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  • 2010-2014  (4)
  • 2000-2004
  • 2010  (4)
  • English  (4)
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  • 2010-2014  (4)
  • 2000-2004
Year
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  • 1
    Book
    Book
    Berlin [u.a.] :Springer,
    Title: Algorithms - ESA 2010 /; ...
    Contributer: Berg, Mark de , Meyer, Ulrich , ESA 〈18, 2010, Liverpool〉
    Publisher: Berlin [u.a.] :Springer,
    Year of publication: 2010
    Series Statement: Lecture notes in computer science ...
    Type of Medium: Book
    Language: English
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  • 2
    Publication Date: 2016-06-09
    Description: The paper considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter-example of Serrin, it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia and the two notions of solutions of Casas and Alibert-Raymond, and show that they are the same. As side results, we reformulate the solution in the sense of Stampacchia, and prove the existence and uniqueness of solutions in in case of mixed boundary conditions.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 3
    Publication Date: 2022-07-19
    Language: English
    Type: article , doc-type:article
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  • 4
    Publication Date: 2022-07-19
    Description: We present a visual approach for the exploration of stress tensor fields. Therefore, we introduce the idea of multiple linked views to tensor visualization. In contrast to common tensor visualization methods that only provide a single view to the tensor field, we pursue the idea of providing various perspectives onto the data in attribute and object space. Especially in the context of stress tensors, advanced tensor visualization methods have a young tradition. Thus, we propose a combination of visualization techniques domain experts are used to with statistical views of tensor attributes. The application of this concept to tensor fields was achieved by extending the notion of shape space. It provides an intuitive way of finding tensor invariants that represent relevant physical properties. Using brushing techniques, the user can select features in attribute space, which are mapped to displayable entities in a three-dimensional hybrid visualization in object space. Volume rendering serves as context, while glyphs encode the whole tensor information in focus regions. Tensorlines can be included to emphasize directionally coherent features in the tensor field. We show that the benefit of such a multi-perspective approach is manifold. Foremost, it provides easy access to the complexity of tensor data. Moreover, including wellknown analysis tools, such as Mohr diagrams, users can familiarize themselves gradually with novel visualization methods. Finally, by employing a focus-driven hybrid rendering, we significantly reduce clutter, which was a major problem of other three-dimensional tensor visualization methods.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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