow convergence. As an example for a highly adapted solver for the time harmonic Maxwell equations we use a combination of a block preconditioner and a domain decomposition method (DDM), which also preforms well for high wave numbers. Additionally we discuss briefly further approaches to solve high frequency problems more efficiently. Our developments are done in the open-source finite element library deal.II.

math.NA↗