1,721,015 research outputs found
Analytic regularity and gpc approximation for control problems constrained by linear parametric elliptic and parabolic PDEs
No full text1 online resource (PDF, 23 pages)Kunoth, Angela; Schwab, Christoph. (2011). Analytic regularity and gpc approximation for control problems constrained by linear parametric elliptic and parabolic PDEs. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/181126
Multiscale methods for the valuation of American options with stochastic volatility
No full text1 online resource (PDF, 20 pages, includes illustrations)Kunoth, Angela; Schneider, Christian; Wiechers, Katharina. (2011). Multiscale methods for the valuation of American options with stochastic volatility. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/181132
An optimization based empirical mode decomposition scheme
No full text1 online resource (PDF, 14 pages, includes illustrations)Huang, Boqiang; Kunoth, Angela. (2012). An optimization based empirical mode decomposition scheme. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/181198
Multiskalen-basierte Finite-Differenzen-Verfahren auf adaptiven dünnen Gittern
Get PDFIn der Arbeit werden Lösungsverfahren für partielle Differential- gleichungen vorgestellt, die auf Multiskalen-Ansatzfunktionen (Wavelets) basieren. Zur adaptiven Approximation der numerischen Lösung werden anisotrope Tensorprodukte von Verallgemeinerungen der Hierarchischen Basis (Interpolets) benutzt. Diese erlauben eine sehr effiziente Approximation von Funktionen, z.B. Funktionen mit beschränkter gemischter Ableitung. Weiterhin ist eine einfache Transformation zwischen Knotenwerten bzgl. eines adaptiven Gitters und der Multiskalendarstellung möglich. Für die Diskretisierung von Differentialoperatoren werden ein spezielles biorthogonales Petrov-Galerkin--Verfahren und Finite Differenzen-Verfahren betrachtet. Erstmalig wird für diese Diskretisierungen eine allgemeine Konvergenztheorie angegeben, die auch den adaptiven Fall abdeckt. Dabei wird der Konvergenzfehler über einen Approximationsfehler und einen Konsistenzfehler abgeschätzt. Für den Fall spezieller an die Lösung angepasster adaptiver Basen werden für den Konsistenzfehler a priori Schranken angegeben. Ein weiterer Schwerpunkt ist das schnelle Lösen der bei obiger Diskretisierung entstehenden linearen Gleichungssysteme. Es werden zwei sehr effiziente Vorkonditionier vorgestellt und analysiert, wobei einer auf dem Lifting-Schema basiert. Mit diesem erhält man Konditionszahlen, die unabhängig von der feinsten Maschenweite beschränkt sind. Das Lösungsverfahren wird auf eine Reihe von Testproblemen angewandt, z.B. die adaptive Simulation von zwei- bzw. drei-dimensionalen turbulenten Scherschichten
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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Mini-Workshop: Adaptive Methods for Control Problems Constrained by Time-Dependent PDEs
Get PDFOptimization problems constrained by time-dependent PDEs (Partial Differential Equations) are challenging from a computational point of view: even in the simplest case, one needs to solve a system of PDEs coupled globally in time and space for the unknown solutions (the state, the costate and the control of the system). Typical and practically relevant examples are the control of nonlinear heat equations as they appear in laser hardening or the thermic control of flow problems (Boussinesq equations). Specifically for PDEs with a long time horizon, conventional time-stepping methods require an enormous storage of the respective other variables. In contrast, adaptive methods aim at distributing the available degrees of freedom in an a-posteriori-fashion to capture singularities and are, therefore, most promising
Mini-Workshop: Adaptive Methods for Control Problems Constrained by Time-Dependent PDEs
No full textOptimization problems constrained by time-dependent PDEs (Partial Differential Equations) are challenging from a computational point of view: even in the simplest case, one needs to solve a system of PDEs coupled globally in time and space for the unknown solutions (the state, the costate and the control of the system). Typical and practically relevant examples are the control of nonlinear heat equations as they appear in laser hardening or the thermic control of flow problems (Boussinesq equations). Specifically for PDEs with a long time horizon, conventional time-stepping methods require an enormous storage of the respective other variables. In contrast, adaptive methods aim at distributing the available degrees of freedom in an a-posteriori-fashion to capture singularities and are, therefore, most promising
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Fast Optimised Wavelet Methods for Control Problems Constrained by Elliptic PDEs
Get PDFIn this thesis, a wavelet method for the numerical solution of an optimal control problem constrained by a linear elliptic partial differential equation is developed. The particular challenge here lies in considering and combining two areas of research, namely the efficient solution of an elliptic partial differential equation (shortly PDE) on the one hand and an optimisation problem specified by an objective functional and PDE constraints on the other. To cope with the finite amount of computer memory, the problem needs to be discretised. Already for the numerical solution of a single PDE, this gives rise to a large and ill-conditioned sparse linear system of equations, which necessitates the use of iterative solvers combined with suitable preconditioning techniques. The reformulation of the control problem in terms of a Lagrangian functional leads to a coupled system of PDEs. Its iterative solution requires repeated solutions of a single PDE in inner loops, such that the computation time is multiplied accordingly. Moreover, the introduction of control and adjoint variables leads to a significant increase of the memory requirements. Here we address these difficulties in a unified way by the systematic use of biorthogonal B-spline wavelet bases, which results in optimally preconditioned operators. Therefore, iterative solution schemes such as the method of conjugate gradients need only a constant amount of iterations to reduce the error by a fixed factor. The introduction of specific transformations additionally improves the condition numbers of the wavelet bases and the discretised differential operators, which leads to a significant speedup of the computations. Furthermore, the wavelet framework permits the numerical evaluation of fractional Sobolev norms in the objective functional by means of Riesz matrices, for which we present a novel construction which yields exact results for a wider range of functions and smoothness indices than the currently used approaches. To construct an algorithm of optimal computational complexity, that is, with a runtime proportional to the number of unknowns, we design a two-layer nested iteration strategy and combine it with an inner-outer conjugate gradient scheme, employing specifically balanced error tolerances and stopping criteria. An adaptive variant of the algorithm is devised by the incorporation of routines which have been recently proposed as part of adaptive wavelet methods for elliptic PDEs and nonlinear variational problems. This ansatz allows for different distributions of active wavelet coefficients for the state, adjoint and control variables. Extensive parameter studies are presented for both uniform and adaptive discretisations. It is demonstrated that the freedom in modelling introduced by the enhanced construction of Riesz operators allows to influence the character of the state and the control by varying the Sobolev norms in the objective functional. The algorithm is indeed of optimal linear computational complexity. Moreover, we verify that the adaptive scheme leads to a considerable reduction of active wavelet coefficients and a slightly superlinear rate of convergence
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