Holdings: Topological optimization and optimal transport

Topological optimization and optimal transport: in the applied sciences

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Other Authors:	Bergounioux, Maïtine (Editor), Oudet, Édouard (Editor), Rumpf, Martin (Editor), Carlier, Guillaume (Editor), Champion, Thierry (Editor), Santambrogio, Filippo (Editor)
Format:	Book
Language:	English
Published:	Berlin De Gruyter [2017]
Series:	Radon Series on Computational and Applied Mathematics volume 17
Subjects:	Numerisches Verfahren Gestaltoptimierung Geometrische Analysis Transporttheorie Topologieoptimierung Mehrskalenanalyse Transportproblem
Online Access:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439267&searchTitles=true Inhaltsverzeichnis
Physical Description:	XI, 418 Seiten Illustrationen
ISBN:	9783110439267 3110439263

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245	1	0	\|a Topological optimization and optimal transport \|b in the applied sciences \|c edited by Maïtine Bergounioux, Édouard Oudet, Martin Rumpf, Guillaume Carlier, Thierry Champion, Filippo Santambrogio
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Record in the Search Index

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adam_text	CONTENTS PARTI GRAZIANO CRASTA AND LLARIA FRAGALAE GEOMETRIE ISSUES IN PDE PROBLEMS RELATED TO THE INFINITY LAPLACE OPERATOR * 5 1.1 INTRODUCTION * 5 1.2 ON THE DIRICHLET PROBLEM ----- 6 1.3 ON THE OVERDETERMINED PROBLEM: THE SIMPLE (WEB) CASE * 8 1.4 ON STADIUM-LIKE DOMAINS * 11 1.5 ON THE OVERDETERMINED PROBLEM: THE GENERAL (NON-WEB) CASE * 13 1.6 OPEN PROBLEMS * 18 H. HARBRECHT AND M. D. PETERS SOLUTION OF FREE BOUNDARY PROBLEMS IN THE PRESENCE OF GEOMETRIC UNCERTAINTIES * 20 2.1 INTRODUCTION * 20 2.2 MODELLING UNCERTAIN DOMAINS * 22 2.2.1 NOTATION ----- 22 2.2.2 RANDOM INTERIOR BOUNDARY * 22 2.2.3 RANDOM EXTERIOR BOUNDARY * 23 2.2.4 EXPECTATION AND VARIANCE OF THE DOMAIN * 24 2.2.5 STOCHASTIC QUADRATURE METHOD * 26 2.2.6 ANALYTICAL EXAMPLE * 27 2.3 COMPUTING FREE BOUNDARIES * 28 2.3.1 TRIAL METHOD * 28 2.3.2 DISCRETIZING THE FREE BOUNDARY* 29 2.3.3 BOUNDARY INTEGRAL EQUATIONS * 30 2.3.4 EXPECTATION AND VARIANCE OF THE POTENTIAL * 31 2.4 NUMERICAL RESULTS * 32 2.4.1 FIRST EXAMPLE * 32 2.4.2 SECOND EXAMPLE * 34 2.4.3 THIRD EXAMPLE ----- 34 2.4.4 FOURTH EXAMPLE * 36 2.5 CONCLUSION * 38 M. HINTERMUELLERAND D. WEGNER DISTRIBUTED AND BOUNDARY CONTROL PROBLEMS FOR THE SEMIDISCRETE CAHN-HILLIARD/NAVIER-STOKES SYSTEM WITH NONSMOOTH GINZBURG-LANDAU ENERGIES * 40 3.1 INTRODUCTION * 40 3.2 OPTIMAL CONTROL PROBLEM FOR THE TIME DISCRETIZATION * 43 3.3 YOSIDA APPROXIMATION AND GRADIENT METHOD * 47 3.3.1 SEQUENTIAL YOSIDA APPROXIMATION ------- 47 3.3.2 STEEPEST