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Modern science utilizes advanced measurement and simulation techniques to analyzephenomena from fields such as medicine, physics, or mechanics. The dataproduced by application of these techniques takes the form of multi-dimensionalfunctions or fields, which have to be processed in order to provide meaningfulparts of the data to domain experts. Definition and implementation of such processingtechniques with the goal to produce visual representations of portions ofthe data are topic of research in scientific visualization or multi-field visualizationin the case of multiple fields.In this thesis, we contribute novel feature extraction and visualization techniquesthat are able to convey data from multiple fields created by scientificsimulations or measurements. Furthermore, our scalar-, vector-, and tensor fieldprocessing techniques contribute to scattered field processing in general and introducenovel ways of analyzing and processing tensorial quantities such as strainand displacement in flow fields, providing insights into field topology.We introduce novel mesh-free extraction techniques for visualization of complexvaluedscalar fields in acoustics that aid in understanding wave topology in lowfrequency sound simulations. The resulting structures represent regions withlocally minimal sound amplitude and convey wave node evolution and soundcancellation in time-varying sound pressure fields, which is considered an importantfeature in acoustics design.Furthermore, methods for flow field feature extraction are presented that facilitateanalysis of velocity and strain field properties by visualizing deformation ofinfinitesimal Lagrangian particles and macroscopic deformation of surfaces andvolumes in flow. The resulting adaptive manifolds are used to perform flow fieldsegmentation which supports multi-field visualization by selective visualizationof scalar flow quantities.The effects of continuum displacement in scattered moment tensor fields can bestudied by a novel method for multi-field visualization presented in this thesis.The visualization method demonstrates the benefit of clustering and separateviews for the visualization of multiple fields.