Parameter preserving model order reduction for MEMS applications

References

• Lienemann , J. , Rudnyi , E.B. and Korvink , J.G. 2006 . MST MEMS model order reduction: requirements and benchmarks . Linear Algebra Appl. , 415 : 469 – 498 .
   Google Scholar
• Miller , R.W. 1996 . Flow Measurement Engineering Handbook , New York : McGraw-Hill .
   Google Scholar
• Moosmann , C. , Rudnyi , E.B. , Greiner , A. and Korvink , J.G. 2004 . “ Model order reduction for linear convective thermal flow ” . In THERMINIC 2004 , 317 – 321 . France : Sophia Antipolis .
   Google Scholar
• Lienemann , J. , Billger , D. , Rudnyi , E.B. , Greiner , A. and Korvink , J.G. MEMS compact modeling meets model order reduction: examples of the application of Arnoldi methods for microsystem devices . Proceedings of Nanotech . March 7–11 2004 , Boston, MA. Vol. 2 , pp. 303 – 306 . Austin, TX : Nano Science and Technology Institute .
   Google Scholar
• Baur , U. , Beattie , C.A. , Benner , P. and Gugercin , S. 2009 . Interpolatory projection methods for parameterized model reduction , Chemnitz : Fakultät fü Mathematik . Tech. Rep. CSC/09-08TU Chemnitz, 09107FRG
   Google Scholar
• Rozza , G. , Huynh , D.B.P. and Patera , A.T. 2008 . Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: application to transport and continuum mechanics . Arch. Comput. Methods Eng. , 15 ( 3 ) : 229 – 275 .
   Web of Science ®Google Scholar
• Zienkiewicz , O.C. 1997 . The Finite Element Method , New York : McGraw-Hill .
   Google Scholar
• Farle , O. , Hill , V. , Ingelström , P. and Dyczij-Edlinger , R. 2008 . Multi-parameter polynomial order reduction of linear finite element models . Math. Comput. Model. Dyn. Syst. , 14 ( 5 ) : 421 – 434 .
   Web of Science ®Google Scholar
• Feng , L. and Benner , P. 2008 . A robust algorithm for parametric model order reduction based on implicit moment matching . PAMM Proc. Appl. Math. Mech. , 7 : 1021501 – 1021502 .
   Google Scholar
• Daniel , L. , Ong , C.S. , Low , S.C. , Lee , K.H. and White , J. 2004 . A multiparameter moment-matching modelreduction approach for generating geometrically parameterized interconnect performance models . IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. , 23 ( 5 ) : 678 – 693 .
   Web of Science ®Google Scholar
• Gunupudi , P.K. , Khazaka , R. , Nakhla , M.S. , Smy , T. and Celo , D. 2003 . Passive parameterized time-domain macromodels for high-speed transmission-line networks . IEEE Trans. Microw. Theory Tech. , 51 : 2347 – 2354 .
   Google Scholar
• Moosmann , C. 2007 . ParaMOR – model order reduction for parameterized MEMS applications , Ph.D. thesis, University of Freiburg – IMTEK .
   Google Scholar
• Moosmann , C. , Rudnyi , E.B. , Greiner , A. , Korvink , J.G. and Hornung , M. Parameter Preserving Model Order Reduction of a Flow Meter . Proceedings of Nanotech . May 8–12 2005 , Austin, TX. Vol. 3 , pp. 684 – 687 . Anaheim, CA : Nano Science and Technology Institute .
   Google Scholar
• Pillage , L.T. and Rohrer , R.A. 1990 . Asymptotic waveform evaluation for timing analysis . IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst , 9 : 325 – 336 .
   Google Scholar
• Farle , O. , Hill , V. , Nickel , P. and Dyczij-Edlinger , R. 2005 . An Arnoldi-type algorithm for parametric finite element modelling of microwave components . Proc. Appl. Math. Mech , 5 ( 1 ) : 655 – 656 .
   Google Scholar
• Li , Y.T. , Bai , Z. and Su , Y. 2009 . A two-directional Arnoldi process and its application to parametric model order reduction . J. Comput. Appl. Math , 226 ( 1 ) : 10 – 21 .
   Google Scholar
• Feng , L. and Benner , P. 2010 . “ Model order reduction for systems with non-rational transfer function arising in computational electromagnetics ” . In Scientific Computing in Electrical Engineering SCEE 2008 , Edited by: Mathematics in Industry , Roos , J. and Costa , L.R.J. Vol. 14 , 515 – 522 . Berlin : Springer-Verlag .
   Google Scholar
• Bechtold , T. , Rudnyi , E.B. and Korvink , J.G. 2005 . Error indicators for fully automatic extraction of heattransfer macromodels for MEMS . J. Micromech. Microeng. , 15 ( 3 ) : 430 – 440 .
   Google Scholar
• Chiprout , E. and Nakhla , M.S. 1995 . Analysis of interconnect networks using complex frequency hopping (CFH) . IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. , 14 ( 2 ) : 186 – 200 .
   Google Scholar
• Baur , U. and Benner , P. 2009 . Modellreduktion für parametrisierte Systeme durch balanciertes Abschneiden und Interpolation (Model reduction for parametric systems using balanced truncation and interpolation) . at-Automatisierungstechnik , 57 ( 8 ) : 411 – 420 .
   Web of Science ®Google Scholar
• Berrut , J.-P. , Baltensperger , R. and Mittelmann , H.D. 2005 . “ Recent developments in barycentric rational interpolation ” . In Trends and Applications in Constructive Approximation , Vol. 151 , 27 – 51 . Basel : Birkhäuser . Int. Ser. Numer. Math.
   Google Scholar
• Klimke , A. 2007 . Sparse grid interpolation toolbox – user's guide , IANS rep. 2007/017, University of Stuttgart .
   Google Scholar
• Bungartz , H.-J. and Griebel , M. 2004 . Sparse grids . Acta Numer. , 13 : 147 – 269 .
   Google Scholar
• Griebel , M. 2006 . “ Sparse grids and related approximation schemes for higher dimensional problems ” . In Foundations of Computational Mathematics (FoCM05), Santander , Edited by: Pardo , L. , Pinkus , A. , Suli , E. and Todd , M.J. 106 – 161 . London : Cambridge University Press .
   Google Scholar
• Zenger , C. 1991 . “ Sparse grids ” . In Parallel Algorithms for Partial Differential Equations (Kiel, 1990) , Vol. 31 , 241 – 251 . Braunschweig : Vieweg . Notes Numer. Fluid Mech
   Google Scholar