DESCENT METHOD WITH EXPANSIVE LINE SEARCH * 48 3.3.3 NEWTONS METHOD FOR THE PRIMAL SYSTEM ----- 49 3.4 FINITE ELEMENT APPROXIMATION 49 3.5 NUMERICAL RESULTS * 51 3.5.1 DISK TO A RING SEGMENT * 53 3.5.2 RING TO DISKS ----- 54 3.5.3 GRID PATTERN OF DISKS * 57 3.5.4 GRID PATTERN OF FINGER-LIKE REGIONS * 59 3.6 CONCLUSIONS * 60 VICTOR A. KOVTUNENKO HIGH-ORDER TOPOLOGICAL EXPANSIONS FOR HELMHOLTZ PROBLEMS IN 2D * 64 4.1 INTRODUCTION * 64 4.2 BACKGROUND HELMHOLTZ PROBLEM * 66 4.2.1 INNER ASYMPTOTIC EXPANSION BY FOURIER SERIES IN NEAR FIELD * 68 4.3 HELMHOLTZ PROBLEMS FOR GEOMETRIC OBJECTS UNDER NEUMANN (SOUND HARD) BOUNDARY CONDITION ----- 74 4.3.1 OUTER ASYMPTOTIC EXPANSION BY FOURIER SERIES IN FAR FIELD * 77 4.3.2 UNIFORM ASYMPTOTIC EXPANSION OF SOLUTION OF THE NEUMANN PROBLEM * 83 4.3.3 INVERSE HELMHOLTZ PROBLEM UNDER NEUMANN BOUNDARY CONDITION * 85 4.4 HELMHOLTZ PROBLEMS FOR GEOMETRIC OBJECTS UNDER DIRICHLET (SOUND SOFT) BOUNDARY CONDITION ----- 92 4.4.1 OUTER AND INNER ASYMPTOTIC EXPANSIONS BY FOURIER SERIES * 93 4.4.2 HIGH-ORDER UNIFORM ASYMPTOTIC EXPANSION OF THE DIRICHLET PROBLEM ----- 100 4.4.3 INVERSE HELMHOLTZ PROBLEM UNDER DIRICHLET BOUNDARY CONDITION * 102 4.5 HELMHOLTZ PROBLEMS FOR GEOMETRIC OBJECTS UNDER ROBIN (IMPEDANCE) BOUNDARY CONDITION ----- 105 4.5.1 OUTER ASYMPTOTIC EXPANSION BY FOURIER SERIES IN FAR FIELD * 107 4.5.2 COMBINED UNIFORM ASYMPTOTIC EXPANSION OF THE ROBIN PROBLEM * 111 4.5.3 INVERSE HELMHOLTZ PROBLEM UNDER ROBIN BOUNDARY CONDITION * 113 4.5.4 NECESSARY OPTIMALITY CONDITION FOR THE TOPOLOGY OPTIMIZATION * 118 ELIE BRETIN AND SIMON MASNOU ON A NEW PHASE FIELD MODEL FOR THE APPROXIMATION OF INTERFACIAL ENERGIES OF MULTIPHASE SYSTEMS * 123 5.1 INTRODUCTION * 123 5.2 DERIVATION OF THE PHASE-FIELD MODEL * 125 5.2.1 THE CLASSICAL CONSTANT CASE A/J --1 * 125 5.2.2 ADDITIVE SURFACE TENSIONS * 127 5.2.3 ^-EMBEDDABLE SURFACE TENSIONS ----- 128 5.2.4 DERIVATION OF THE APPROXIMATION PERIMETER FOR E1 -EMBEDDABLE SURFACE TENSIONS * 130 5.3 CONVERGENCE OF THE APPROXIMATING MULTIPHASE PERIMETER* 133 5.4 -GRADIENT FLOW AND SOME EXTENSIONS * 134 5.4.1 ADDITIONAL VOLUME CONSTRAINTS * 134 5.4.2 APPLICATION TO THE WETTING OF MULTIPHASE DROPLETS ON SOLID SURFACES * 135 5.5 NUMERICAL EXPERIMENTS* 136 5.5.1 EVOLUTION OF PARTITIONS * 137 5.5.2 WETTING OF MULTIPHASE DROPLETS ON SOLID SURFACES * 138 ANCA-MARIA LOADER AND CRISTIAN BARBAROSIE OPTIMIZATION OF EIGENVALUES AND EIGENMODES BY USING THE ADJOINT METHOD * 142 6.1 INTRODUCTION * 142 6.2 SETTING OF THE PROBLEM AND THE OBJECTIVE FUNCTIONALS * 144 6.3 THE DERIVATIVES OF THE EIGENVALUES AND EIGENMODES OF VIBRATION * 145 6.4 THE DERIVATIVE OF THE OBJECTIVE FUNCTIONAL BY THE ADJOINT METHOD * 148 6.5 MULTIPLE EIGENVALUES * 149 6.6 THE ADJOINT METHOD IN THE FRAMEWORK OF BLOCH WAVES * 152 BLANCHE BUET, GIAN PAOLO LEONARDI, AND SIMON MASNOU DISCRETE VARIFOLDS AND SURFACE APPROXIMATION * 159 7.1 INTRODUCTION * 159 7.2 VARIFOLDS ----- 160 7.3 DISCRETE VARIFOLDS * 161 7.4 APPROXIMATION OF RECTIFIABLE VARIFOLDS BY DISCRETE VARIFOLDS * 162 7.5 CURVATURE OF A VARIFOLD: A NEW CONVOLUTION APPROACH * 164 7.5.1 REGULARIZATION OF THE FIRST VARIATION AND CONDITIONS OF BOUNDED FIRST VARIATION ----- 164 7.5.2 E-APPROXIMATION OF THE MEAN CURVATURE VECTOR * 165 7.6 MEAN CURVATURE OF POINT-CLOUD VARIFOLDS * 166 PART II JEAN-DAVID BENAMOU AND BRITTANY D. FROESE WEAK MONGE-AMPERE SOLUTIONS OF THE SEMI-DISCRETE OPTIMAL TRANSPORTATION PROBLEM * 175 8.1 INTRODUCTION ----- 175 8.2 DUALITY OF ALEKSANDROV AND POGORELOV SOLUTIONS ----- 178 8.2.1 PROPERTIES OF THE LEGENDRE-FENCHEL DUAL * 178 8.2.2 ALEKSANDROV SOLUTIONS ----- 180 8.2.3 GEOMETRIC CHARACTERISATION * 182 8.3 MIXED ALEKSANDROV-VISCOSITY FORMULATION ----- 183 8.3.1 VISCOSITY SOLUTIONS * 183 8.3.2 MIXED ALEKSANDROV-VISCOSITY SOLUTIONS * 184 8.3.3 CHARACTERISATION OF SUBGRADIENT MEASURE * 186 8.4 APPROXIMATION SCHEME * 188 8.4.1 MONGE-AMPERE OPERATOR AND BOUNDARY CONDITIONS * 188 8.4.2 DISCRETIZATION OF SUBGRADIENT MEASURE * 189 8.4.3 PROPERTIES OF THE APPROXIMATION SCHEME ------ 190 8.5 NUMERICAL RESULTS * 191 8.5.1 COMPARISON TO VISCOSITY SOLVER* 191 8.5.2 COMPARISON TO EXACT SOLVER * 193 8.5.3 MULTIPLE DIRACS ----- 194 8.6 CONCLUSIONS * 197 A CONVEXITY * 197 B DISCRETIZATION OF MONGE-AMP6RE ------ 199 C EXTENSION TO NON-CONSTANT DENSITIES ------ 200 SIMONE DI MARINO, AUGUSTO GEROLIN, AND LUCA NENNA OPTIMAL TRANSPORTATION THEORY WITH REPULSIVE COSTS * 204 9.1 WHY MULTI-MARGINAL TRANSPORT THEORY FOR REPULSIVE COSTS? * 207 9.1.1 BRIEF INTRODUCTION TO QUANTUM MECHANICS OF /V-BODY SYSTEMS * 207 9.1.2 PROBABILISTIC INTERPRETATION AND MARGINALS * 211 9.1.3 DENSITY FUNCTIONAL THEORY (DFT) ----- 212 9.1.4 SEMI-CLASSICAL LIM IT AND OPTIMAL TRANSPORT PROBLEM * 214 9.2 DFT MEETS OPTIMAL TRANSPORTATION THEORY ----- 217 9.2.1 COUPLINGS AND MULTI-MARGINAL OPTIMAL TRANSPORTATION PROBLEM * 217 9.2.2 MULTI-MARGINAL OPTIMAL TRANSPORTATION PROBLEM ----- 218 9.2.3 DUAL FORMULATION ----- 221 9.2.4 GEOMETRY OF THE OPTIMAL TRANSPORT SETS * 223 9.2.5 SYMMETRIC CASE * 224 9.3 MULTI-MARGINAL OT WITH COULOMB COST ----- 226 9.3.1 GENERAL THEORY: DUALITY, EQUIVALENT FORMULATIONS, AND MANY PARTICLES LIM IT ----- 226 9.3.2 THE MONGE PROBLEM: DETERMINISTIC EXAMPLES AND COUNTEREXAMPLES * 228 9.4 MULTI-MARGINAL OT WITH REPULSIVE HARMONIC COST ----- 231 9.5 MULTI-MARGINAL OT FOR THE DETERMINANT * 238 9.6 NUMERICS ----- 242 9.6.1 THE REGULARIZED PROBLEM AND THE ITERATIVE PROPORTIONAL FITTING