Fast simulation of electro-thermal MEMS: efficient dynamic compact models
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
2007
|
| Series: | Microtechnology and MEMS
|
| Subjects: | |
| Online Access: | Umschlagtext Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 143 - 155 |
| Physical Description: | XI, 180 S. Ill., graph. Darst. |
| ISBN: | 9783540346128 3540346120 |
Staff View
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Record in the Search Index
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| adam_text |
T. BECHTOLD E.B. RUDNYI J.G. KORVINK
FAST SIMULATION
OF ELECTRO-THERMAL MEMS
EFFICIENT DYNAMI
C COMPAC
T MODELS
WITH 108 FIGURES, 8 IN COLOR AND 9 TABLES
4UE SPRIN
G'
ER
CONTENTS
1 TNTRODUCTION 1
1.1 MF.MS, COMPACT MODELING AND MODEL ORDER REDUCTION 2
1.2 MEMS AND ELECTRO-THERMAL SIMULATION 4
1.3 THEMATIC OUTLINE 5
2 DYNAMIC ELECTRO-THERMAL SIMULATION OF MICROSYSTEMS 7
2.1 OVCRVICW OF COUPLCD ELECTRO-THERMAL AND.
THERMO-ELECTRIC EFFECTS 8
2.2 JOULE HEARING IN MICROSYSTEMS 10
2.3 PHYSICAL MODEL - HEAT TRANSFER EQUATION 13
2.4 DECOUPLING THC HEAT TRANSFER EQUATION FROM
OTHER PHYSICAL DOMAINS 15
2.5 SOLVING THE HEAT TRANSFER PARTIAL DIFFERENTIAL EQUATION 17
2.5.1 LINEARIZATION 18
2.5.2 ANALYTICAL SOLUTIONS 18
2.5.3 NUMERICAL METHODS 19
2.6 DYNAMIC COMPACT THERMAL MODELING 21
2.6.1 RC EADDER APPROACH 21
2.6.2 MODAL APPROACHES 23
2.6.3 MODEL ORDER REDUCTION 24
2.7 SUMMARY 28
3 OVERVIEW OF LINEAR MODEL ORDER REDUCTION 31
3.1 CONTROL THCORY METHODS 31
3.1.1 BALANCED TRUNCATION APPROXIMATION 32
3.1.2 SINGULAR PERTURBATIO!! APPROXIMATION 35
3.1.3 HANKEL NORM APPROXIMATION 35
3.1.4 COMPARISON OF METHODS 36
3.2 KRYLOV SUBSPACE METHODS 36
3.2.1 LANCZOS ALGORITHM 39
3.2.2 AMOLDI PROCESS 41
3.2.3 AMOLDI VERSUS LANCZOS 43
X CONTENTS
3.3 GUYAN REDUCTION 45
3.3.1 STATIC MATRIX CONDENSATION 45
3.3.2 DYNAMIC MATRIX CONDENSATION 46
3.4 SUMMARY 48
4 SELECTED MODEL REDUCTION SOFTWARE 51
4.1 SLICOT LIBRARY 51
4.2 MOR FOR ANSYS - MODEL ORDER REDUCTION FOR ANSYS 53
4.3 USING PACKAGE POST4MOR AND MATHLINK INTERFACE TO
SLICOT IN MATHEMATICA 57
