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62
A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part II: Implementation and Tests in DUNE
, 2007
"... In a companion paper [5] we introduced an abstract definition of a parallel and adaptive hierarchical grid for scientific computing. Based on this definition we derive an efficient interface specification as a set of C++ classes. This interface separates the applications from the grid data structure ..."
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Cited by 24 (9 self)
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In a companion paper [5] we introduced an abstract definition of a parallel and adaptive hierarchical grid for scientific computing. Based on this definition we derive an efficient interface specification as a set of C++ classes. This interface separates the applications from the grid data structures. Thus, user implementations become independent of the underlying grid implementation. Modern C++ template techniques are used to provide an interface implementation without big performance losses. The implementation is realized as part of the software environment DUNE [10]. Numerical tests demonstrate the flexibility and the efficiency of our approach. 1 1
Boundary switch connectors for topological visualization of complex 3D vector fields
 In Proc. VisSym 04
, 2004
"... One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that their topological structures contain a number of separating stream surfaces. Since these stream surfaces tend to hide each other as well as other topological feature ..."
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Cited by 23 (17 self)
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One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that their topological structures contain a number of separating stream surfaces. Since these stream surfaces tend to hide each other as well as other topological features, for complex 3D topologies the visualizations become cluttered and hardly interpretable. One solution of this problem is the recently introduced concept of saddle connectors which treats separation surfaces emanating from critical points. In this paper we extend this concept to separation surfaces starting from boundary switch curves. This way we obtain a number of particular stream lines called boundary switch connectors. They connect either two boundary switch curves or a boundary switch curve with a saddle. We discuss properties and computational issues of boundary switch connectors and apply them to topologically complex flow data.
Gridindependent detection of closed stream lines in 2D vector fields
 in Proc. Vision, Modeling and Visualization
, 2004
"... We present a new approach to detecting isolated closed stream lines in 2D vector fields. This approach is based on the idea of transforming the 2D vector field into an appropriate 3D vector field such that detecting closed stream lines in 2D is equivalent to intersecting certain stream surfaces in 3 ..."
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Cited by 22 (4 self)
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We present a new approach to detecting isolated closed stream lines in 2D vector fields. This approach is based on the idea of transforming the 2D vector field into an appropriate 3D vector field such that detecting closed stream lines in 2D is equivalent to intersecting certain stream surfaces in 3D. Contrary to preexisting methods, our approach does not rely on any underlying grid structure of the vector field. We demonstrate the applicability and stability by applying it to a test data set. 1
Topological methods for 2D timedependent vector fields based on stream lines and path lines
 IEEE Transactions on Visualization and Computer Graphics
"... Abstract — This paper describes approaches to topologically segmenting 2D timedependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines, ..."
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Cited by 22 (12 self)
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Abstract — This paper describes approaches to topologically segmenting 2D timedependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines, or of path lines. While topological features based on stream lines are well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations as well as a method to tracking all isolated closed stream lines. To get the path line oriented topology we segment the vector field into areas of attracting, repelling and saddlelike behavior of the path lines. We compare both kinds of topologies and apply them to a number of test data sets. Index Terms — flow visualization, vector field topology, bifurcations, stream lines, path lines I.
Extraction of parallel vector surfaces in 3d timedependent fields and application to vortex core line tracking
 IN PROC. IEEE VISUALIZATION 2005
, 2005
"... We introduce an approach to tracking vortex core lines in timedependent 3D flow fields which are defined by the parallel vectors approach. They build surface structures in the 4D spacetime domain. To extract them, we introduce two 4D vector fields which act as feature flow fields, i.e., their inte ..."
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Cited by 19 (8 self)
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We introduce an approach to tracking vortex core lines in timedependent 3D flow fields which are defined by the parallel vectors approach. They build surface structures in the 4D spacetime domain. To extract them, we introduce two 4D vector fields which act as feature flow fields, i.e., their integration gives the vortex core structures. As part of this approach, we extract and classify local bifurcations of vortex core lines in spacetime. Based on a 4D stream surface integration, we provide an algorithm to extract the complete vortex core structure. We apply our technique to a number of test data sets.
Extracting higher order critical points and topological simplification of 3D vector fields
 In VIS ’05: Proceedings of the 8th conference on Visualization ’05 (2005), IEEE Computer
, 2005
"... (a) 184 first order critical points. The box around the molecule represents the chosen area for topological simplification. (b) Topologically simplified representation with one higher order critical point elucidates the far field behavior of the benzene. Figure 1: Topological representations of the ..."
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Cited by 17 (4 self)
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(a) 184 first order critical points. The box around the molecule represents the chosen area for topological simplification. (b) Topologically simplified representation with one higher order critical point elucidates the far field behavior of the benzene. Figure 1: Topological representations of the electrostatic field of the benzene molecule. This paper presents an approach to extracting and classifying higher order critical points of 3D vector fields. To do so, we place a closed convex surface s around the area of interest. Then we show that the complete 3D classification of a critical point into areas of different flow behavior is equivalent to extracting the topological skeleton of an appropriate 2D vector field on s, if each critical point is equipped with an additional Bit of information. Out of this skeleton, we create an icon which replaces the complete topological structure inside s for the visualization. We apply our method to find a simplified visual representation of clusters of critical points, leading to expressive visualizations of topologically complex 3D vector fields.
