Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed -- diagonal dominantization and symbolic algorithms.Comment: 4 pages, 1 figure, 1 tabl

Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs

This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity. These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes. Performance analysis of the implementations is done using the high-performance computing (HPC) platforms "HybriLIT" and "Avitohol". The experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed. An analysis of the three algorithms is performed.Comment: 7 pages, 9 tables, 4 figure

Increasing efficiency of on-line shopping by optimizing the staff schedule

Problem proposed by: COOP Drive (online food shopping service provided by COOP Liguria), http://www.e-COOP.it/virtualShop/. The customers are making an online purchase and choose a time range for pick up. Making optimal staff scheduling such that each employee has ‘constant’ working hours, satisfying customers and employees in the same time. Constraints: Each employee can work at most 6 days a week. Each employee can work maximum 8 hours a day. Each employee needs to work continuous hours

Performance Analysis of Effective Methods for Solving Band Matrix SLAEs after Parabolic Nonlinear PDEs

This paper presents an experimental performance study of implementations of three different types of algorithms for solving band matrix systems of linear algebraic equations (SLAEs) after parabolic nonlinear partial differential equations -- direct, symbolic, and iterative, the former two of which were introduced in Veneva and Ayriyan (arXiv:1710.00428v2). An iterative algorithm is presented -- the strongly implicit procedure (SIP), also known as the Stone method. This method uses the incomplete LU (ILU(0)) decomposition. An application of the Hotelling-Bodewig iterative algorithm is suggested as a replacement of the standard forward-backward substitutions. The upsides and the downsides of the SIP method are discussed. The complexity of all the investigated methods is presented. Performance analysis of the implementations is done using the high-performance computing (HPC) clusters "HybriLIT" and "Avitohol". To that purpose, the experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed.Comment: 10 pages, 2 figure

COMPUTER AIDED (FILAMENT WINDING) TAPE PLACEMENT FOR ELBOWS. PRACTICALLY ORIENTATED ALGORITHM

Filament winding is one of the most used automated techniques for manufacturing of composite objects with different open-end or closed-end structures. Mathematical model for covering an elbow mandrel with composite material is considered. The nature of the comprising equations is elaborated in detail. A practically orientated algorithm for filament winding for elbows is formulated and its open-source implementations in Python and MATLAB are presented. The results from the constructed algorithm are presented and discussed. Keywords: filament winding for elbows, tape placement for elbows, practical algorithm, open-source, CAD

An Early Stage Researcher's Primer on Systems Medicine Terminology

Background: Systems Medicine is a novel approach to medicine, that is, an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modeling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields.Methods: In this review, we collect and explain more than100 terms related to Systems Medicine. These include both modeling and data science terms and basic systems medicine terms, along with some synthetic definitions, examples of applications, and lists of relevant references.Results: This glossary aims at being a first aid kit for the Systems Medicine researcher facing an unfamiliar term, where he/she can get a first understanding of them, and, more importantly, examples and references for digging into the topic