Prof. Dr. Melina Freitag

Professorin

Kontakt
Raum:
2.09.2.09
Telefon:
+49 331 977-203121
...
  • Numerical linear algebra, in particular iterative methods for eigenvalue problems and linear systems, Krylov subspace methods.
  • Model order reduction, matrix theory and applications.
  • Data assimilation and inverse problems.

Publications

2022 | Conditioning analysis for discrete Helmholtz problems | A. Kaya, M.A. FreitgZeitschrift: Computers & Mathematics with ApplicationsVerlag: ElsevierSeiten: 171‒182Band: 118Link zur Publikation

Conditioning analysis for discrete Helmholtz problems

Autoren: A. Kaya, M.A. Freitg (2022)

In this paper, we examine conditioning of the discretization of the Helmholtz problem. Although the discrete Helmholtz problem has been studied from different perspectives, to the best of our knowledge, there is no conditioning analysis for it. We aim to fill this gap in the literature. We propose a novel method in 1D to observe the near-zero eigenvalues of a symmetric indefinite matrix. Standard classification of ill-conditioning based on the matrix condition number is not true for the discrete Helmholtz problem. We relate the ill-conditioning of the discretization of the Helmholtz problem with the condition number of the matrix. We carry out analytical conditioning analysis in 1D and extend our observations to 2D with numerical observations. We examine several discretizations. We find different regions in which the condition number of the problem shows different characteristics. We also explain the general behavior of the solutions in these regions.

Zeitschrift:
Computers & Mathematics with Applications
Verlag:
Elsevier
Seiten:
171‒182
Band:
118

2021 | POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations | S. Hijazi, M.A. Freitag, N. LandwehrZeitschrift: arXivBand: 2112.11950Link zum Preprint

POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations

Autoren: S. Hijazi, M.A. Freitag, N. Landwehr (2021)

We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by two cases which are the steady flow around a backward step and the unsteady turbulent flow around a surface mounted cubic obstacle.

Zeitschrift:
arXiv
Band:
2112.11950

2021 | Autonomous Exploration and Identification of High Performing Adsorbents using Active Learning | G. Donval, C. Hand, J. Hook, E. Dupont, M. S. Landman, M.A. Freitag, M. Lennox, T. DürenVerlag: submittedLink zum Preprint

Autonomous Exploration and Identification of High Performing Adsorbents using Active Learning

Autoren: G. Donval, C. Hand, J. Hook, E. Dupont, M. S. Landman, M.A. Freitag, M. Lennox, T. Düren (2021)

MOFs and COFs are porous materials with a large variety of applications including gas storage and separation. Synthesised in a modular fashion from distinct building blocks, a near infinite number of structures can be constructed and the properties of the material can be tailored for a specific application. While this modularity is a very attractive feature it also poses a challenge. Attempting to identify the best performing material(s) for a given application is experimentally intractable. Current research efforts combine molecular simulations and machine learning techniques to evaluate the simulated performance of hundreds of thousands of materials to identify top performing MOFs and COFs for a given application. These approaches typically rely on moderated brute-force screening which is still resource-intensive as typically between 70‒100 % of the hundreds of thousands of materials must be simulated to create a training set for the machine learning models used, restricting screening to relatively simple molecules. In this work we demonstrate our novel Bayesian mining approach to materials screening which allows 62‒92 % of the top 100 porous materials for a range of applications to be readily identified from large materials databases after only assessing less than one percent of all materials. This is a stark contrast to the 0‒1 % achieved by conventional brute-force screening where porous materials are just chosen at random during a high throughput screening. Through this accelerated virtual screening process, the identification of high performing materials can be used to more rapidly inform experimental efforts and hence lead to an acceleration of the entire research and development pipeline of porous materials.

Verlag:
submitted

2021 | Optimization based model order reduction for stochastic systems | M. Redmann, M.A. FreitagZeitschrift: Appl. Math. Comput., 398Link zur Publikation

Optimization based model order reduction for stochastic systems

Autoren: M. Redmann, M.A. Freitag (2021)

Zeitschrift:
Appl. Math. Comput., 398

2020 | Inexact methods for the low-rank solution to large-scale Lyapunov equations | P. Kürschner, M.A. FreitagZeitschrift: BIT, 60:1221-1259Link zur Publikation , Link zum Preprint

Inexact methods for the low-rank solution to large-scale Lyapunov equations

Autoren: P. Kürschner, M.A. Freitag (2020)

Zeitschrift:
BIT, 60:1221-1259

2020 | Numerical linear algebra in data assimilation | M.A. FreitagZeitschrift: GAMM MitteilungenLink zur Publikation

