An ultraweak variational method for parameterized linear differential-algebraic equations

We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations (DAEs) w.r.t. the time variable which yields an optimally stable system. This is used within a Petrov-Galerkin method to derive a certified detailed discretization which provides an approx...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Beurer, Emil, Feuerle, Moritz, Reich, Niklas, Urban, Karsten
Format: Article
Language:English
Subjects:
Algebra
Differential equations
Galerkin method
Mathematical analysis
Model reduction
Parameterization
Systems theory
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Summary:We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations (DAEs) w.r.t. the time variable which yields an optimally stable system. This is used within a Petrov-Galerkin method to derive a certified detailed discretization which provides an approximate solution in an ultraweak setting as well as for model reduction w.r.t. time in the spirit of the Reduced Basis Method (RBM). A computable sharp error bound is derived. Numerical experiments are presented that show that this method yields a significant reduction and can be combined with well-known system theoretic methods such as Balanced Truncation to reduce the size of the DAE.
ISSN:2331-8422