Title: Mesh[PATCHED] Free Approximation Methods With Matlab ....rar

When numerically solving partial differential equations (PDEs), the first step is often to discretize the geometry using a mesh and to solve a corresponding discretization of the PDE. Standard finite and spectral element methods require that the underlying mesh has no skinny elements for numerical stability. Here, we develop a novel spectral element method that is numerically stable on meshes that contain skinny elements, while also allowing for high degree polynomials on each element. Our method is particularly useful for PDEs for which anisotropic mesh elements are beneficial and we demonstrate it with a Navier--Stokes simulation. Code for our method can be found at this URL .

Disease spread monitoring data often comes with a significant delay and low geospatial resolution. We aim to develop a software tool for data collection, which enables daily monitoring and prediction of the spread of disease in a small community. We have developed a crowdsourcing application that collects users' health statuses and locations. It allows users to update their daily status online, and, in return, provides a visual map of geospatial distribution of sick people in a community, outlining locations with increased disease incidence. Currently, due to the lack of a large user base, we substitute this information with simulated data, and demonstrate our program's capabilities on a hypothetical outbreak. In addition, we use analytical methods for predicting town-level disease spread in the future. We model the disease spread via interpersonal probabilistic interactions on an undirected social graph. The network structure is based on scale-free networks integrated with Census data. The epidemic is modeled using the Susceptible-Infected-Recovered (SIR) model and a set of parameters, including transmission rate and vaccination patterns. The developed application will provide better methods for early detection of epidemics, identify places with high concentrations of infected people, and predict localized disease spread.