{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:1914"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:1914","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Model order reduction of electro-thermal MEMS","abstract":"The modeling of electro-thermal processes, for example Joule heating, is becoming increasingly important in microsystems (in the following MEMS) development. In microelectronic systems, for example, high temperatures may cause the malfunction or even destruction of the device. Other devices, such as microsensors and microactuators need high temperatures to improve transduction efficiency. In both cases the designer should be able to predict the temperature distribution for the given electrical input and the impact of the temperature on the devices electronics in turn. In other words, one must run a joint electro-thermal simulation. <br>Conventionally, in each sequence of electro-thermal simulation the temperature field is computed on a discrete grid whose size, due to increasingly complex microstructures, easily exceeds 100,000 degrees of freedom (DOF), i. e. ordinary differential equations. Although modern computers are able to handle engineering problems of this size, the system-level simulation would become prohibitive if full models were directly used. Hence, the reduction of the problem's size is the first milestone of efficient MEMS modeling and simulation. <br>This thesis presents the application of mathematical model order reduction (MOR) methods (preferably Arnoldi algorithm) to the automatic generation of accurate dynamic compact thermal models (DCTM) of electro-thermal microsystems. Unlike conventional approaches to DCTM, which are based on the lumped-element decomposition of the model followed by parameter fitting, mathematical MOR is formal, robust and can be made fully automated. The reduced order models can be formally converted into Hardware Description Language (HDL) form and directly used in system-level simulation. <br>The results obtained in this thesis led to the creation of the software tool mor4ansys at the chair for simulation of the university of Freiburg. Presently it is possible to use mor4ansys to automatically create reduced order thermal models (with approximately 50 DOF) directly from ANSYS models (with more than 100,000 DOF). <br>In this work we apply model order reduction to successfully create dynamic compact thermal models of several novel MEMS devices. We consider the different aspects of the Arnoldi algorithm which make it stand out against other linear MOR methods, such as the approximation of the complete output and the reduction of weekly nonlinear systems. We propose three heuristic methods to estimate the error of Arnoldi-based reduction. We present and apply two methods for model order reduction of thermal MEMS-array structures, namely Block Arnoldi and Guyan-based substructuring and describe a general technique of coupling two reduced thermal models via surface fluxes.","abstract_html":"The modeling of electro-thermal processes, for example Joule heating, is becoming increasingly important in microsystems (in the following MEMS) development. In microelectronic systems, for example, high temperatures may cause the malfunction or even destruction of the device. Other devices, such as microsensors and microactuators need high temperatures to improve transduction efficiency. In both cases the designer should be able to predict the temperature distribution for the given electrical input and the impact of the temperature on the devices electronics in turn. In other words, one must run a joint electro-thermal simulation. &lt;br&gt;Conventionally, in each sequence of electro-thermal simulation the temperature field is computed on a discrete grid whose size, due to increasingly complex microstructures, easily exceeds 100,000 degrees of freedom (DOF), i. e. ordinary differential equations. Although modern computers are able to handle engineering problems of this size, the system-level simulation would become prohibitive if full models were directly used. Hence, the reduction of the problem&#x27;s size is the first milestone of efficient MEMS modeling and simulation. &lt;br&gt;This thesis presents the application of mathematical model order reduction (MOR) methods (preferably Arnoldi algorithm) to the automatic generation of accurate dynamic compact thermal models (DCTM) of electro-thermal microsystems. Unlike conventional approaches to DCTM, which are based on the lumped-element decomposition of the model followed by parameter fitting, mathematical MOR is formal, robust and can be made fully automated. The reduced order models can be formally converted into Hardware Description Language (HDL) form and directly used in system-level simulation. &lt;br&gt;The results