Numerical linear algebra in data assimilation

Autoren: M.A. Freitag (2020)

Zeitschrift:
GAMM Mitteilungen

2019 | Teaching of Computing to Mathematics Students: Programming and Discrete Mathematics | J. Betteridge, J.H. Davenport, M.A. Freitag, W. Heijtljes, S. Kynaston, G. Sankaran, G. TraustasonZeitschrift: Proceedings of the 3rd Conference on Computing Education Practice, 12, 1-4Link zur Publikation

Teaching of Computing to Mathematics Students: Programming and Discrete Mathematics

Autoren: J. Betteridge, J.H. Davenport, M.A. Freitag, W. Heijtljes, S. Kynaston, G. Sankaran, G. Traustason (2019)

Zeitschrift:
Proceedings of the 3rd Conference on Computing Education Practice, 12, 1-4

2019 | Projection methods for weak constraint variational data assimilation | M.A. Freitag, D.L.H. Green

Projection methods for weak constraint variational data assimilation

Autoren: M.A. Freitag, D.L.H. Green (2019)

2018 | GMRES convergence bounds for eigenvalue problems | M.A. Freitag, P. Kürschner, J. PestanaZeitschrift: Comput. Methods Appl. Math.Seiten: 203-222Band: 18(2)Link zur Publikation

GMRES convergence bounds for eigenvalue problems

Autoren: M.A. Freitag, P. Kürschner, J. Pestana (2018)

Zeitschrift:
Comput. Methods Appl. Math.
Seiten:
203-222
Band:
18(2)

2018 | Model reduction and approximation: theory and algorithms | M. A. FreitagZeitschrift: SIAM Rev.Seiten: 763–767Band: 60(3) (review of book)

Model reduction and approximation: theory and algorithms

Autoren: M. A. Freitag (2018)

Zeitschrift:
SIAM Rev.
Seiten:
763–767
Band:
60(3)
(review of book)

2018 | Balanced model order reduction for linear random dynamical systems driven by Lévy noise | M. Redmann, M.A. FreitagZeitschrift: To appear in J. Comput. Dyn.Link zum Preprint

Balanced model order reduction for linear random dynamical systems driven by Lévy noise

Autoren: M. Redmann, M.A. Freitag (2018)

Zeitschrift:
To appear in J. Comput. Dyn.

2018 | A low-rank approach to the solution of weak constraint variational data assimilation problems | M.A. Freitag, D.L.H. GreenZeitschrift: J. Comput. Phys.Seiten: 263-281Band: 357Link zur Publikation

A low-rank approach to the solution of weak constraint variational data assimilation problems

Autoren: M.A. Freitag, D.L.H. Green (2018)

Zeitschrift:
J. Comput. Phys.
Seiten:
263-281
Band:
357

2015 | Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration | M.A. Freitag, P. KürschnerZeitschrift: Numer. Linear Algebra Appl.Seiten: 175–196Band: 22(1)Link zur Publikation

Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration

Autoren: M.A. Freitag, P. Kürschner (2015)

Zeitschrift:
Numer. Linear Algebra Appl.
Seiten:
175–196
Band:
22(1)

2015 | The effect of numerical model error on data assimilation | S.E. Jenkins, C.J. Budd, M.A. Freitag, N.D. SmithZeitschrift: J. Comput. Appl. Math.Seiten: 567 – 588Band: 290Link zur Publikation

The effect of numerical model error on data assimilation

Autoren: S.E. Jenkins, C.J. Budd, M.A. Freitag, N.D. Smith (2015)

Zeitschrift:
J. Comput. Appl. Math.
Seiten:
567 – 588
Band:
290

2014 | A new approach for calculating the real stability radius | M.A. Freitag, A. SpenceZeitschrift: BITVerlag: SpringerSeiten: 381-400Band: 54(2)Link zur Publikation

A new approach for calculating the real stability radius

Autoren: M.A. Freitag, A. Spence (2014)

Zeitschrift:
BIT
Verlag:
Springer
Seiten:
381-400
Band:
54(2)

2014 | Calculating the $H_\infty$-norm using the implicit determinant method | M.A. Freitag, A Spence, P. Van DoorenZeitschrift: SIAM J. Matrix Anal. Appl.Seiten: 619-635Band: 35(2)Link zur Publikation

Calculating the $H_\infty$-norm using the implicit determinant method

Autoren: M.A. Freitag, A Spence, P. Van Dooren (2014)

Zeitschrift:
SIAM J. Matrix Anal. Appl.
Seiten:
619-635
Band:
35(2)