4.4 SUMMARY 59
5 APPLICATION OF MODEL REDUCTION TO ELECTRO-THERMAL MEMS.
. 61
5.1 MEMS CASE STUDIES 62
5.1.1 PYROLECHNICAL MICROTHRUSTER 62
5.1.2 TUNABIE OPTICAL FILTER 65
5.1.3 MICROHOTPLATC GAS SENSOR 67
5.2 PREPARATION FOR AUTOMATIC MODEL ORDER REDUCTION 70
5.3 MODEL REDUCTION OF THERMAL MEMS VIA THE ANIOLDI ALGORITHM 74
5.3.1 APPROXIMATION OF THE COMPLCTE OUTPUT 81
5.3.2 REDUCTION OF SYSTEMS WITH NONLINEAR IN PUT FUNCTIONS 82
5.3.3 SYSTEM-LEVEL SIMULATION 84
5.3.4 COMPUTATIONAL EFFICIENCY 86
5.4 ANIOLDI VERSUS GUYAN VERSUS CONTROL THEORY METHODS 88
5.5 INVCRSE THERMAL PROBLEM VIA MODE! ORDER REDUCTION 91
5.6 SUMMARY 96
6 ADVANCED DEVELOPMENT 97
6.1 ERROR INDICATORS FOR HEAT-TRANSFER MACROMODELIUG OF MEMS 97
6.1.1 CONVERGENCE OF RELATIVE ERROR 99
6.1.2 CONVERGENCE OFLLANKE
L SINGULAR VALUES 107
6.1.3 SEQUENTIAL MODEL ORDER REDUCTION 112
6.1.4 ADVANTAGES AND DISADVANTAGES OF THE PROPOSED STRATEGIES 115
6.2 ORDER REDUCTION OF INTERCONNECTED THERMAL MEMS MODELS 116
6.2.1 MICROHOTPLATE ARRAY 1 IS
6.2.2 BLOCK ARNOLDI 120
6.2.3 COUPLINGOFREDUCE
D ORDER MODELS VIA SUBSTRUCTURING 127
6.2.4 COUPLINGOFREDUCE
D ORDER MODELS IN THE GENERAL CASE 131
6.2.5 OVERVIEW OF PROPOSED STRATEGIES 137
6.3 LATEST RESULTS IN MODEL REDUCTION 137
6.3.1 PARAMETRIC MODEL REDUCTION 138
6.3.2 MODEL REDUCTION FOR SECOND-ORDER SYSTEMS 140
6.3.3 NONLINEAR MODEL REDUCTION 140
6.4 SUMMARY 141
7 REFCRENCES YY 143
8 APPENDIX YY '5
7
8.1 MOR FOR ANSYS 157
8.1.1 BASIC THEORY 158
CONTENTS X
I
8.1.2 PREPARING ANSYS FILES 159
8.1.3 PERFORMING MODEL REDUCTION 162
8.1.4 ADVANCED OPTIONS 163
8.1.5 RUNNING MOR FOR ANSYS: SUMMARY 164
8.1.6 REFERENCES 165
8.2 POST4MOR 166
8.2.1 DYNAMICSYSTEM 166
8.2.2 SIMULATIONRESULT 169
8.2.3 FUNCTIONS FOR TRANSIENT AND HARMONIE SIMULATION 172
8.3 MATHLINK INTERFACE TO SLICOT 173
8.3.1 HOW TO COMPILE THE INTERFACE 174
8.3.2 HOW TO USE THE INTERFACE 174
8.3.3 HOW TO CALL SLICOT 175
INDEX 177 |
| adam_txt |
T. BECHTOLD E.B. RUDNYI J.G. KORVINK
FAST SIMULATION
OF ELECTRO-THERMAL MEMS
EFFICIENT DYNAMI
C COMPAC
T MODELS
WITH 108 FIGURES, 8 IN COLOR AND 9 TABLES
4UE SPRIN
G'
