920 research outputs found
Optimal convergence rates of an adaptive hybrid FEM-BEM method for full-space linear transmission problems
No full textWe consider a hybrid FEM-BEM method to compute approximations of full space linear elliptic transmission problems. First, we derive a priori and a posteriori error estimates. Then, building on the latter, we present an adaptive algorithm and prove that it converges at optimal rates with respect to the number of mesh elements. Finally, we provide numerical experiments, demonstrating the practical performance of the adaptive algorithm
The piano music by Čestmír Gregor
Get PDFIn my thesis, I introduce a complete list of piano works by Cestmír Gregor, a contemporary Czech composer of modern classical music. 1 have tried to define his compositional techniques and sources of inspiration by analysing the individual pieces of music. I have found that the major features of the author's highly unique style are polyphonic thinking, the development of motives from small nuclei, expressive themes, plastic tunes, inventive work with rhythm, and the absence of a tonal centre which he compensates for by distinctive melodies . The author finds his inspiration in folklore, especially Moravian (Leoš Janácek), the works of Czech interwar avantgarde (Pavel Borkovec) and in jazz (Jaroslav Ježek). His music reflects the emotional states of a man living in the twenty-first century whose life style is predominantly determined by an urban environment. Gregor does not use any of the Musica Nova theories, instead he founded his own music language. The basis for his compositions is communicative music, which follows the patterns of human perceptive psychology. Gregor's concertant compositions are typical for a new instrument stylization and nontraditional attitudes towards instrument virtuosity (playing with a palm, elbow; an unconventional fingering). His piano sonatas and concerts enable the..
Čestmír Gregor: The Piano Compositions of the Composer
Get PDFIn my thesis, I introduce a complete list of piano works by Čestmír Gregor, a contemporary Czech composer of modern classical music. 1 have tried to define his compositional techniques and sources of inspiration by analysing the individual pieces of music. I have found that the major features of the author's highly unique style are polyphonic thinking, the development of motives from small nuclei, expressive themes, plastic tunes, inventive work with rhythm, and the absence of a tonal centre which he compensates for by distinctive melodies . The author finds his inspiration in folklore, especially Moravian (Leoš Janáček), the works of Czech interwar avantgardě (Pavel Borkovec) and in jazz (Jaroslav Ježek). His music reflects the emotional states of a man living in the twenty-first century whose life style is predominantly determined by an urban environment. Gregor does not use any of the Musica Nova theories, instead he founded his own music language. The basis for his compositions is communicative music, which follows the patterns of human perceptive psychology. Gregor's concertant compositions are typical for a new instrument stylization and nontraditional attitudes towards instrument virtuosity (playing with a palm, elbow; an unconventional fingering). His piano sonatas and concerts enable the..
IGABEM2D
No full textThis MATLAB library implements adaptive isogeometric boundary element methods in 2D for the weakly-singular integral equation and the hyper-singular integral equation. Practical and theoretical details on the implementation are found in the accompanying paper [Gantner, Praetorius, Schimanko, Stable implementation of adaptive IGABEM in 2D in MATLAB, 2022]
Adaptive isogeometric methods with optimal convergence rates
No full textThe CAD standard for spline representation in 2D or 3D relies on tensor-product splines.
To allow for adaptive refinement, several extensions have emerged, e.g., analysis-suitable T-splines, hierarchical splines, or LR-splines.
All these concepts have been studied via numerical experiments.
However, so far there exists only little literature concerning the thorough analysis of adaptive isogeometric finite element methods (IGAFEMs).
[Buffa, Giannelli, Math. Mod. Meth. Appl. S. 26 (2016)] investigates linear convergence of an IGAFEM with truncated hierarchical B-splines, where optimal convergence of the proposed algorithm was only recently proved in [Buffa, Giannelli, Math. Mod. Meth. Appl. S. 27 (2017)] .
This talk is based on our recent work [Gantner, Haberlik, Praetorius, Math. Mod. Meth. Appl. S. 27 (2017)] .
We consider an adaptive IGAFEM for second-order linear elliptic PDEs.
We employ hierarchical B-splines.
We propose a refinement strategy to generate a sequence of locally refined meshes and corresponding discrete solutions, where adaptivity is driven by some weighted-residual a posteriori error estimator.
