Holdings: A space-time meshfree collocation method for coupled problems on irregularly-shaped domains

A space-time meshfree collocation method for coupled problems on irregularly-shaped domains:

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Bibliographic Details
Main Author:	Netuzhylov, Hennadiy 1978- (Author)
Format:	Thesis Book
Language:	English
Published:	2008
Subjects:	Gitterfreie Methode Interpolation Gekoppeltes System Hochschulschrift
Online Access:	Inhaltsverzeichnis
Physical Description:	IX, 170 S. Ill., graph. Darst.
ISBN:	9783000267444

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MARC


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_version_	1804138914469904384
adam_text	A SPACE-TIME MESHFREE COLLOCATION METHOD FOR COUPLED PROBLEMS ON IRREGULARLY-SHAPED DOMAINS VON DER FAKULTAET ARCHITEKTUR, BAUINGENIEURWESEN UND UMWELTWISSENSCHAFTEN DER TECHNISCHEN UNIVERSITAET CAROLO-WILHELMINA ZU BRAUNSCHWEIG ZUR ERLANGUNG DES GRADES EINES DOKTOR-INGENIEURS (DR.-ING.) GENEHMIGTE DISSERTATION VON HENNADIY NETUZHYLOV, MSC GEBOREN AM 20.11.1978 AUS LVIV, UKRAINE EINGEREICHT AM DISPUTATION AM BERICHTERSTATTER 12. JUNI 2008 10.~OVEMBER2008 PROF. DR.-ING. ANDREAS ZILIAN PROF. DR. RER. NATO THOMAS SONAR 2008 CONTENTS KURZFASSUNG ABSTRACT PREFACE U LU LX 1 INTRODUCTION 1 1.1 MOTIVATION........................................... 1 1.2 HISTORICAL DEVELOPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 CURRENT STATE OF RESEARCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 CLASSIFICATION OF MESHFREE METHODS .. . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 OUTLINE OF THE THESIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 BASIC CONCEPTS AND METHODOLOGY 11 2.1 DEDUCTION OF THE METHOD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 2.2 (INTERPOLATING) MOVING LEAST SQUARES . . . . . . . . . . . . . . . . . . . . . . . . .. 12 2.3 COMPARISON WITH OTHER LEAST SQUARES METHODS . . . . . . . . . . . . . . . . . .. 15 2.4 BASIS FUNCTIONS 16 2.5 WEIGHT FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 2.5.1 APPROXIMATION CASE :: MLS . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 2.5.2 INTERPOLATION CASE :: IMLS . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18 2.6 SINGULARITY-BY-CONSTRUCTION................................ 19 CONTENTS 2.7 2.8 2.6.1 SINGULAR VALUE DECOMPOSITION . 2.6.2 REGULARIZATION TECHNIQUE . 2.6.3 DERIVATIVES AND NODAL VALUES OF THE KERNE! FUNCTIONS . BOUNDARY AND INITIAL CONDITIONS .. . . . . . . . . . . . . . . . . . . . . . . . . NUMERICAL PROPERTIES OF IMLS FUNCTIONS . 2.8.1 PATCH TESTS :: A LINEAR ELASTICITY EXAMPLE . 2.8.2 POSITIVITY CONDITIONS IN MESHFREE COLLOCATIONS . 20 21 23 28 29 31 34 3 A SPACE-TIME MESHFREE COLLOCATION METHOD 35 3.1 SPLITTING INTO SPACE-TIME SLABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35 3.2 DISCRETIZATION OF A COUPLED PROBLEM 37 3.3 STRATEGY FOR NONLINEARITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38 3.4 POINT DISTRIBUTION TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 3.4.1 HALTON POINTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 3.4.2 DATA MANAGEMENT .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40 3.5 NUMERICAL STABILITY AND TRADE-OFF PRINCIPLES . . . . . . . . . . . . . . . . . . . . .. 43 3.5.1 CHOICE OF PARAMETERS 43 3.6 WORKFLOW............................................ 46 4 DISCRETIZATION OF IRREGULARLY-SHAPED DOMAINS 47 4.1 SCATTERED DATA INTERPOLATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47 4.2 A MULTILEVEL SURFACE RECONSTRUCTION 48 4.3 INTERPOLATION OF POINT CLOUD DATA BY IMPLICIT SURFACES 50 4.3.1 DEMONSTRATION OF THE APPROACH IN 2D. . . . . . . . . . . . . . . . . . . .. 54 4.3.2 EXAMPLES IN 3D 55 5 INTERPOLATING FUNCTIONS AND DERIVATIVES 63 5.1 ERROR INDICATORS AND CONVERGENCE 63 5.2 HIGHLY-OSCILLATING FUNCTIONS :: FRANKE S FUNCTION ON A QUADRATIC DOMAIN 66 5.3 HIGHLY-OSCILLATING FUNCTIONS :: A BLUPP FUNCTION ON A CIRCULAR DOMAIN ... 69 CONTENTS 6 NUMERICAL STUDY OF STMCM FOR DIFFERENTIAL EQUATIONS 73 6.1 INTRODUCTION.......................................... 73 6.2 CLASSIFICATION OF EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74 6.2.1 PROBLEM TYPES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74 6.2.2 WELL-POSEDNESS................................... 75 6.2.3 EQUATION TYPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76 6.3 LINEAR ORDINARY DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . .. 77 6.3.1 A SPRING-MASS OSCILLATOR 77 6.3.2 FOUCAULT PENDULUM .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82 6.3.3 STABILITY AND FILTER PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . .. 86 6.4 NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . .. 