Effect of the Roof Slope on the Cost Variation of Residential Houses

The building industry has been one of the fast-growing sectors in Rwanda, and multiple residential houses with amazing pitched roofs are being implemented in different cities. As the country is very hilly, the influence of wind loads on the buildings is high and therefore the selection step of roof slopes needs to be carefully undertaken, in order to ensure not only the structure safety, but also the economy. Available international and national guidelines give details about safety and functionality requirements, but don’t talk much about economic aspect, and this was the purpose of the given study. Using a well elaborated methodology, the influence of the roof slope on its cost was checked, and it was established that the slope’s increase of one degree would raise the roof cost by 3.6%. Therefore, during the roof slope selection and design process, economic requirements need more attention.

A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection

In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. An artificial stabilizing term $ A{\tau }^2\frac{\mathrm{\partial }{\Delta }^2u}{\mathrm{\partial }t}$ is added to the physical model to achieve energy stability, with ETD-based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed 𝓁∞(0,T;𝓁2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. In addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.