Micro, small and medium enterprises play a very important role in economic development of a country, what is the reason that they are subject to so many studies and analyzes. In addition to contributing to the creation of the Gross Domestic Product, they also play a key social role as they reduce unemployment. The aim of the article is to evaluate the relations between the components of gross domestic product (GDP) and the development of small and medium-sized enterprises (SMEs) in Poland in the years 1996-2016. To achieve this goal, we conducted a literature review, presented statistical data confirming the importance of these enterprises in the development of the economy, such as: entrepreneurship indicator (calculated as the number of SME enterprises per 1000 inhabitants), SME participation in total employment and SME participation in generating value added. We have presented this data for selected EU countries. In the further part of the work, we conduct a statistical analysis of data collected for Polish SMEs, which allowed us to verify the hypotheses set in the article. The results are presented at the end of the article.

We study three-dimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p-1}$Cp-1 basis functions, which provide multiple benefits in terms of stability and convergence properties. However, smooth basis significantly deteriorate the direct solver performance and its parallel scalability. As a partial remedy for this, refined Isogeometric Analysis (rIGA) method improves the sequential execution of direct solvers. The refinement strategy enriches traditional highly-continuous $C^{p-1}$Cp-1 IGA spaces by introducing low-continuity $C^0$C0-hyperplanes along the boundaries of certain pre-defined macro-elements. In this work, we propose a solution strategy for rIGA for parallel distributed memory machines and compare the computational costs of solving rIGA versus IGA discretizations. We verify our estimates with parallel numerical experiments. Results show that the weak parallel scalability of the direct solver improves approximately by a factor of $p^2$p2 when considering rIGA discretizations rather than highly-continuous IGA spaces.