Theory and applications of the multiwavelets for compression of boundary integral operators

In general the numerical solution of boundary integral equations leads to full coefficientmatrices. The discrete system can be solved in O(N2) operations by iterative solvers ofthe Conjugate Gradient type. Therefore, we are interested in fast methods such as fastmultipole and wavelets, that reduce the computational cost to O(N lnp N).In this thesis we are concerned with wavelet methods. They have proved to be veryefficient and effective basis functions due to the fact that the coefficients of a wavelet expansiondecay rapidly for a large class of functions. Due to the multiresolution propertyof wavelets they provide accurate local descriptions of functions efficiently. For examplein the presence of corners and edges, the functions can still be approximated with a linearcombination of just a few basis functions. Wavelets are attractive for the numericalsolution of integral equations because their vanishing moments property leads to operatorcompression. However, to obtain wavelets with compact support and high order of vanishingmoments, the length of the support increases as the order of the vanishingmomentsincreases. This causes difficulties with the practical use of wavelets particularly at edgesand corners. However, with multiwavelets, an increase in the order of vanishing momentsis obtained not by increasing the support but by increasing the number of mother wavelets.In chapter 2 we review the methods and techniques required for these reformulations,we also discuss how these boundary integral equations may be discretised by a boundaryelement method. In chapter 3, we discuss wavelet and multiwavelet bases. In chapter4, we consider two boundary element methods, namely, the standard and non-standardGalerkin methods with multiwavelet basis functions. For both methods compressionstrategies are developed which only require the computation of the significant matrix elements.We show that they are O(N logp N) such significant elements. In chapters 5 and6 we apply the standard and non-standard Galerkin methods to several test problems

Schnelle Löser für partielle Differentialgleichungen

The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds

Schnelle Löser für Partielle Differentialgleichungen

The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch (Leipzig), and Gabriel Wittum (Frankfurt am Main), was held May 22nd–May 28th, 2011. This meeting was well attended by 54 participants with broad geographic representation from 7 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds

Modelling, Simulation and Data Analysis in Acoustical Problems

Modelling and simulation in acoustics is currently gaining importance. In fact, with the development and improvement of innovative computational techniques and with the growing need for predictive models, an impressive boost has been observed in several research and application areas, such as noise control, indoor acoustics, and industrial applications. This led us to the proposal of a special issue about “Modelling, Simulation and Data Analysis in Acoustical Problems”, as we believe in the importance of these topics in modern acoustics’ studies. In total, 81 papers were submitted and 33 of them were published, with an acceptance rate of 37.5%. According to the number of papers submitted, it can be affirmed that this is a trending topic in the scientific and academic community and this special issue will try to provide a future reference for the research that will be developed in coming years

Time- and frequency-domain modeling of passive interconnection structures in field and circuit analysis

Die vorliegende Arbeit widmet sich den theoretischen Grundlagen und numerischen Verfahren zur Analyse passiver Verbindungsstrukturen auf der Basis der elektromagnetischen Feld- und Netzwerktheorie. Die Simulation elektromagnetischer Phänomene gewinnt eine immer stärkere Bedeutung sowohl im Entwicklungsprozess elektronischer Komponenten und Systeme als auch bei der EMV-Analyse. Ständig steigende Operationsfrequenzen erfordern die Einbeziehung der passiven Verbindungsstrukturen in die Analyse sowohl im Frequenz- als auch im Zeitbereich. Dabei wächst insbesondere die Bedeutung von Zeitbereichsmethoden bei der Behandlung elektrodynamischer Probleme infolge zunehmender Schaltfrequenzen und immer steilerer Anstiegsflanken. Frequenzbereichsmethoden in Kombination mit der Fourierrücktransformation erfordern bei extrem breiten Frequenzspektren einen hohen Rechenaufwand, um Zeitbereichslösungen mit hinreichender Genauigkeit zu erhalten. Im Falle von Nichtlinearitäten sind Zeitbereichsmethoden sogar die einzige Möglichkeit. Aus diesem Grunde wird in der vorliegenden Arbeit ein besonderer Schwerpunkt auf die Zeitbereichsmodellierung der Verbindungsstrukturen einschließlich der Schaltungsumgebung sowie die Behandlung mittels Netzwerksimulatoren gelegt.  Throughout the first period of electrical-engineering history, passive interconnections, i.e., conductors serving as the connection of electronic devices or system components, were typically not considered in the system modeling, except for some special cases and "electrically long" structures, which were successfully described via the transmission-line theory. This changed dramatically after the wide-spread introduction of digital, radio-frequency, and microwave technologies, which required transmission via the passive interconnection structures of high-frequency (HF) signals. The parasitic effects introduced by passive interconnections at high frequencies have motivated modern digital-system designers to consider such interconnections more precisely. &nbsp

Uncertainty modeling : fundamental concepts and models

This book series represents a commendable effort in compiling the latest developments on three important Engineering subjects: discrete modeling, inverse methods, and uncertainty structural integrity. Although academic publications on these subjects are plenty, this book series may be the first time that these modern topics are compiled together, grouped in volumes, and made available for the community. The application of numerical or analytical techniques to model complex Engineering problems, fed by experimental data, usually translated in the form of stochastic information collected from the problem in hand, is much closer to real-world situations than the conventional solution of PDEs. Moreover, inverse problems are becoming almost as common as direct problems, given the need in the industry to maintain current processes working efficiently, as well as to create new solutions based on the immense amount of information available digitally these days. On top of all this, deterministic analysis is slowly giving space to statistically driven structural analysis, delivering upper and lower bound solutions which help immensely the analyst in the decisionmaking process. All these trends have been topics of investigation for decades, and in recent years the application of these methods in the industry proves that they have achieved the necessary maturity to be definitely incorporated into the roster of modern Engineering tools. The present book series fulfills its role by collecting and organizing these topics, found otherwise scattered in the literature and not always accessible to industry. Moreover, many of the chapters compiled in these books present ongoing research topics conducted by capable fellows from academia and research institutes. They contain novel contributions to several investigation fields and constitute therefore a useful source of bibliographical reference and results repository. The Latin American Journal of Solids and Structures (LAJSS) is honored in supporting the publication of this book series, for it contributes academically and carries technologically significant content in the field of structural mechanics