The adaptive algorithm guarantees linear convergence of the error estimator (or equivalently: energy error plus data oscillations) with optimal algebraic rates.
Unlike our strategy, the algorithm of [Buffa, Giannelli, Math. Mod. Meth. Appl. S. 26 (2016)] was designed for truncated hierarchical B-splines only and the use of hierarchical B-splines may lead to non-sparse Galerkin matrices.
Further, the analysis of [Buffa, Giannelli, Math. Mod. Meth. Appl. S. 27 (2017)] which appeared independently of [Gantner, Haberlik, Praetorius, Math. Mod. Meth. Appl. S. 27 (2017)] is restricted to symmetric PDEs.
Similar results were also obtained for an adaptive 3D boundary element method in [Gantner, PhD thesis, TU Wien (2017)]
Applications of a space-time FOSLS formulation for parabolic PDEs
Get PDFAbstractIn this work, we show that the space-time first-order system least-squares formulation (Führer, T. & Karkulik, M. (2021) Space–time least-squares finite elements for parabolic equations. Comput. Math. Appl.92, 27–36) for the heat equation and its recent generalization (Gantner, G. & Stevenson, R. (2021) Further results on a space-time FOSLS formulation of parabolic PDEs. ESAIM Math. Model. Numer. Anal.55, 283–299) to arbitrary second-order parabolic partial differential equations can be used to efficiently solve parameter-dependent problems, optimal control problems and problems on time-dependent spatial domains.</jats:p
Gregor Piatigorsky
No full textIn this Master disertation, the author talks about the life and career of a legendary virtuoso cellist Gregor Piatigorsky. Gregor Piatigorsky is one of the most important figures in the history of cello. Piatigorsky has not only achieved an incredible solo career, but as a teacher he also raised a large number of great cellists and cello teachers of today. Among his most famous pupil are Mischa Maisky, Steven Isserlis or Raphael Wallfish. Disertation also includes authors own experience with teaching of Laurence Lesser, who was an assistant of Piatigorsky for almost 7 years, and whose style of teaching is nearly the same as Piatigorsky's
Statewide congestion overview
No full textprepared by Oregon Department of Transportation, Transportation Planning Analysis Unit ; principal author: Brian Gregor ; staff support: Michal Wert, MW Consulting.Title from PDF title page.Covers OCLC #1390891081, OCLC #1378912112, OCLC #1201266716, and OCLC #1201266486.This archived document is maintained by the State Library of Oregon as part of the Oregon Documents Depository Program. It is for informational purposes and may not be suitable for legal purposes.Includes bibliographical references.Mode of access: Internet from the Oregon Government Publications Collection.Text in English
Rate optimal adaptive FEM with inexact solver for nonlinear operators
No full textWe present our recent work [Gantner et al., IMA J Numer Anal 38, 2018], where we prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. We consider an algorithm proposed by [Congreve et al., J Comp Appl Math 311, 2017]. Unlike prior works, e.g., [Carstensen et al., Comp Math Appl 67, 2014], our analysis also includes the iterative and inexact solution of the arising nonlinear systems by means of the Picard iteration. Using nested iteration, we prove, in particular, that the number of Picard iterations is uniformly bounded in generic cases. Finally, we aim to discuss that the overall computational cost is optimal. Numerical experiments confirm the theoretical results
Axioms of adaptivity revisited: Optimal adaptive IGAFEM
No full textThe axioms of adaptivity from [C. Carstensen, M. Feischl, M. Page, D. Praetorius. Axioms of adaptivity. Computers & Mathematics with Applications, 67, 1195-1253, 2014] analyze under which assumptions on the a posteriori error estimator and the mesh-refinement strategy, a mesh re fining adaptive algorithm yields convergence with optimal algebraic rates. In our talk, which is based on our recent work [G. Gantner, D. Haberlik, D. Praetorius. Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines. Mathematical Models and Methods in Applied Sciences, 27, 2631-2674, 2017], we now address the question which properties of the FEM are sufficient to ensure that the usual weighted-residual error estimator is well-defined and satisfies the axioms of adaptivity. In particular, our analysis covers conforming FEM in the framework of isogeometric analysis with hierarchical splines
- …