2014 | The computation of Jordan blocks in parameter-dependent matrices | R.O. Akinola, M.A. Freitag, A. SpenceZeitschrift: IMA J. Numer. Anal.Verlag: Oxford University PressSeiten: 955-976Band: 34(3)Link zur Publikation

The computation of Jordan blocks in parameter-dependent matrices

Autoren: R.O. Akinola, M.A. Freitag, A. Spence (2014)

Zeitschrift:
IMA J. Numer. Anal.
Verlag:
Oxford University Press
Seiten:
955-976
Band:
34(3)

2014 | The calculation of the distance to a nearby defective matrix | R.O. Akinola, M.A. Freitag, A. SpenceZeitschrift: Numer. Linear Algebra Appl.Seiten: 403-414Band: 21(3)Link zur Publikation

The calculation of the distance to a nearby defective matrix

Autoren: R.O. Akinola, M.A. Freitag, A. Spence (2014)

Zeitschrift:
Numer. Linear Algebra Appl.
Seiten:
403-414
Band:
21(3)

2013 | Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences | M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors)Reihe: Radon Series on Computational and Applied Mathematics, Vol. 13Verlag: De Gruyter, BerlinLink zur Publikation

Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences

Autoren: M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors) (2013)

Reihe:
Radon Series on Computational and Applied Mathematics, Vol. 13
Verlag:
De Gruyter, Berlin

2013 | Synergy of inverse problems and data assimilation techniques. Large Scale Inverse Problems | M.A. Freitag, R.W.E PotthastZeitschrift: Radon Ser. Comput. Appl. Math.Verlag: De GruyterBand: 13 (Preprint)

Synergy of inverse problems and data assimilation techniques. Large Scale Inverse Problems

Autoren: M.A. Freitag, R.W.E Potthast (2013)

Zeitschrift:
Radon Ser. Comput. Appl. Math.
Verlag:
De Gruyter
Band:
13

2013 | The Origin of Power-Law Emergent Scaling in Large Binary Networks | D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. SmithZeitschrift: Phys. ASeiten: 1004-1027Band: 392(4)Link zur Publikation , Link zum Preprint

The Origin of Power-Law Emergent Scaling in Large Binary Networks

Autoren: D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. Smith (2013)

Zeitschrift:
Phys. A
Seiten:
1004-1027
Band:
392(4)

2013 | Resolution of sharp fronts in the presence of model error in variational data assimilation | M.A. Freitag, N.K. Nichols, C.J. BuddZeitschrift: Q. J. R. Meteorol. Soc.Seiten: 742-757Band: 139Link zur Publikation

Resolution of sharp fronts in the presence of model error in variational data assimilation

Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd (2013)

Zeitschrift:
Q. J. R. Meteorol. Soc.
Seiten:
742-757
Band:
139

2011 | A Newton-based method for the calculation of the distance to instability | M.A. Freitag, A. SpenceZeitschrift: Linear Alg. Appl.Seiten: 3189-3205Band: 435(12)Link zur Publikation

A Newton-based method for the calculation of the distance to instability

Autoren: M.A. Freitag, A. Spence (2011)

Zeitschrift:
Linear Alg. Appl.
Seiten:
3189-3205
Band:
435(12)

2011 | Regularization techniques for ill-posed inverse problems in data assimilation | M.A. Freitag, N.K. Nichols, C.J. BuddZeitschrift: Comput. & FluidsSeiten: 168-173Band: 46(1)Link zur Publikation

Regularization techniques for ill-posed inverse problems in data assimilation

Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd (2011)

Zeitschrift:
Comput. & Fluids
Seiten:
168-173
Band:
46(1)

2010 | L1-regularisation for ill-posed problems in variational data assimilation | M.A. Freitag, N.K. Nichols, C.J. BuddZeitschrift: PAMMSeiten: 665-668Band: 10(1)Link zur Publikation

L1-regularisation for ill-posed problems in variational data assimilation

Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd (2010)

Zeitschrift:
PAMM
Seiten:
665-668
Band:
10(1)

2009 | Shift-invert Arnoldi's method with preconditioned iterative solves | M.A. Freitag, A. SpenceZeitschrift: SIAM J. Matrix Anal. Appl.Seiten: 942-969Band: 31(3)Link zur Publikation

Shift-invert Arnoldi's method with preconditioned iterative solves

Autoren: M.A. Freitag, A. Spence (2009)

Zeitschrift:
SIAM J. Matrix Anal. Appl.
Seiten:
942-969
Band:
31(3)

2009 | The calculation of the distance to instability by the computation of a Jordan block | M. Freitag (joint work with A. Spence) Oberwolfach Report No. 37/2009. (Report)

