Candidate: Shujun Li

Degree of: Doctor of Philosophy

Department: Computer Science

Title:Online Support for Multivariate Integration

Committee: Dr. Elise de Doncker, Chair
Dr. Karlis Kaugars
Dr. Ian Robinson

Date: Tuesday, November 1, 2005 6:00 p.m.- 8:00 p.m.
C-258 CEAS College Conference Room, Parkview Campus

Abstract: In this dissertation, we present an online problem solving environment for multivariate numerical integration. To build an environment for users with various backgrounds, we address issues of Web interface support for end users, remote application program interfaces for distributed system programmers, visualization of multivariate integrand functions for problem analysis, and highly efficient integration methods.

Compared to previous implementations, our new load balancing schemes increase the scalability of parallel integration, and hence are suitable for large scale computation. A parallel integration service, called PI service, was implemented based on Web services technologies to support both remote integration and remote visualization. The multivariate function visualization makes use of adaptive numerical integration to sample points more efficiently. On the other hand, it helps solve numerical integration problems.

Theoretical and experimental results show that the iterated integration method outperforms traditional adaptive strategies significantly for a broad class of problems, including those with non-smooth integrands. Iterated methods were previously considered unsuitable for the latter. We implemented this approach in our integration package and recommend it as one of the basic numerical integration methods.

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