89 6.4.1 LORENZ ATTRACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 90 6.5 STATIONARY PROBLEMS :: ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS 92 6.5.1 THEORETICAL ISSUES 95 6.5.2 DISCRETIZATION AND BOUNDARY CONDITIONS . . . . . . . . . . . . . . . . . .. 97 6.5.3 LAPLACE EQUATION ON A UNIT SQUARE . . . . . . . . . . . . . . . . . . . . . .. 100 6.5.4 LAPLACE EQUATION ON A CIRCLE . . . . . . . . . . . . . . . . . . . . . . . . . .. 100 6.5.5 A BOUNDARY LAYER PROBLEM 101 6.5.6 HEIMHOLTZ EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 106 6.6 TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS , 110 6.6.1 DIFFUSIONS :: HEAT EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . .. 110 6.6.2 VIBRATIONS :: WAVE EQUATION , 112 6.6.3 CONVECTION :: TRANSPORT EQUATION . . . . . . . . . . . . . . . . . . . . . .. 118 6.6.4 HAMILTON-JACOBI EQUATIONS :: LEVEL-SET EQUATION . . . . . . . . . . . . .. 122 6.6.5 CURVATURE DRIVEN EVOLVING INTERFACES . . . . . . . . . . . . . . . . . . . .. 124 6.7 NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS , 126 6.7.1 SHOCK WAVES :: BURGERS EQUATION. . . . . . . . . . . . . . . . . . . . . . .. 126 6.7.2 METASTABILITY :: ALLEN-CAHN EQUATION . . . . . . . . . . . . . . . . . . . .. 128 6.8 DISCUSSION........................................... 129 CONTENTS 7 APPLICATION TO BIOFILM AND TUMOUR GROWTH MODELLING 131 7.1 BIOFILMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 131 7.2 STATE OF RESEARCH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 132 7.3 A MATHEMATICAL MODEL OF BIOFILM GROWTH . . . . . . . . . . . . . . . . . . . . . .. 133 7.3.1 MATERIAL DESCRIPTION , 134 7.3.2 NUTRIENT DESCRIPTION 135 7.3.3 INTERFACE DESCRIPTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 135 7.3.4 NUTRIENT CONSUMPTION AND BIOMASS FORMATION 136 7.3.5 VALIDATION...................................... 137 7.4 TUMOURS............................................ 143 7.4.1 A MATHEMATICAL MODEL OF TUMOUR GROWTH . . . . . . . . . . . . . . . . .. 145 7.4.2 VALIDATION :: A SPHERICAL AVASCULAR TUMOUR . . . . . . . . . . . . . . . . .. 146 8 SUMMARY AND OUTLOOK 149 8.1 SUMMARY............................................ 149 8.2 OUTLOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 150 A ANALYTICAL EXPRESSIONS 151 B INVARIANCE OF THE LAPLACIAN 155 BIBLIOGRAPHY 157 INDEX 167
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author	Netuzhylov, Hennadiy 1978-
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spelling	Netuzhylov, Hennadiy 1978- Verfasser (DE-588)137974361 aut A space-time meshfree collocation method for coupled problems on irregularly-shaped domains von Hennadiy Netuzhylov A space-time meshfree collocation method for coupled problems on irregularly-shaped domains 2008 IX, 170 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Braunschweig, Techn. Univ., Diss., 2008 Gitterfreie Methode (DE-588)4796173-9 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Gekoppeltes System (DE-588)4414616-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Gekoppeltes System (DE-588)4414616-4 s Interpolation (DE-588)4162121-9 s Gitterfreie Methode (DE-588)4796173-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017379805&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Netuzhylov, Hennadiy 1978- A space-time meshfree collocation method for coupled problems on irregularly-shaped domains Gitterfreie Methode (DE-588)4796173-9 gnd Interpolation (DE-588)4162121-9 gnd Gekoppeltes System (DE-588)4414616-4 gnd
subject_GND	(DE-588)4796173-9 (DE-588)4162121-9 (DE-588)4414616-4 (DE-588)4113937-9
title	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains
title_alt	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains
title_auth	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains
title_exact_search	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains
title_full	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains von Hennadiy Netuzhylov
title_fullStr	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains von Hennadiy Netuzhylov
title_full_unstemmed	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains von Hennadiy Netuzhylov
title_short	A space-time meshfree collocation method for coupled problems on irregularly-shaped domains
title_sort	a space time meshfree collocation method for coupled problems on irregularly shaped domains
topic	Gitterfreie Methode (DE-588)4796173-9 gnd Interpolation (DE-588)4162121-9 gnd Gekoppeltes System (DE-588)4414616-4 gnd
topic_facet	Gitterfreie Methode Interpolation Gekoppeltes System Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017379805&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT netuzhylovhennadiy aspacetimemeshfreecollocationmethodforcoupledproblemsonirregularlyshapeddomains

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