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Stability analysis of some non-conforming FETI Domain Decomposition Methods for electromagnetic problems

Georgios N. Paraschos, Marinos N. Vouvakis

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Abstract

This paper aims to study the stability of a proposed finite element tearing and interconnecting (FETI) formulation as well as some existing FETI and FETI-like ones. Only cement type non-conforming formulations are considered because they are amenable to FETI and lead to convergent formulations at the continuous level because they enforce Robin transmission conditions. From this stability study it will become clear that no existing cement FETI method is both efficient and stable, whereas cement FETI-like methods although stable are not as efficient as the FETI ones.

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What this paper is about

This paper aims to study the stability of a proposed finite element tearing and interconnecting (FETI) formulation as well as some existing FETI and FETI-like ones. Only cement type non-conforming formulations are considered because they are amenable to FETI and lead to convergent formulations at the continuous level because they enforce Robin transmission conditions. From this stability study it will become clear that no existing cement FETI method is both efficient and stable, whereas cement FETI-like methods although stable are not as efficient as the FETI ones.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper aims to study the stability of a proposed finite element tearing and interconnecting (FETI) formulation as well as some existing FETI and FETI-like ones. Only cement type non-conforming formulations are considered because they are amenable to FETI and lead to convergent formulations at the continuous level because they enforce Robin transmission conditions. From this stability study it will become clear that no existing cement FETI method is both efficient and stable, whereas cement FETI-like methods although stable are not as efficient as the FETI ones.

Key concepts: FETI, Domain decomposition methods, Tearing, Stability (learning theory), Finite element method, Mortar methods, Computer science, Materials science

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