obtained in this thesis led to the creation of the software tool mor4ansys at the chair for simulation of the university of Freiburg. Presently it is possible to use mor4ansys to automatically create reduced order thermal models (with approximately 50 DOF) directly from ANSYS models (with more than 100,000 DOF). &lt;br&gt;In this work we apply model order reduction to successfully create dynamic compact thermal models of several novel MEMS devices. We consider the different aspects of the Arnoldi algorithm which make it stand out against other linear MOR methods, such as the approximation of the complete output and the reduction of weekly nonlinear systems. We propose three heuristic methods to estimate the error of Arnoldi-based reduction. We present and apply two methods for model order reduction of thermal MEMS-array structures, namely Block Arnoldi and Guyan-based substructuring and describe a general technique of coupling two reduced thermal models via surface fluxes.","abstract_has_math":false,"creators":["Bechtold, Tamara"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Korvink, Jan G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:22:33Z","subjects":["elektro-thermische modelle","Arnoldi Algorithmus","Order reduction, MEMS","compact modeling","Arnoldi algorithm","electro-thermal"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/1914","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Korvink, Jan G."]},{"key":"dc:creator","label":"Author","values":["Bechtold, Tamara"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["elektro-thermische modelle","Arnoldi Algorithmus","Order reduction, MEMS","compact modeling","Arnoldi algorithm","electro-thermal"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The modeling of electro-thermal processes, for example Joule heating, is becoming increasingly important in microsystems (in the following MEMS) development. In microelectronic systems, for example, high temperatures may cause the malfunction or even destruction of the device. Other devices, such as microsensors and microactuators need high temperatures to improve transduction efficiency. In both cases the designer should be able to predict the temperature distribution for the given electrical input and the impact of the temperature on the devices electronics in turn. In other words, one must run a joint electro-thermal simulation. <br>Conventionally, in each sequence of electro-thermal simulation the temperature field is computed on a discrete grid whose size, due to increasingly complex microstructures, easily exceeds 100,000 degrees of freedom (DOF), i. e. ordinary differential equations. Although modern computers are able to handle engineering problems of this size, the system-level simulation would become prohibitive if full models were directly used. Hence, the reduction of the problem's size is the first milestone of efficient MEMS modeling and simulation. <br>This thesis presents the application of mathematical model order reduction (MOR) methods (preferably Arnoldi algorithm) to the automatic generation of accurate dynamic compact thermal models (DCTM) of electro-thermal microsystems. Unlike conventional approaches to DCTM, which are based on the lumped-element decomposition of the model followed by parameter fitting, mathematical MOR is formal, robust and can be made fully automated. The reduced order models can be formally converted into Hardware Description Language (HDL) form and directly used in system-level simulation. <br>The results obtained in this thesis led to the creation of the software tool mor4ansys at the chair for simulation of the university of Freiburg. Presently it is possible to use mor4ansys to automatically create reduced order thermal models (with approximately 50 DOF) directly from ANSYS models (with more than 100,000 DOF). <br>In this work we apply model order reduction to successfully create dynamic compact thermal models of several novel MEMS devices. We consider the different aspects of the Arnoldi algorithm which make it stand out against other linear MOR methods, such as the approximation of the complete output and the reduction of weekly nonlinear systems. We propose three heuristic methods to estimate the error of Arnoldi-based reduction. We present and apply two methods for model order reduction of thermal MEMS-array structures, namely Block Arnoldi and Guyan-based substructuring and describe a general technique of coupling two reduced thermal models via surface fluxes.","Die Modellierung elektro-thermischer Prozesse, wie z.B. Joule'sche Wärmegenerierung, gewinnt zunehmend an Bedeutung in der Entwicklung von Mikrosystemen (im Folgenden MEMS genannt). In mikroelektronischen Systemen können hohe Temperaturen Fehlfunktionen verursachen oder sogar zur Zerstörung des