A canonical one-dimensional problem

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.


Author(s):  
Lars Taxén

The purpose of this chapter is to analyze prevalent conceptions of basic organizational realms such as coordination, communication, business processes, etc., using ADT as a guiding framework. Based on this analysis, I will suggest the activity domain as the fundamental integrating construct in organizational inquiry, and discuss the implications of this proposal. I argue that the persistent confusion about the definitions of organizational realms is due to the lack of an integrating perspective. Taking any of these realms as a basic perspective for inquiry implies that a multi-dimensional problem is “compressed” into a one-dimensional one where other dimensions are concealed or unfocused. A consequence of this superficial way of approaching a multi-dimensional problem is that interdependencies are veiled. Without an integrative perspective that lays bare these interdependencies, and thus makes them accessible to operationalization, it is likely that the inherent difficulties in managing organizational change programs will be even more aggravated.


2011 ◽  
Vol 11 (2) ◽  
pp. 192-205
Author(s):  
Christian Grossmann ◽  
Lars Ludwig ◽  
Hans-Görg Roos

Abstract In the present paper we analyze linear finite elements on a layer adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel functions. It turns out that as well adapted meshes as adapted basis functions are suitable where for our one-dimensional problem adapted bases work slightly better.


2015 ◽  
Vol 25 (01) ◽  
pp. 15-36 ◽  
Author(s):  
Bettina Speckmann ◽  
Kevin Verbeek

Necklace maps visualize quantitative data associated with regions by placing scaled symbols, usually disks, without overlap on a closed curve (the necklace) surrounding the map regions. Each region is projected onto an interval on the necklace that contains its symbol. In this paper we address the algorithmic question how to maximize symbol sizes while keeping symbols disjoint and inside their intervals. For that we reduce the problem to a one-dimensional problem which we solve efficiently. Solutions to the one-dimensional problem provide a very good approximation for the original necklace map problem. We consider two variants: Fixed-Order, where an order for the symbols on the necklace is given, and Any-Order where any symbol order is possible. The Fixed-Order problem can be solved in O(n log n) time. We show that the Any-Order problem is NP-hard for certain types of intervals and give an exact algorithm for the decision version. This algorithm is fixed-parameter tractable in the thickness K of the input. Our algorithm runs in O(n log n + n2K4K) time which can be improved to O(n log n + nK2K) time using a heuristic. We implemented our algorithm and evaluated it experimentally.


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