Special IssueNo Access

DISTRIBUTED ADAPTIVE MULTIVARIATE FUNCTION VISUALIZATION

SHUJUN LI

Computer Science, Western Michigan University, Kalamazoo, MI 49008, USA

Search for more papers by this author

KARLIS KAUGARS

Computer Science, Western Michigan University, Kalamazoo, MI 49008, USA

Search for more papers by this author

, and

ELISE DE DONCKER

Computer Science, Western Michigan University, Kalamazoo, MI 49008, USA

Search for more papers by this author

https://doi.org/10.1142/S146902680600199XCited by:1 (Source: Crossref)

Abstract

In this article, we introduce a new function visualization method and demonstrate that numerical integration and visualization of multi-dimensional functions are closely related. Adaptive numerical integration is utilized to reduce the number of function evaluations, and generate time series data. The integration region is partitioned into a uniform grid. A grid cell can be sampled many times, or is not sampled at all, depending on the function properties and the integration rule. Function properties are extracted during the process of function evaluation. An aging technique helps visualize functions by retaining the most recently sampled areas and making the older ones transparent. This also results in giving the non-smooth areas more attention than the smooth areas. The new function visualization method gives a view of the whole function while elaborating on important areas such as ridges and troughs, which are critical in many fields, including numerical integration. A Grid service, called Integration Service, is used to solve computationally intensive integration problems. Remote visualization based on the adaptive method helps monitor the progress of a computation, and can be utilized for computational steering. The data are filtered by the server and transferred to the client, which is responsible for visualization mapping and rendering.

Keywords:

Remember to check out the Most Cited Articles!
Check out these titles in artificial intelligence!

References

World Wide Web Consortium, Web Services, visited 02/14/2005, http://www.w3.org/ . Google Scholar
I. Foster, C. Kesselman, J. Nick and S. Tuecke, The physiology of the grid: An open grid services architecture for distributed systems integration (2002). Visited, 06/01/2005, http://www.globus.org/toolkit/citations.html . Google Scholar
M. Challacombe, J. Chem. Phys. 113, 10037 (2000), DOI: 10.1063/1.1316012. Crossref, Google Scholar
E. de Donckeret al., Comput. Phys. Commun. 159, 145 (2004), DOI: 10.1016/j.cpc.2004.01.004. Crossref, Google Scholar
E. de Donckeret al., Nuclear Instruments Meth. Phys. Res. Sec. A 539, 269 (2004), hep-ph/0405098 DOI: 10.1016/j.nima.2004.07.099. Google Scholar
D.H. Son, Feynman loop integrals and their automatic computer-aided evaluation, PhD dissertation, Johannes Gutenberg-Universität Mainz (June 2003) . Google Scholar
A. Genz and F. Bretz, Numerical computation of high-dimensional integrals for multiple comparison problems, Proc. American Statistical Association Statistical Computing Section (American Statistical Association, Alexandria, VA, 2002) pp. 1145–1148. Google Scholar
E. de Donckeret al., Parallel computation of the multivariate t-distribution, Proc. High Performance Computing Symposium (HPC'01) (2001) pp. 129–134. Google Scholar
ParInt Group, ParInt, visited 06/08/2006, http://www.cs.wmich.edu/parint . Google Scholar
S. Li , K. Kaugars and E. de Doncker , Massive scale distributed integration using web service , Hawaii Int. Conf. Computer Sci., CDROM Proceedings ( 2004 ) . Google Scholar
S. Li, K. Kaugars and E. de Doncker, Grid-based numerical integration and visualization, Int. Conf. on Computational Intelligence and Multimedia Application (2005) (2005) pp. 260–265, DOI: 10.1109/ICCIMA.2005.35. Google Scholar
S. Li, Online support for multivariate integration, PhD dissertation, Western Michigan University (December, 2005) . Google Scholar
W. S. Cleveland , Visualizing Data ( Hobart Press , 1993 ) . Google Scholar
K. Tobimatsu and S. Kawabata, Res. Rep. Kogakuin Univ. 85, 7 (1998). Google Scholar
Maplesoft, Maple, visited 02/23/2005, http://www.maplesoft.com/ . Google Scholar
S. Li, E. de Doncker and K. Kaugars, Lecture Notes in Computer Science 3514, ed. (2005) pp. 123–130. Google Scholar
J. Fujimotoet al., Numerical approach to one-loop integrals, Comput. High Energy Phys. '91 (1991) pp. 407–411. Google Scholar
R. B. Haber and D. A. McNabb , Visualization Idioms: A Conceptual Model for Scientific Visualization Systems ( IEEE Computer Society Press , 1990 ) . Google Scholar
W. Bethel et al. , Visportal: Deploying grid-enabled visualization tools through a web-portal interface , Workshop on Advanced Collaborative Environments ( 2003 ) . Google Scholar
J. Tesch, L. Dietze and L. M. Encarnagdo, Personal interfaces-to-go: Mobile devices for data exchange and interaction in heterogeneous visualization environments, Distributed Computing Systems Workshops, 2003. Proc. 23rd Int. Conf. (2003) pp. 290–293, DOI: 10.1109/ICDCSW.2003.1203569. Google Scholar
M. Ahmedet al., Remote services of spectroscopy instruments using grid computing, IEEE Canadian Conference on Electrical and Computer Engineering (CCECE)2 (2003) pp. 1063–1066. Google Scholar
I. Fosteret al., IEEE Comput. 14, 36 (1999), DOI: 10.1109/2.809249. Google Scholar
L. A. Freitag and R. M. Loy, Comparison of remote visualization strategies for interactive exploration of large data sets, Proc. 15th Int. Parallel & Distributed Processing Symposium (IEEE Computer Society, 2001) p. 181. Google Scholar
L. A. Freitag and R. M. Loy , Using desktop graphics workstations for interactive remote exploration of large data sets , Visualization Development Environments 2000 Proceedings ( 2000 ) . Google Scholar
The Apache Software Foundation, Apache Axis, visited 01/10/2005, http://www.apache.org/axis/ . Google Scholar
The gtkmm Development Team, gtkmm, visited 05/02/2005, http://www.gtkmm.org/ . Google Scholar
R. A. van Engelen and K. A. Gallivan , The gSOAP toolkit for web services and peer-to-peer computing networks , Proc. IEEE CCGrid Conf. 2002 ( 2002 ) , DOI: 10.1109/CCGRID.2002.1017120 . Google Scholar
The Apache Software Foundation, Apache Tomcat, visited 01/10/2005, http://jakarta.apache.org/tomcat/ . Google Scholar
The Globus Alliance, Globus Toolkit, visited 01/02/2005, http://www.globus.org . Google Scholar