The calculation of the distance to instability by the computation of a Jordan block

Autoren: M. Freitag (joint work with A. Spence) (2009)

Oberwolfach Report No. 37/2009. (Report)

2008 | Rayleigh quotient iteration and simplified Jacobi-Davidson with preconditioned iterative solves for generalised eigenvalue problems | M.A. Freitag, A. Spence, E. Vainikko (Gzipped PostScript), (PDF)

Rayleigh quotient iteration and simplified Jacobi-Davidson with preconditioned iterative solves for generalised eigenvalue problems

Autoren: M.A. Freitag, A. Spence, E. Vainikko (2008)

2008 | The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems | Melina Freitag 168 pages, VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG (2008). (Available online here)

The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems

Autoren: Melina Freitag (2008)

168 pages, VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG (2008). (Available online here)

2008 | Rayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves | M.A. Freitag, A. SpenceZeitschrift: Linear Alg. Appl.Verlag: ElsevierSeiten: 2049-2060Band: 428(8-9)Link zur Publikation

Rayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves

Autoren: M.A. Freitag, A. Spence (2008)

Zeitschrift:
Linear Alg. Appl.
Verlag:
Elsevier
Seiten:
2049-2060
Band:
428(8-9)

2008 | A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems | M.A. Freitag, A. SpenceZeitschrift: IMA J. Numer. Anal.Verlag: Oxford University PressSeiten: 522-551Band: 28(3)Link zur Publikation

A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems

Autoren: M.A. Freitag, A. Spence (2008)

Zeitschrift:
IMA J. Numer. Anal.
Verlag:
Oxford University Press
Seiten:
522-551
Band:
28(3)

2007 | Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem | M.A. Freitag, A. SpenceZeitschrift: Electron. Trans. Numer. Anal.Seiten: 40-64Band: 28Link zum Preprint

Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem

Autoren: M.A. Freitag, A. Spence (2007)

Zeitschrift:
Electron. Trans. Numer. Anal.
Seiten:
40-64
Band:
28

2007 | Inner-outer Iterative Methods for Eigenvalue Problems - Convergence and Preconditioning | M. A. Freitag PhD Thesis, Department of Mathematical Sciences, University of Bath (2007). (Gzipped PostScript), (PDF)

Inner-outer Iterative Methods for Eigenvalue Problems - Convergence and Preconditioning

Autoren: M. A. Freitag (2007)

PhD Thesis, Department of Mathematical Sciences, University of Bath (2007). (Gzipped PostScript), (PDF)

2007 | The Preissmann box scheme and its modification for transcritical flows | M.A. Freitag, K. W. MortonZeitschrift: Internat. J. Numer. Methods Engrg.Verlag: WileySeiten: 791-811Band: 70(7)Link zur Publikation

The Preissmann box scheme and its modification for transcritical flows

Autoren: M.A. Freitag, K. W. Morton (2007)

Zeitschrift:
Internat. J. Numer. Methods Engrg.
Verlag:
Wiley
Seiten:
791-811
Band:
70(7)

2007 | Convergence rates for inexact inverse iteration with application to preconditioned iterative solves | M.A. Freitag, A. SpenceZeitschrift: BITVerlag: SpringerSeiten: 27-44Band: 47(1)Link zur Publikation

Convergence rates for inexact inverse iteration with application to preconditioned iterative solves

Autoren: M.A. Freitag, A. Spence (2007)

Zeitschrift:
BIT
Verlag:
Springer
Seiten:
27-44
Band:
47(1)

2005 | Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems | M. Freitag, B. HofmannZeitschrift: J. Inverse Ill-Posed Probl.Seiten: 123-148Band: 13(2)Link zur Publikation

Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems

Autoren: M. Freitag, B. Hofmann (2005)

Zeitschrift:
J. Inverse Ill-Posed Probl.
Seiten:
123-148
Band:
13(2)

2004 | On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems | M. Freitag Diplomarbeit, Fakultät für Mathematik, Technische Universität Chemnitz (2004). (Available online here)

On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems

Autoren: M. Freitag (2004)

Diplomarbeit, Fakultät für Mathematik, Technische Universität Chemnitz (2004). (Available online here)

2003 | Transcritical flow modelling with the Box Scheme | M. Freitag MSc Thesis, Department of Mathematical Sciences, University of Bath (2003). (GZipped PostScript), (PDF)

Transcritical flow modelling with the Box Scheme

Autoren: M. Freitag (2003)

MSc Thesis, Department of Mathematical Sciences, University of Bath (2003). (GZipped PostScript), (PDF)