Bauelements führen. Andere Komponenten, wie Mikrosensoren oder -aktoren, benötigen hohe Temperaturen zur Verbesserung ihrer Energiewandlungseigenschaften. In beiden Fällen sollte der Designer in der Lage sein, für vorgegebene elektrische Eingangsleistung die Temperaturverteilung sowie den Einfluss der Temperatur auf die Elektronik zu bestimmen. In anderen Worten, er muss eine elektro-thermische Simulation durchführen. In jedem Iterationsschritt einer konventionellen elektro-thermischen Simulation wird die Temperaturverteilung auf einem diskreten Gitter berechnet. Aufgrund der zunehmenden Komplexität von Mikrostrukturen übersteigt die Größe solcher Gitter (bzw. Anzahl der Differentialgleichungen) leicht 100 000. Obwohl moderne Computer in der Lage sind Probleme dieser Größe zu lösen, ist eine Simulation von solchen Modellen auf Systemebene kaum möglich. Die Reduktion der Modellgröße stellt demnach einen Meilenstein zur effizienten Modellierung und Simulation von (nicht nur elektro-thermischen) MEMS dar. <br>Die vorliegende Arbeit stellt die Anwendung mathematischer Methoden zur Modellordnungsreduktion (MOR) (vorzugsweise den Arnoldi Algorithmus) zur automatischen Generierung von präzisen kompakten dynamisch-thermischen Modellen (DCTM) von elektro-thermischen Mikrosystemen vor. Alternativ zu konventionellen Verfahren zur Erzeugung von DCTM, welche auf dem Erstellen eines Ersatzschaltbildes mit anschließender Parameteroptimierung beruhen, stellt die mathematische MOR einen formalen, robusten und vollständig automatisierbaren Weg dar. Die reduzierten Modelle lassen sich in eine Hardware-Beschreibungssprache (HDL) konvertieren und sind somit in einer Simulation auf Systemebene nutzbar. <br>Die in dieser Arbeit erzielten Ergebnisse führten am Lehrstuhl für Simulation der Universität Freiburg zur Erstellung des Software-Pakets mor4ansys. Gegenwärtig ist es möglich, mor4ansys zur automatischen Erstellung von kompakten thermischen Modellen (mit ungefähr 50 Freiheitsgraden) direkt aus ANSYS Modellen (mit mehr als 100.000 Freiheitsgraden) zu verwenden. <br>Wir haben die Modellordnungsreduktion erfolgreich auf die Erstellung von kompakten dynamisch-thermischen Modellen von mehreren neuen MEMS Komponenten angewandt. Weiterhin haben wir verschiedene Aspekte des Arnoldi-Algorithmus, wie die Approximation des gesamten Temperaturfeldes und die Reduktion von schwach nichtlinearen Systemen, welche ihn von anderen linearen MOR-Methoden abheben, untersucht. Wir haben drei heuristische Methoden zur Abschätzung des Fehlers der Arnoldi-Reduktion vorgeschlagen. Letztendlich haben wir zwei Methoden zur Modellordnungsreduktion von thermischen MEMS-Arrays präsentiert and angewandt. Diese sind Block-Arnoldi und Guyan-basierte Unterteilung (implementiert unter dem Namen substructuring in ANSYS Simulator). Wir haben weiterhin, einen generellen Weg zur Kopplung von reduzierten thermischen Modellen über die Oberflächenflüsse beschrieben."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Model order reduction of electro-thermal MEMS","Ordnungsreduktion von elektro-thermischen MEMS Modellen"]}]}],"canonical_facts":{"dc:contributor":["Korvink, Jan G."],"dc:creator":["Bechtold, Tamara"],"dc:description.abstract":["The modeling of electro-thermal processes, for example Joule heating, is becoming increasingly important in microsystems (in the following MEMS) development. In microelectronic systems, for example, high temperatures may cause the malfunction or even destruction of the device. Other devices, such as microsensors and microactuators need high temperatures to improve transduction efficiency. In both cases the designer should be able to predict the temperature distribution for the given electrical input and the impact of the temperature on the devices electronics in turn. In other words, one must run a joint electro-thermal simulation. <br>Conventionally, in each sequence of electro-thermal simulation the temperature field is computed on a discrete grid whose size, due to increasingly complex microstructures, easily exceeds 100,000 degrees of freedom (DOF), i. e. ordinary differential equations. Although modern computers are able to handle engineering problems of this size, the system-level simulation would become prohibitive if full models were directly used. Hence, the reduction of the problem's size is the first milestone of efficient MEMS modeling and simulation. <br>This thesis presents the application of mathematical model order reduction (MOR) methods (preferably Arnoldi algorithm) to the automatic generation of accurate dynamic compact thermal models (DCTM) of electro-thermal microsystems. Unlike conventional approaches to DCTM, which are based on the lumped-element decomposition of the model followed by parameter fitting, mathematical MOR is