PROCEDURE * 243 9.6.2 NUMERICAL EXPERIMENTS: COULOMB COST * 246 9.6.3 NUMERICAL EXPERIMENTS: REPULSIVE HARMONIC COST * 248 9.6.4 NUMERICAL EXPERIMENTS: DETERMINANT COST * 250 9.7 CONCLUSION ----- 252 ROM6O HATCH! WARDROP EQUILIBRIA: LONG-TERM VARIANT, DEGENERATE ANISOTROPIC PDES AND NUMERICAL APPROXIMATIONS * 257 10.1 INTRODUCTION * 257 10.1.1 PRESENTATION OF THE GENERAL DISCRETE MODEL * 257 10.1.2 ASSUMPTIONS AND PRELIMINARY RESULTS * 259 10.2 EQUIVALENCE WITH BECKMANN PROBLEM * 264 10.3 CHARACTERIZATION OF MINIMIZERS VIA ANISOTROPIC ELLIPTIC PDES ----- 267 10.4 REGULARITY WHEN THE TV S AND C /S ARE CONSTANT * 269 10.5 NUMERICAL SIMULATIONS * 273 10.5.1 DESCRIPTION OF THE ALGORITHM * 273 10.5.2 NUMERICAL SCHEMES AND CONVERGENCE STUDY * 275 PAUL PEGON ON THE LAGRANGIAN BRANCHED TRANSPORT MODEL AND THE EQUIVALENCE WITH ITS EULERIAN FORMULATION * 281 11.1 THE LAGRANGIAN MODEL: IRRIGATION PLANS * 282 11.1.1 NOTATION AND GENERAL FRAMEWORK * 282 11.1.2 THE LAGRANGIAN IRRIGATION PROBLEM * 284 11.1.3 EXISTENCE OF MINIMIZERS ----- 285 11.2 THE ENERGY FORMULA * 290 11.2.1 RECTIFIABLE IRRIGATION PLANS * 290 11.2.2 PROOF OF THE ENERGY FORMULA * 294 11.2.3 OPTIMAL IRRIGATION PLANS ARE SIMPLE * 296 11.3 THE EULERIAN MODEL: IRRIGATION FLOWS * 297 11.3.1 THE DISCRETE MODEL * 298 11.3.2 THE CONTINUOUS MODEL ----- 298 11.4 EQUIVALENCE BETWEEN MODELS * 300 11.4.1 FROM LAGRANGIAN TO EULERIAN ----- 300 11.4.2 FROM EULERIAN TO LAGRANGIAN * 301 11.4.3 THE EQUIVALENCE THEOREM ----- 302 MAXIME LABORDE ON SOME NONLINEAR EVOLUTION SYSTEMS WHICH ARE PERTURBATIONS OF WASSERSTEIN GRADIENT FLOWS * 304 12.1 INTRODUCTION ----- 304 12.2 WASSERSTEIN SPACE AND MAIN RESULT * 305 12.2.1 THE WASSERSTEIN DISTANCE ----- 306 12.2.2 MAIN RESULT ----- 307 12.3 SEMI-IMPLICIT JKO SCHEME ----- 308 12.4 X-FLOWS AND GRADIENT ESTIMATE * 313 12.4.1 K-FLOWS ----- 313 12.4.2 GRADIENT ESTIMATE * 315 12.5 PASSAGE TO THE LIM IT ----- 317 12.5.1 WEAK AND STRONG CONVERGENCES * 318 12.5.2 LIMIT OF THE DISCRETE SYSTEM ----- 321 12.6 THE CASE OF A BOUNDED DOMAIN 0 ----- 324 12.7 UNIQUENESS OF SOLUTIONS * 328 B. MAURY AND A. PREUX PRESSURELESS EULER EQUATIONS WITH MAXIMAL DENSITY CONSTRAINT: A TIM E-SPLITTING SCHEME * 333 13.1 INTRODUCTION * 333 13.2 TIME-STEPPING SCHEME * 339 13.2.1 TIME DISCRETIZATION STRATEGY * 339 13.2.2 THE SCHEME * 341 13.3 NUMERICAL ILLUSTRATIONS * 347 13.3.1 SPACE DISCRETIZATION SCHEME * 347 13.3.2 NUMERICAL TESTS ----- 349 13.4 CONCLUSIVE REMARKS ----- 350 HORST OSBERGER AND DANIEL MATTHES CONVERGENCE OF A FULLY DISCRETE VARIATIONAL SCHEME FOR A THIN-FILM EQUATION * 356 14.1 INTRODUCTION * 356 14.1.1 THE EQUATION AND ITS PROPERTIES * 356 14.1.2 DEFINITION OF THE DISCRETIZATION * 358 14.1.3 MAIN RESULTS ----- 