ER
CONTENTS
1 TNTRODUCTION 1
1.1 MF.MS, COMPACT MODELING AND MODEL ORDER REDUCTION 2
1.2 MEMS AND ELECTRO-THERMAL SIMULATION 4
1.3 THEMATIC OUTLINE 5
2 DYNAMIC ELECTRO-THERMAL SIMULATION OF MICROSYSTEMS 7
2.1 OVCRVICW OF COUPLCD ELECTRO-THERMAL AND.
THERMO-ELECTRIC EFFECTS 8
2.2 JOULE HEARING IN MICROSYSTEMS 10
2.3 PHYSICAL MODEL - HEAT TRANSFER EQUATION 13
2.4 DECOUPLING THC HEAT TRANSFER EQUATION FROM
OTHER PHYSICAL DOMAINS 15
2.5 SOLVING THE HEAT TRANSFER PARTIAL DIFFERENTIAL EQUATION 17
2.5.1 LINEARIZATION 18
2.5.2 ANALYTICAL SOLUTIONS 18
2.5.3 NUMERICAL METHODS 19
2.6 DYNAMIC COMPACT THERMAL MODELING 21
2.6.1 RC EADDER APPROACH 21
2.6.2 MODAL APPROACHES 23
2.6.3 MODEL ORDER REDUCTION 24
2.7 SUMMARY 28
3 OVERVIEW OF LINEAR MODEL ORDER REDUCTION 31
3.1 CONTROL THCORY METHODS 31
3.1.1 BALANCED TRUNCATION APPROXIMATION 32
3.1.2 SINGULAR PERTURBATIO!! APPROXIMATION 35
3.1.3 HANKEL NORM APPROXIMATION 35
3.1.4 COMPARISON OF METHODS 36
3.2 KRYLOV SUBSPACE METHODS 36
3.2.1 LANCZOS ALGORITHM 39
3.2.2 AMOLDI PROCESS 41
3.2.3 AMOLDI VERSUS LANCZOS 43
X CONTENTS
3.3 GUYAN REDUCTION 45
3.3.1 STATIC MATRIX CONDENSATION 45
3.3.2 DYNAMIC MATRIX CONDENSATION 46
3.4 SUMMARY 48
4 SELECTED MODEL REDUCTION SOFTWARE 51
4.1 SLICOT LIBRARY 51
4.2 MOR FOR ANSYS - MODEL ORDER REDUCTION FOR ANSYS 53
4.3 USING PACKAGE POST4MOR AND MATHLINK INTERFACE TO
SLICOT IN MATHEMATICA 57
4.4 SUMMARY 59
5 APPLICATION OF MODEL REDUCTION TO ELECTRO-THERMAL MEMS.
. 61
5.1 MEMS CASE STUDIES 62
5.1.1 PYROLECHNICAL MICROTHRUSTER 62
5.1.2 TUNABIE OPTICAL FILTER 65
5.1.3 MICROHOTPLATC GAS SENSOR 67
5.2 PREPARATION FOR AUTOMATIC MODEL ORDER REDUCTION 70
5.3 MODEL REDUCTION OF THERMAL MEMS VIA THE ANIOLDI ALGORITHM 74
5.3.1 APPROXIMATION OF THE COMPLCTE OUTPUT 81
5.3.2 REDUCTION OF SYSTEMS WITH NONLINEAR IN PUT FUNCTIONS 82
5.3.3 SYSTEM-LEVEL SIMULATION 84
5.3.4 COMPUTATIONAL EFFICIENCY 86
5.4 ANIOLDI VERSUS GUYAN VERSUS CONTROL THEORY METHODS 88
5.5 INVCRSE THERMAL PROBLEM VIA MODE! ORDER REDUCTION 91
5.6 SUMMARY 96
6 ADVANCED DEVELOPMENT 97
6.1 ERROR INDICATORS FOR HEAT-TRANSFER MACROMODELIUG OF MEMS 97
6.1.1 CONVERGENCE OF RELATIVE ERROR 99
6.1.2 CONVERGENCE OFLLANKE
L SINGULAR VALUES 107
6.1.3 SEQUENTIAL MODEL ORDER REDUCTION 112
6.1.4 ADVANTAGES AND DISADVANTAGES OF THE PROPOSED STRATEGIES 115
6.2 ORDER REDUCTION OF INTERCONNECTED THERMAL MEMS MODELS 116
6.2.1 MICROHOTPLATE ARRAY 1 IS
6.2.2 BLOCK ARNOLDI 120
6.2.3 COUPLINGOFREDUCE
D ORDER MODELS VIA SUBSTRUCTURING 127
6.2.4 COUPLINGOFREDUCE
D ORDER MODELS IN THE GENERAL CASE 131
6.2.5 OVERVIEW OF PROPOSED STRATEGIES 137
6.3 LATEST RESULTS IN MODEL REDUCTION 137
6.3.1 PARAMETRIC MODEL REDUCTION 138
6.3.2 MODEL REDUCTION FOR SECOND-ORDER SYSTEMS 140
6.3.3 NONLINEAR MODEL REDUCTION 140
6.4 SUMMARY 141
7 REFCRENCES YY 143
8 APPENDIX YY '5
7
8.1 MOR FOR ANSYS 157
8.1.1 BASIC THEORY 158
CONTENTS X
I
8.1.2 PREPARING ANSYS FILES 159
8.1.3 PERFORMING MODEL REDUCTION 162
8.1.4 ADVANCED OPTIONS 163
8.1.5 RUNNING MOR FOR ANSYS: SUMMARY 164
8.1.6 REFERENCES 165
8.2 POST4MOR 166
8.2.1 DYNAMICSYSTEM 166
8.2.2 SIMULATIONRESULT 169
8.2.3 FUNCTIONS FOR TRANSIENT AND HARMONIE SIMULATION 172
8.3 MATHLINK INTERFACE TO SLICOT 173
8.3.1 HOW TO COMPILE THE INTERFACE 174
8.3.2 HOW TO USE THE INTERFACE 174
8.3.3 HOW TO CALL SLICOT 175
INDEX 177 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bechtold, Tamara Rudnyi, Evgenii B. Korvink, Jan G. |
| author_facet | Bechtold, Tamara Rudnyi, Evgenii B. Korvink, Jan G. |
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| discipline | Maschinenbau / Maschinenwesen Technik Elektrotechnik / Elektronik / Nachrichtentechnik |