formal, robust and can be made fully automated. The reduced order models can be formally converted into Hardware Description Language (HDL) form and directly used in system-level simulation. <br>The results obtained in this thesis led to the creation of the software tool mor4ansys at the chair for simulation of the university of Freiburg. Presently it is possible to use mor4ansys to automatically create reduced order thermal models (with approximately 50 DOF) directly from ANSYS models (with more than 100,000 DOF). <br>In this work we apply model order reduction to successfully create dynamic compact thermal models of several novel MEMS devices. We consider the different aspects of the Arnoldi algorithm which make it stand out against other linear MOR methods, such as the approximation of the complete output and the reduction of weekly nonlinear systems. We propose three heuristic methods to estimate the error of Arnoldi-based reduction. We present and apply two methods for model order reduction of thermal MEMS-array structures, namely Block Arnoldi and Guyan-based substructuring and describe a general technique of coupling two reduced thermal models via surface fluxes.","Die Modellierung elektro-thermischer Prozesse, wie z.B. Joule'sche Wärmegenerierung, gewinnt zunehmend an Bedeutung in der Entwicklung von Mikrosystemen (im Folgenden MEMS genannt). In mikroelektronischen Systemen können hohe Temperaturen Fehlfunktionen verursachen oder sogar zur Zerstörung des Bauelements führen. Andere Komponenten, wie Mikrosensoren oder -aktoren, benötigen hohe Temperaturen zur Verbesserung ihrer Energiewandlungseigenschaften. In beiden Fällen sollte der Designer in der Lage sein, für vorgegebene elektrische Eingangsleistung die Temperaturverteilung sowie den Einfluss der Temperatur auf die Elektronik zu bestimmen. In anderen Worten, er muss eine elektro-thermische Simulation durchführen. In jedem Iterationsschritt einer konventionellen elektro-thermischen Simulation wird die Temperaturverteilung auf einem diskreten Gitter berechnet. Aufgrund der zunehmenden Komplexität von Mikrostrukturen übersteigt die Größe solcher Gitter (bzw. Anzahl der Differentialgleichungen) leicht 100 000. Obwohl moderne Computer in der Lage sind Probleme dieser Größe zu lösen, ist eine Simulation von solchen Modellen auf Systemebene kaum möglich. Die Reduktion der Modellgröße stellt demnach einen Meilenstein zur effizienten Modellierung und Simulation von (nicht nur elektro-thermischen) MEMS dar. <br>Die vorliegende Arbeit stellt die Anwendung mathematischer Methoden zur Modellordnungsreduktion (MOR) (vorzugsweise den Arnoldi Algorithmus) zur automatischen Generierung von präzisen kompakten dynamisch-thermischen Modellen (DCTM) von elektro-thermischen Mikrosystemen vor. Alternativ zu konventionellen Verfahren zur Erzeugung von DCTM, welche auf dem Erstellen eines Ersatzschaltbildes mit anschließender Parameteroptimierung beruhen, stellt die mathematische MOR einen formalen, robusten und vollständig automatisierbaren Weg dar. Die reduzierten Modelle lassen sich in eine Hardware-Beschreibungssprache (HDL) konvertieren und sind somit in einer Simulation auf Systemebene nutzbar. <br>Die in dieser Arbeit erzielten Ergebnisse führten am Lehrstuhl für Simulation der Universität Freiburg zur Erstellung des Software-Pakets mor4ansys. Gegenwärtig ist es möglich, mor4ansys zur automatischen Erstellung von kompakten thermischen Modellen (mit ungefähr 50 Freiheitsgraden) direkt aus ANSYS Modellen (mit mehr als 100.000 Freiheitsgraden) zu verwenden. <br>Wir haben die Modellordnungsreduktion erfolgreich auf die Erstellung von kompakten dynamisch-thermischen Modellen von mehreren neuen MEMS Komponenten angewandt. Weiterhin haben wir verschiedene Aspekte des Arnoldi-Algorithmus, wie die Approximation des gesamten Temperaturfeldes und die Reduktion von schwach nichtlinearen Systemen, welche ihn von anderen linearen MOR-Methoden abheben, untersucht. Wir haben drei heuristische Methoden zur Abschätzung des Fehlers der Arnoldi-Reduktion vorgeschlagen. Letztendlich haben wir zwei Methoden zur Modellordnungsreduktion von thermischen MEMS-Arrays präsentiert and angewandt. Diese sind Block-Arnoldi und Guyan-basierte Unterteilung (implementiert unter dem Namen substructuring in ANSYS Simulator). Wir haben weiterhin, einen generellen Weg zur Kopplung von reduzierten thermischen Modellen über die Oberflächenflüsse beschrieben."],"dc:format.medium":["application/pdf"],"dc:subject":["elektro-thermische modelle","Arnoldi Algorithmus","Order reduction, MEMS","compact modeling","Arnoldi algorithm","electro-thermal"],"dc:title":["Model order reduction of electro-thermal MEMS","Ordnungsreduktion von elektro-thermischen MEMS Modellen"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:22:33Z"}