Trefftz co-chain calculus
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Date
2022-06-03
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Journal Article
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Abstract
We are concerned with a special class of discretizations of general linear transmission problems stated in the calculus of differential forms and posed on Rn. In the spirit of domain decomposition, we partition Rn= Ω ∪ Γ ∪ Ω +, Ω a bounded Lipschitz polyhedron, Γ : = ∂Ω , and Ω + unbounded. In Ω , we employ a mesh-based discrete co-chain model for differential forms, which includes schemes like finite element exterior calculus and discrete exterior calculus. In Ω +, we rely on a meshless Trefftz–Galerkin approach, i.e., we use special solutions of the homogeneous PDE as trial and test functions. Our key contribution is a unified way to couple the different discretizations across Γ. Based on the theory of discrete Hodge operators, we derive the resulting linear system of equations. As a concrete application, we discuss an eddy-current problem in frequency domain, for which we also give numerical results.
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published
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Volume
73
Pages / Article No.
43
Publisher
Birkhäuser
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Subject
Co-chain calculus; finite element exterior calculus; Discrete exterior calculus; Trefftz method
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03632 - Hiptmair, Ralf / Hiptmair, Ralf
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Is new version of: http://hdl.handle.net/20.500.11850/364550