Periodic Reporting for period 1 - ISOMAXENT (Development of a design-through-analysis methodology based on a coupled isogemetrcic-maximumentropy approach) Reporting period: 2018-10-01 to 2020-09-30 Summary of the context and overall objectives of the project Although Computer Aided Design (CAD) and Numerical Analysis have usually been two detached disciplines, a lot of effort has been made over the last few years to seek a tighter integration. The recent development of Isogeometric Analysis (IGA) was one of the main achievement in this direction. The key idea of IGA is to use for the Analysis the same basis functions employed in CAD, which in most of the cases are non-uniform rational B-splines (NURBS). However, their tensor product nature poses some limitations in the trivariate volume parametrization of complex shapes and in local refinement, operations not needed for CAD but particularly important for Analysis. The project aimed at developing a coupled approach where IGA is blended with Maximum Entropy meshless approximants to overcome to such limitations, which prevents IGA to fully develop outside of the academic world into industry, and thus to create a design-through-analysis methodology with many potential industrial applications.On implementing the action, the blending theory previously developed by the Researcher and the Supervisor in 2D was extended to the 3D case. While the extension to watertight NURBS geometries with conforming patches was straightforward, the case of complex trimmed multi-patch geometries appeared significantly challenging. Therefore, a collocation approach based on high order Maxent approximants was developed, allowing the direct resolution of differential problems on a grid of points adapted to the boundary. The proposed framework was applied to the simulation of different types of problems and its applicability to industrial relevant cases was proved by solving high-scale problems with a computational time in the same order of that required by standard finite element methodologies.The Researcher considered also the use of smooth surface approximants for mechanobiology and focused on the specific case of the intestinal crypt mechanics, where important contributions to the state of the art were found. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far Results overview:The Researcher developed a collocation approach based on high order Maxent schemes which represents an important contribution to the state of the art of this type of numerical methodologies. While dealing with the optimization of the computational times, the Researcher also contributed to a work on the GPU implementation of Maxent methods. Finally, the Researcher worked on the simulation of the intestinal crypt mechanical behavior, contributing to a relevant study on the topic.Progress of the activities:The initial idea of the project was to extend the IGA-Maxent blending previously developed by the Researcher and the Supervisor to the 3D case, using NURBS first (WP1) and then Subdivision Surfaces and T-splines (WP2). The activities of WP1 started as planned with the extension to three dimension using first watertight NURBS geometries with conforming patches. However, the general case of complex 3D multi-patch NURBS models appeared significantly challenging to treat and an alternative approach based on collocation was developed. This method appears more flexible and suitable for industrial applications. The simulation of different problems was indeed considered in detail with satisfactory results. The proposed formulation is based on the use of high-order local maximum-entropy schemes (HOLMES), which was initially planned for WP3. Given the satisfactory results obtained with collocation and given the higher relevance in industry of NURBS with respect to Subdivision Surfaces and T-splines, the activities of WP2 where considered only partially with a Subdivision Surfaces application.The optimization of the computational times, planned in WP4, was implemented by first analyzing and optimizing the main bottlenecks of the codes and then by developing an efficient parallel implementation. The use of GPUs was also considered.Finally, as planned in WP5, different numerical applications where considered with an emphasis on industrial relevant applications. The use of smooth surface approximants for mechanobiology was also considered focusing on the specific case of the intestinal crypt mechanics.Results exploitation and dissemination:The main scientific findings of the project were disseminated in publications on peer reviewed journals with proper reference to the EU funding. These publications are also deposed in the UPC repository DRAC and open access is arranged. The Researcher reported the publications also on his ResearchGate profile and together with the Supervisor disseminated the results through his individual scientific network. Furthermore, a section dedicated to the project was included in the Researcher’s homepage.Because of the Covid 19 emergency, it was not possible to realize all the activities initially planned in the DoA and some delays were encountered. In particular, the Researcher planned to attend the 2020 WCCM-ECCOMAS conference which is particularly relevant for the project goal, since ECCOMAS promotes joint efforts of European universities, research institutes and industries which are active in the broader field of numerical methods and computer simulation in Engineering and Applied Sciences. The conference was cancelled but an online version will be held in Jenuary 2021, where the Researcher will present on the findings of the project. The Researcher was also invited to present at the CSF workshop on generalized barycentric coordinates but the event is now postponed to 2022. The Researcher still plans to participate, since this workshop aims at fostering the interchange of researchers from computer graphics and computational mechanics on this research topic. Beside the dissemination at an academic level the Researcher intends to transfer the results of the project to a much wider audience. To this end, he proposed is candidature as “MSCA Fellow of the week” on the Facebook page of the Marie Curie actions, where he is scheduled to appear in January 2021, and plans to participate to the Researcher’s night 2020 edition, which was postponed to the end of November. These two actions are expected to attract a wide attention of general public. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) The results of the project are relevant not only at an academic level but also because of the industrial importance of the integration between Computer Aided Design and numerical analysis. In fact, in the traditional approach, the two processes are separated and a considerable amount of time is required for the generation of analysis suitable FEM models with a significant human intervention . On the other hand, the development of an automated design-through-analysis methodology allows one to optimize the process by reducing its duration and the human resources required. This leads then to a better reallocation of the resources and a consequent improvement of the productivity.In addition, the findings on the mechanical behavior of intestinal crypts are particularly relevant for biology and medicine because understanding the proliferation of intestinal cells in the crypt is important in many biological processes. For instance, the loss of proliferation control in the crypt is known to lead to intestinal cancer.