Browsing by Author "Kaltenbacher, Barbara"

Now showing 1 - 5 of 5
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    Computational Inverse Problems
    (Zürich : EMS Publ. House, 2012) Borcea, Liliana; Hohage, Thorsten; Kaltenbacher, Barbara
    Inverse problem typically deal with the identification of unknown quantities from indirect measurements and appear in many areas in technology, medicine, biology, finance, and econometrics. The computational solution of such problems is a very active, interdisciplinary field with close connections to optimization, control theory, differential equations, asymptotic analysis, statistics, and probability. The focus of this workshop was on hybrid methods, model reduction, regularization in Banach spaces, and statistical approaches.
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    Computational Inverse Problems for Partial Differential Equations
    (Zürich : EMS Publ. House, 2017) Hohage, Thorsten; Kaltenbacher, Barbara
    The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges.
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    Computational Inverse Problems for Partial Differential Equations (hybrid meeting)
    (Zürich : EMS Publ. House, 2020) Hohage, Thorsten; Kaltenbacher, Barbara
    Inverse problems in partial differential equations (PDEs) consist in reconstructing some part of a PDE such as a coefficient, a boundary condition, an initial condition, the shape of a domain, or a singularity from partial knowledge of solutions to the PDE. This has numerous applications in nondestructive testing, medical imaging, seismology, and optical imaging. Whereas classically mostly boundary or far field data of solutions to deterministic PDEs were considered, more recently also statistical properties of solutions to random PDEs have been studied. The study of numerical reconstruction methods of inverse problems in PDEs is at the interface of numerical analysis, PDE theory, functional analysis, statistics, optimization, and differential geometry. This workshop has mainly addressed five related topics of current interest: model reduction, control-based techniques in inverse problems, imaging with correlation data of waves, fractional diffusion, and model-based approaches using machine learning.
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    The Mathematics of Fluids and Solids
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2019) Kaltenbacher, Barbara; Kukavica, Igor; Lasiecka, Irena; Triggiani, Roberto; Tuffaha, Amjad; Webster, Justin
    Fluid-structure interaction is a rich and active field of mathematics that studies the interaction between fluids and solid objects. In this short article, we give a glimpse into this exciting field, as well as a sample of the most significant questions that mathematicians try to answer.
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    Nonlinear Acoustics
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2019) Kaltenbacher, Barbara; Brunnhuber, Rainer
    Nonlinear acoustics has been a topic of research for more than 250 years. Driven by a wide range and a large number of highly relevant industrial and medical applications, this area has expanded enormously in the last few decades. Here, we would like to give a glimpse of the mathematical modeling techniques that are commonly employed to tackle problems in this area of research, with a selection of references for the interested reader to further their knowledge into this mathematically interesting field.