| discipline_str_mv | Maschinenbau / Maschinenwesen Technik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:22:01Z |
| indexdate | 2024-07-20T09:15:59Z |
| institution | BVB |
| isbn | 9783540346128 3540346120 |
| language | English |
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| oclc_num | 74270477 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-1043 DE-634 DE-83 DE-91 DE-BY-TUM |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-1043 DE-634 DE-83 DE-91 DE-BY-TUM |
| physical | XI, 180 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Microtechnology and MEMS |
| spelling | Bechtold, Tamara Verfasser aut Fast simulation of electro-thermal MEMS efficient dynamic compact models T. Bechtold ; E. B. Rudnyi ; J. G. Korvink Berlin ; Heidelberg ; New York Springer 2007 XI, 180 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Microtechnology and MEMS Literaturverz. S. 143 - 155 Mathematisches Modell Microelectromechanical systems Mathematical models MEMS (DE-588)4824724-8 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Ordnungsreduktion (DE-588)4136085-0 gnd rswk-swf Thermoelektrizität (DE-588)4185148-1 gnd rswk-swf MEMS (DE-588)4824724-8 s Thermoelektrizität (DE-588)4185148-1 s Computersimulation (DE-588)4148259-1 s Ordnungsreduktion (DE-588)4136085-0 s DE-604 Rudnyi, Evgenii B. Verfasser aut Korvink, Jan G. Verfasser aut http://www.gbv.de/dms/ilmenau/toc/516262424becht.PDF Umschlagtext text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2842183&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015619313&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bechtold, Tamara Rudnyi, Evgenii B. Korvink, Jan G. Fast simulation of electro-thermal MEMS efficient dynamic compact models Mathematisches Modell Microelectromechanical systems Mathematical models MEMS (DE-588)4824724-8 gnd Computersimulation (DE-588)4148259-1 gnd Ordnungsreduktion (DE-588)4136085-0 gnd Thermoelektrizität (DE-588)4185148-1 gnd |
| subject_GND | (DE-588)4824724-8 (DE-588)4148259-1 (DE-588)4136085-0 (DE-588)4185148-1 |
| title | Fast simulation of electro-thermal MEMS efficient dynamic compact models |
| title_auth | Fast simulation of electro-thermal MEMS efficient dynamic compact models |
| title_exact_search | Fast simulation of electro-thermal MEMS efficient dynamic compact models |
| title_exact_search_txtP | Fast simulation of electro-thermal MEMS efficient dynamic compact models |
| title_full | Fast simulation of electro-thermal MEMS efficient dynamic compact models T. Bechtold ; E. B. Rudnyi ; J. G. Korvink |
| title_fullStr | Fast simulation of electro-thermal MEMS efficient dynamic compact models T. Bechtold ; E. B. Rudnyi ; J. G. Korvink |
| title_full_unstemmed | Fast simulation of electro-thermal MEMS efficient dynamic compact models T. Bechtold ; E. B. Rudnyi ; J. G. Korvink |
| title_short | Fast simulation of electro-thermal MEMS |
| title_sort | fast simulation of electro thermal mems efficient dynamic compact models |
| title_sub | efficient dynamic compact models |
| topic | Mathematisches Modell Microelectromechanical systems Mathematical models MEMS (DE-588)4824724-8 gnd Computersimulation (DE-588)4148259-1 gnd Ordnungsreduktion (DE-588)4136085-0 gnd Thermoelektrizität (DE-588)4185148-1 gnd |
| topic_facet | Mathematisches Modell Microelectromechanical systems Mathematical models MEMS Computersimulation Ordnungsreduktion Thermoelektrizität |
| url | http://www.gbv.de/dms/ilmenau/toc/516262424becht.PDF http://deposit.dnb.de/cgi-bin/dokserv?id=2842183&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015619313&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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