Pavarino: Adaptivity in Space and Time for ReactionDiffusion Systems in Electrocardiology
 SIAM J. SISC
, 2006
"... Abstract. The paper introduces and studies numerical methods that are fully adaptive in both threedimensional (3D) space and time to challenging multiscale cardiac reactiondiffusion models. In these methods, temporal adaptivity comes via stepsize control in function space oriented linearly implici ..."
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Cited by 16 (2 self)
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Abstract. The paper introduces and studies numerical methods that are fully adaptive in both threedimensional (3D) space and time to challenging multiscale cardiac reactiondiffusion models. In these methods, temporal adaptivity comes via stepsize control in function space oriented linearly implicit time integration, while spatial adaptivity is realized within multilevel finite element methods controlled by a posteriori local error estimators. In contrast to other recent adaptivity approaches to cardiac modeling that discretize first in space and then in time (socalled method of lines), our method discretizes first in time and then in space (socalled Rothe method)—an approach that has already proven to be highly efficient in a number of challenging multiscale problems in science and technology (KARDOS code library). With this method, the evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated both in the frame of the anisotropic monodomain models and in the more realistic anisotropic bidomain models, coupled with either a variant of the simple FitzHugh–Nagumo model or the more complex phaseI Luo–Rudy ionic model. The numerical results exhibit a rather satisfactory performance of our adaptive method for complex cardiac reactiondiffusion models on 3D domains up to moderate sizes. In particular, the method accurately resolves the evolution of the intra and extracellular potentials, gating variables, and ion concentrations during the excitation, plateau, and recovery phases. Key words. reactiondiffusion equations, cardiac bidomain and monodomain models, adaptive finite elements, multilevel methods, error estimates, adaptive time integration, adaptive Rothe method AMS subject classifications. 65N55, 65M DOI. 10.1137/050634785
Multifieldgraphs: An approach to visualizing correlations in multifield scalar data
 IEEE Transactions on Visualization and Computer Graphics
"... We present an approach to visualizing correlations in 3D multifield scalar data. The core of our approach is the computation of correlation fields, which are scalar fields containing the local correlations of subsets of the multiple fields. While the visualization of the correlation fields can be do ..."
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Cited by 16 (0 self)
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We present an approach to visualizing correlations in 3D multifield scalar data. The core of our approach is the computation of correlation fields, which are scalar fields containing the local correlations of subsets of the multiple fields. While the visualization of the correlation fields can be done using standard 3D volume visualization techniques, their huge number makes selection and handling a challenge. We introduce the MultifieldGraph to give an overview of which multiple fields correlate and to show the strength of their correlation. This information guides the selection of informative correlation fields for visualization. We use our approach to visually analyze a number of real and synthetic multifield datasets. Index Terms—Visualization, multifield, correlation. 1
Interactive exploration of large remote microct scans
 in 15th IEEE Visualization 2004 Conference (VIS 2004), 2004
"... Datasets of tens of gigabytes are becoming common in computational and experimental science. This development is driven by advances in imaging technology, producing detectors with growing resolutions, as well as availability of cheap processing power and memory capacity in commoditybased computing ..."
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Cited by 15 (4 self)
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Datasets of tens of gigabytes are becoming common in computational and experimental science. This development is driven by advances in imaging technology, producing detectors with growing resolutions, as well as availability of cheap processing power and memory capacity in commoditybased computing clusters. In this article we describe the design of a visualization system that allows scientists to interactively explore large remote data sets in an efficient and flexible way. The system is broadly applicable and currently used by medical scientists conducting an osteoporosis research project. Human vertebral bodies are scanned using a high resolution microCT scanner producing scans of roughly 8 GB size each. All participating research groups require access to the centrally stored data. Due to the rich internal bone structure, scientists need to interactively explore the full dataset at coarse levels, as well as visualize subvolumes of interest at the highest resolution. Our solution is based on HDF5 and GridFTP. When accessing data remotely, the HDF5 data processing pipeline is modified to support efficient retrieval of subvolumes. We reduce the overall latency and optimize throughput by executing highlevel operations on the remote side. The GridFTP protocol is used to pass the HDF5 requests to a customized server. The approach takes full advantage of local graphics hardware for rendering. Interactive visualization is accomplished using a background thread to access the datasets stored in a multiresolution format. A hierarchical volume renderer provides seamless integration of high resolution details with low resolution overviews.
Path line attributes  an information visualization approach to analyzing the dynamic behavior of 3d timedependent flow fields
 In Proceedings of TopoInVis 2007
, 2007
"... We describe an approach to visually analyzing the dynamic behavior of 3D timedependent flow fields by considering the behavior of the path lines. At selected positions in the 4D spacetime domain, we compute a number of local and global properties of path lines describing relevant features of them. ..."
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Cited by 14 (4 self)
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We describe an approach to visually analyzing the dynamic behavior of 3D timedependent flow fields by considering the behavior of the path lines. At selected positions in the 4D spacetime domain, we compute a number of local and global properties of path lines describing relevant features of them. The resulting multivariate data set is analyzed by applying stateoftheart information visualization approaches in the sense of a set of linked views (scatter plots, parallel coordinates, etc.) with interactive brushing and focus+context visualization. The selected path lines with certain properties are integrated and visualized as colored 3D curves. This approach allows an interactive exploration of intricate 4D flow structures. We apply our method to a number of flow data sets and describe how path line attributes are used for describing characteristic features of these flows. 1