G Smo DevDays 24 ‐ Talks - gismo/gismo GitHub Wiki

"Transfinite elements: From FEM to IGA."

Christopher Provatidis ( NTU Athens )

The talk overviews older attempts toward the construction of large finite elements based on Coons-Gordon interpolation. A published work regarding the utilization of particular blending functions and trial functions for the construction of 'transfinite Bezier' elements, which accurately represent the geometry, is reviewed. The formulation is extended to cover the case of B-splines and NURBS.

"Some advances and applications in isogeometric analysis of coupled and complex problems."

Alessandro Reali ( University of Pavia )

Isogeometric Analysis (IGA) is a successful simulation framework originally proposed by T.J.R. Hughes et al., in 2005, with the aim of bridging Computational Mechanics and Computer Aided Design. In addition to this, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per degree-of-freedom and an enhanced robustness with respect to standard finite elements in many applications - ranging from solids and structures to fluids, as well as to different kinds of coupled problems - opening also the door for the approximation in primal form of higher-order partial differential equations. After a concise introduction of the basic isogeometric concepts, this lecture aims at presenting an overview of some recent advances in IGA with a special focus on coupled problems where the characteristics of IGA seem to be of great advantage. In particular, applications that will be discussed include the simulation of fluid-structure interaction in different contexts like, e.g., biomechanical problems, studies on the effect of mechanically-induced stresses on prostate cancer growth, thermo-mechanical simulations of additive manufacturing processes, electro-mechanical simulations for biological tissues, and the use of phase-field modeling for fracture and topology optimization problems or for predicting the polarization evolution in elastic ferroelectric materials.

"Using G+Smo in Python with cppyy bindings."

Felix Scholz ( Johannes Keppler University Linz )

As an alternative to the pybind11 Python bindings of G+Smo, we can use Python bindings generated with cppyy. The main difference is that the cppyy bindings do not need to be precompiled when building the library but they can also be generated at run-time by just-in-time compilation. This enables us to dynamically use class and function templates from G+Smo. In particular, the gsExprAssembler can be used in Python to assemble matrices for arbitrary bilinear forms defined by expressions, in the same way as in C++.

"G+Smo interactive."

Matthias Möller ( TU Delft )

In this talk we present a new WebGL tool for the interactive modelling and visualisation of G+Smo geometries and solution results, respectively. The tool was originally developed for IgANets and is now being extended to G+Smo. The front-end tool connects to a back-end server via the WebApp protocol. The back-end server is realised as a modular platform. New modules need to implement a minimalistic protocol and can then be loaded by the back-end server (comparable to Paraview's plug-in mechanism). We discuss the general client-server design and show how to convert a G+Smo application into a module.

"Isogeometric analysis-suitable parameterization: Advancements inside and outside G+Smo."

Ye Ji ( TU Delft )

This talk will introduce robust parameterization methodologies, particularly through the generation of high-quality domain parameterizations from CAD boundary representations, utilizing and transcending the capabilities of G+Smo. We commence with an exploration of barrier-type optimization-based methods and PDE-driven parameterization techniques, which have carved a niche in industry, particularly in mesh generation for complex machinery such as twin-screw compressors.

We then pivot to the pivotal aspect of boundary correspondence, a linchpin in modeling the nuanced dynamics of fluid flow within slender and extended geometries. An innovative adoption of Schwarz-Christoffel mapping will be unveiled, showcasing its potential to preserve the fidelity of geometric features during parameterization. This is instrumental in achieving precision in fluid dynamics simulations and enhancing optimization processes.

"Integrating G+SMO in the CONTACT software for wheel/rail contact evaluation."

Edwin Vollebregt ( Vtech CMCC )

CONTACT is an advanced physics-based simulation model for wheel-rail interaction. It was aimed originally at basic configurations, computing the contact forces for a round wheel on a prismatic rail. The scope is broadened in an ongoing project. We added support for rails with a variable cross-section as found in switches and crossings, and for defects such as a wheel flat or other localized damage. These applications put high demands on the representation of surface geometry and subsequent search for contact patches. G+SMO could be the tool to help us with that, and we're developing a prototype for its evaluation.

"Numerical modeling of the cardiac tissue via an isogeometric collocation approach."