360 14.1.4 RELATION TO THE LITERATURE ----- 361 14.1.5 KEY ESTIMATES ----- 362 14.1.6 STRUCTURE OF THE PAPER ----- 363 14.2 DEFINITION OF THE FULLY DISCRETE SCHEME * 364 14.2.1 ANSATZ SPACE AND DISCRETE ENTROPY/INFORMATION FUNCTIONALS * 364 14.2.2 DISCRETIZATION IN TIME * 366 14.2.3 SPATIAL INTERPOLATIONS ----- 368 14.2.4 A DISCRETE SOBOLEV-TYPE ESTIMATE * 369 14.3 A PRIORI ESTIMATES AND COMPACTNESS * 370 14.3.1 ENERGY AND ENTROPY DISSIPATION * 370 14.3.2 COMPACTNESS * 372 14.3.3 CONVERGENCE OF TIME INTERPOLANTS * 374 14.4 WEAK FORMULATION OF THE LIMIT EQUATION * 377 14.5 NUMERICAL RESULTS * 392 14.5.1 NONUNIFORM MESHES * 392 14.5.2 IMPLEMENTATION * 393 14.5.3 NUMERICAL EXPERIMENTS * 393 A APPENDIX * 397 F. AI REDA AND B. MAURY INTERPRETATION OF FINITE VOLUME DISCRETIZATION SCHEMES FOR THE FOKKER-PLANCK EQUATION AS GRADIENT FLOWS FOR THE DISCRETE WASSERSTEIN DISTANCE * 400 15.1 INTRODUCTION * 400 15.2 PRELIMINARIES * 403 15.3 DISCRETIZATION OF THE FOKKER-PLANCK EQUATION * 411 15.4 CONCLUSIVE REMARKS, PERSPECTIVES ---- 414 INDEX* 417
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id	DE-604.BV043556387
illustrated	Illustrated
indexdate	2024-07-10T07:28:46Z
institution	BVB
isbn	9783110439267 3110439263
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-028971545
oclc_num	1002274631
open_access_boolean
owner	DE-703 DE-384 DE-29T
owner_facet	DE-703 DE-384 DE-29T
physical	XI, 418 Seiten Illustrationen
publishDate	2017
publishDateSearch	2017
publishDateSort	2017
publisher	De Gruyter
record_format	marc
series	Radon Series on Computational and Applied Mathematics
series2	Radon Series on Computational and Applied Mathematics
spelling	Topological optimization and optimal transport in the applied sciences edited by Maïtine Bergounioux, Édouard Oudet, Martin Rumpf, Guillaume Carlier, Thierry Champion, Filippo Santambrogio Berlin De Gruyter [2017] XI, 418 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Radon Series on Computational and Applied Mathematics volume 17 Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Gestaltoptimierung (DE-588)4329076-0 gnd rswk-swf Geometrische Analysis (DE-588)4156708-0 gnd rswk-swf Transporttheorie (DE-588)4185936-4 gnd rswk-swf Topologieoptimierung (DE-588)7662388-9 gnd rswk-swf Mehrskalenanalyse (DE-588)4416235-2 gnd rswk-swf Transportproblem (DE-588)4060694-6 gnd rswk-swf Gestaltoptimierung (DE-588)4329076-0 s Topologieoptimierung (DE-588)7662388-9 s Transportproblem (DE-588)4060694-6 s Transporttheorie (DE-588)4185936-4 s Geometrische Analysis (DE-588)4156708-0 s Mehrskalenanalyse (DE-588)4416235-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Bergounioux, Maïtine edt Oudet, Édouard edt Rumpf, Martin edt Carlier, Guillaume (DE-588)171874501 edt Champion, Thierry edt Santambrogio, Filippo edt Erscheint auch als Online-Ausgabe, PDF 978-3-11-043041-7 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-043050-9 Radon Series on Computational and Applied Mathematics volume 17 (DE-604)BV023335470 17 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439267&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028971545&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Topological optimization and optimal transport in the applied sciences Radon Series on Computational and Applied Mathematics Numerisches Verfahren (DE-588)4128130-5 gnd Gestaltoptimierung (DE-588)4329076-0 gnd Geometrische Analysis (DE-588)4156708-0 gnd Transporttheorie (DE-588)4185936-4 gnd Topologieoptimierung (DE-588)7662388-9 gnd Mehrskalenanalyse (DE-588)4416235-2 gnd Transportproblem (DE-588)4060694-6 gnd
subject_GND	(DE-588)4128130-5 (DE-588)4329076-0 (DE-588)4156708-0 (DE-588)4185936-4 (DE-588)7662388-9 (DE-588)4416235-2 (DE-588)4060694-6
title	Topological optimization and optimal transport in the applied sciences
title_auth	Topological optimization and optimal transport in the applied sciences
title_exact_search	Topological optimization and optimal transport in the applied sciences
title_full	Topological optimization and optimal transport in the applied sciences edited by Maïtine Bergounioux, Édouard Oudet, Martin Rumpf, Guillaume Carlier, Thierry Champion, Filippo Santambrogio
title_fullStr	Topological optimization and optimal transport in the applied sciences edited by Maïtine Bergounioux, Édouard Oudet, Martin Rumpf, Guillaume Carlier, Thierry Champion, Filippo Santambrogio
title_full_unstemmed	Topological optimization and optimal transport in the applied sciences edited by Maïtine Bergounioux, Édouard Oudet, Martin Rumpf, Guillaume Carlier, Thierry Champion, Filippo Santambrogio
title_short	Topological optimization and optimal transport
title_sort	topological optimization and optimal transport in the applied sciences
title_sub	in the applied sciences
topic	Numerisches Verfahren (DE-588)4128130-5 gnd Gestaltoptimierung (DE-588)4329076-0 gnd Geometrische Analysis (DE-588)4156708-0 gnd Transporttheorie (DE-588)4185936-4 gnd Topologieoptimierung (DE-588)7662388-9 gnd Mehrskalenanalyse (DE-588)4416235-2 gnd Transportproblem (DE-588)4060694-6 gnd
topic_facet	Numerisches Verfahren Gestaltoptimierung Geometrische Analysis Transporttheorie Topologieoptimierung Mehrskalenanalyse Transportproblem
url	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439267&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028971545&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV023335470
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