The Use of Model Order Reduction in Design Optimization Algorithms (Het gebruik van modelreductie in algoritmen voor ontwerpoptimalisatie)

Abstract iii Abbreviations vii List of Symbols ix Contents xiii List of Figures xvii List of Tables xix 1 Introduction 1 1.1 Design optimization . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Examples of design optimization . . . . . . . . . . . . . . . . . 3 1.3 Using model order reduction to speed up design optimization . . 11 1.4 Using interpolatory model order reduction for further speedups 13 1.5 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . 15 2 Background on numerical optimization 17 2.1 A brief introduction to line search methods and trust region methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 An optimization algorithm for design optimization . . . . . . . 23 3 Background on Krylov-Padé type model order reduction 29 3.1 Krylov subspace . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 Krylov-Padé type MOR with one parameter . . . . . . . . . . . 33 3.3 Krylov-Padé type MOR with multiple parameters . . . . . . . . 40 3.4 Two-sided PIMTAP . . . . . . . . . . . . . . . . . . . . . . . . 43 4 Combining (P)MOR with optimization 47 4.1 Derivative computations via Krylov-Padé Type MOR/PMOR . 48 4.2 Two frameworks to use MOR/PMOR in accelerating optimization 58 4.3 Improvement of the PMOR Framework for smooth objective functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5 Using surrogate models with error estimators in optimization 73 5.1 The relaxed first order condition . . . . . . . . . . . . . . . . . 74 5.2 An error-aware sufficient decrease condition for convergence under 77 the relaxed first order condition . . . . . . . . . . . . . . . . . . 5.3 Two design optimization algorithms based on the relaxed first 87 order condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Implementation details for ETR and EP . . . . . . . . . . . . . 92 6 Using Interpolatory MOR in optimization 93 6.1 A heuristic error bound . . . . . . . . . . . . . . . . . . . . . . 93 6.2 Combining interpolatory reduced models with ETR and EP . . 97 6.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 99 7 Using block Krylov methods to preserve design parameters for low-rank structures 107 7.1 Block Krylov methods for low-rank parametric structures . . . 107 7.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8 Conclusions and future directions 117 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 8.3 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . 120 A Using line search methods in exploiting interpolatory reduced models 123 A.1 Error-aware Armijo conditions and a practical working procedure 123 A.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Bibliography 129 Curriculum Vitae 143nrpages: 144status: publishe