Michele Torre ( University of Pavia )

In-vitro replicas of the human heart recapitulating several relevant features are becoming an alternative to more classical animal models. However, their diffusion is limited by the high cost of the assay design, since it mainly relies on a trial-and-error approach. To provide a numerical tool for design such a kind of electro-mecanical devices constituted by cardiac tissue, we develop an isogeometric approach based on a collocation method. In particular, a solver for the Monodomain equation is proposed and extended to the immersed framework to simplify the geometrical modeling. Finally, coupled electro-mechanics is addressed as well. Numerical tests illustrate the main aspects of the proposed approach."

"Reduced order modelling of forced time-periodic flows."

Jacob Lotz ( TU Delft )

Periodic flows are omnipresent in a large number of industrial applications. Examples include the flow past wind turbines, rotating flows in turbomachines and the pulsatile flow of blood. Simulation of periodic flows is computationally demanding for design and control applications as they need a long time domain for periodicity in the flow to develop. We circumvent the problem by using a parametric POD-Galerkin reduced order model, which exploits the nature of the problem. The time-periodic basis contains information on space and time, allowing for a dimension reduction in both. We base the reduced order model on a full-order model in which we convert the initial value problem to a boundary value problem by applying a periodic boundary condition in time to compute the time-periodic states directly. We discretise the system using iso-geometric analysis and solve the incompressible Navier-Stokes equations. We apply the reduced-order model to flow past periodically heaving and pitching hydrofoils at a Reynolds number of order 10^3.

"Geometrically Smooth Splines on Meshes."

Michelangelo Marsala ( University of Florence )

Geometrically smooth spline functions are piecewice polynomial functions defined on a mesh, that satisfy properties of differentiability across shared edges; their unstructured nature provide them a wide range of applications like, for example, Isogeometric Analysis simulations on surfaces of arbitrary topology and point cloud fitting problems. In this presentation, we consider G1 splines on quadrangular meshes with given quadratic gluing data along shared edges. We describe briefly their properties, analyse their spaces, and provide dimension formula. The novel construction is then applied to solve two practical problems, that are the conversion of CAD models into spline geometries and the numerical computation of free oscillations on a shallow lake.

"Adaptive spline fitting with moving parameterizations."

Sofia Imperatore ( University of Florence )

In this talk, we address the reconstruction of highly accurate computer-aided design models from real-world scattered point clouds. Specifically, we introduce two novel adaptive fitting schemes that combine moving parameterization methods with adaptive refinement using truncated hierarchical B-splines. In particular, the first proposed scheme alternates steps of surface fitting and parameter correction, hence optimizing the parameter locations associated with the input data separately from the control points of the (hierarchical) spline geometric model. The second proposed scheme jointly optimizes the parameter locations together with the control points. In the numerical examples, we apply the proposed procedure also to the reconstruction of aircraft engine components from scanned point data. The use of moving parameterization instead of fixed parameter values, when suitably combined with adaptive spline approximation, can significantly improve the resulting geometric model, thus outperforming state-of-the-art hierarchical spline model reconstruction schemes.

"Advanced Algorithms For Time-Stepping and Fluid-Structure Interaction in G+Smo."

Jingya Li (TU Delft) & Hugo Verhelst (U. Florence)

Almost two decades after the introduction of isogeometric analysis, its advantages over the finite element method are widely known and discussed. Among these advantages is the fact that higher smoothness of the basis functions enables larger element sizes for structural dynamics for the same accuracy, and therefore larger time steps for explicit dynamics computations can be used. In addition, the use of splines for geometry and analysis in interface problems – for example fluid-structure interaction – shows great benefits in terms of exact communication of quantities over the interface . In this presentation, we present ongoing research and development of advanced algorithms for structural dynamics and fluid-structure interaction in G+Smo. The contents of the presentation are two-fold. Firstly, we present a family of solvers for structural dynamics within the gsStructuralAnalysis module. We demonstrate their use, after which we show how they can be seamlessly used within the third-party XBraid module for parallel time integration. Secondly, we present the first results for fluid-structure interaction using the preCICE library. We briefly show the implementation of preCICE, after which we provide examples using the gsElasticity and the gsKLShell modules providing mechanical back-ends.