The paper presents a new enclosure method for initial value problems in systems of ordinary di erential equations. Like the common enclosure methods (eg Lohner's algorithm AWA), it is based on Taylor expansion. In contrast to them, however, it is an implicit method. The solution sets of nonlinear inequalities have to be enclosed by a Newton-like algorithm. As the presented examples show, the ne...

In this paper we present CUDA kernels that compute an interval matrix product. Starting from a naive implementation we investigate possible speedups using commonly known techniques from standard matrix multiplication. We also evaluate the achieved speedup when our kernels are used to accelerate a variant of an existing algorithm that finds an enclosure for the solution of a linear system. Moreo...

Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances. This is the simplest instance of a subdividable linear efficient variety enclosure, short sleve. We develop general criteria, that certify correctness of a global, polygonal enclosure built from a ...

Abstract—Conjugate natural convection in a differentially heated square enclosure containing a polygon shaped object is studied numerically in this article. The effect of various polygon types on the fluid flow and thermal performance of the enclosure is addressed for different thermal conductivities. The governing equations are modeled and solved numerically using the built-in finite element m...

Water flow has been widely accepted as a target to suppress algae blooms. However, the effectiveness of the flow regulation is unclear due to lack of hard evidences to illuminate the direct cause-effect relationship between hydrodynamic forces and algae growth. In this study, a field observation at a freshwater lake was conducted weekly or biweekly from July 2007 to December 2009. Phytoplankton...

The x-ray radiation shielding requirements beyond the first optics enclosure have been considered for the beam transport of the 2-ID-B and 2-ID-C branch lines of Sector 2 (SRI-CAT) of the APS. The first three optical components (mirrors) of the 2-ID-B branch are contained within the shielded first optics enclosure. Calculations indicate that scattering of the primary synchrotron beam by beamlin...

A transonic air stream flowing over a rectangular cavity or enclosure is unsteady. At certain flow conditions, large scale oscillations develop in the shear layer which, for an open cavity, spans across the whole enclosure. The convected shear layer instabilities interact with the cavity geometry, they generate resonance, and induce large amplitude wall pressure fluctuations, aerodynamic pressu...