An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations
We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations with respect to 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 appr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-07-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2022.910786/full |
| _version_ | 1811224412596207616 |
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| author | Emil Beurer Moritz Feuerle Niklas Reich Karsten Urban |
| author_facet | Emil Beurer Moritz Feuerle Niklas Reich Karsten Urban |
| author_sort | Emil Beurer |
| collection | DOAJ |
| description | We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations with respect to 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 with respect to time in the spirit of the Reduced Basis Method. 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. |
| first_indexed | 2024-04-12T08:48:57Z |
| format | Article |
| id | doaj.art-f572e7dc9bba44e4ae970a90f65efe41 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-12T08:48:57Z |
| publishDate | 2022-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-f572e7dc9bba44e4ae970a90f65efe412022-12-22T03:39:38ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872022-07-01810.3389/fams.2022.910786910786An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic EquationsEmil BeurerMoritz FeuerleNiklas ReichKarsten UrbanWe investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations with respect to 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 with respect to time in the spirit of the Reduced Basis Method. 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.https://www.frontiersin.org/articles/10.3389/fams.2022.910786/fulldifferential-algebraic equationsparametric equationsultraweak formulationsPetrov-Galerkin methodsmodel reduction |
| spellingShingle | Emil Beurer Moritz Feuerle Niklas Reich Karsten Urban An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations Frontiers in Applied Mathematics and Statistics differential-algebraic equations parametric equations ultraweak formulations Petrov-Galerkin methods model reduction |
| title | An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations |
| title_full | An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations |
| title_fullStr | An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations |
| title_full_unstemmed | An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations |
| title_short | An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations |
| title_sort | ultraweak variational method for parameterized linear differential algebraic equations |
| topic | differential-algebraic equations parametric equations ultraweak formulations Petrov-Galerkin methods model reduction |
| url | https://www.frontiersin.org/articles/10.3389/fams.2022.910786/full |
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