Minisymposia

This session focuses on recent mathematical developments arising in Isogeometric Analysis (IGA). Contributions addressing the mathematical foundations of IGA as well as introducing novel theoretical frameworks motivated by IGA are particularly welcome. 

Topics of interest include, but are not limited to:

• approximation properties 

• error and stability analysis 

• smooth splines on unstructured meshes 

• compatible splines 

• locally refinable spline spaces and adaptivity 

• preconditioners and multilevel solvers 

• low-rank approximation and tensor methods

The goal of this MS is to discuss ways to extend the applicability of isogeometric analysis to large scale problems. Main challenges include the higher computational cost of isogeometric methods per degree of freedom, the treatment of complex geometries, the efficient matrix assembly, and linear solving. Among the topics of interest are efficient isogeometric solvers and preconditioning, large-scale parallelization and high-performance computing, specialized quadrature and numerical integration of isogeometric discretizations, low-rank approximation, matrix-free approaches, and other relevant state-of-the-art techniques.

Standard spline basis functions, including B-splines, NURBS, and box-splines, are defined only on structured meshes and must be suitably extended for domains with non-trivial topology. Therefore, easy-to-construct and optimally convergent generalizations of splines to unstructured meshes with extraordinary vertices are vital for applying isogeometric analysis to most industrial problems. Numerous techniques have been proposed to handle extraordinary vertices, including geometrically G^k and parametrically C^k continuous constructions, subdivision surfaces, macro-elements and manifold constructions. This mini-symposium aims to provide a platform for discussing the analysis and extensions of known techniques, as well as for introducing novel unstructured spline constructions.

Keywords: C^k constructions, extraordinary vertices, G^k constructions, IgA, local refinements, subdivision surfaces, unstructured meshes

Isogeometric analysis was originally proposed considering polynomial and rational tensor-product B-spline constructions. A lot of research has been successively devoted to developing spline tools to properly combine computer aided design methods and standards with numerical methods for partial differential equations in different directions. In particular, several alternatives to overcome the limitations of the tensor-product model and enable local refinement possibilities were proposed over the years, as for example T-splines, LR B-splines, THB-splines, and different spline constructions on triangulations. This minisymposium aims at showcasing the state of the art and presenting recent developments in the field of adaptive spline technologies and related extensions, as well as applications for the design of adaptive isogeometric methods. Both theoretical and application-oriented contributions from any field of (iso-)geometric design and analysis are highly encouraged.

Isogeometric Analysis (IGA) enables numerical simulation using spline-based geometric representations. While smooth splines provide powerful approximation spaces, constructing analysis-suitable spline models remains a central challenge. In practice, Computer-Aided Design (CAD) geometries are typically given as boundary representations (B-Reps), often assembled from trimmed tensor-product spline surfaces that are not connected in a watertight manner.

Trimming, immersed, and non-conforming methods tackle the associated numerical difficulties—such as deriving volumetric discretizations from B-Reps, integrating over arbitrarily cut elements, and establishing connectivity across non-watertight interfaces. As such, these approaches provide key tools toward IGA's core goal: seamless integration of design and analysis.

This mini-symposium brings together experts working on these topics. Contributions are welcome on, but are not limited to:

• Simulation methods for trimmed geometries

• Global and local reparameterization techniques for trimmed geometries

• Analysis-suitable Boolean operations

• Immersed methods and related concepts, including Immersogeometric methods, CutFEM, Finite Cell, TraceFEM, etc.

• Volumetric representations (V-reps)

• Analysis-suitable smooth splines on multi-patch quad/hex meshes

In addition to theoretical studies, the mini-symposium also welcomes related application-oriented contributions.

The concept of isogeometric analysis (IGA) has had an especially great impact in the field of thin structures, i.e., shells, plates and beams. The high continuity properties of isogeometric discretizations allowed for a variety of novel, highly efficient shell formulations, like rotation-free Kirchhoff-Love shells and hierarchic formulations for Reissner-Mindlin and solid shells, which show significant advantages over well-established shell formulations within traditional finite element methods. At the same time, shell analysis allows for the realization of the isogeometric paradigm, i.e., performing structural analysis directly on CAD geometries, which typically are surface models. Today, isogeometric shell analysis is already used in industrial applications, e.g. in the automotive industry. The efficient treatment of complex CAD geometries with multiple trimmed patches is a key aspect here and represents still a vital field of active research. Besides shells, a variety of novel and efficient formulations for plates and beams have been developed over the years, taking advantage of isogeometric discretizations. 

The proposed mini-symposium invites all contributions from the field of isogeometric analysis of thin structures, both from method development and application. Typical topics are expected to be, but not restricted to:

• Isogeometric discretizations for shells, plates, membranes, beams, rods and cables

• Locking and un-locking in isogeometric structural elements

• Patch coupling

• Analysis of trimmed surfaces

• Coupling with solids and fluids

• CAD integration

• Industrial applications

Keywords: Isogeometric, Thin Structures, Shells, Plates, Beams, Locking, CAD Integration

From the beginning, isogeometric analysis has been successfully applied to the discretization of a wide range of problems in solid and structural mechanics. This minisymposium provides a platform for exchanging novel and innovative research in this area, including new method developments and applications in continuum solid mechanics, structural mechanics, damage and fracture.

Many problems in science and technology are characterized by the interaction of multiple fields, multiple scales and/or multiple bodies. This can include thermal, electrical, chemical, and mechanical fields that interact across various time and length scales. Challenges arise in their theoretical and computational description, and from the fact that coupled problems generally are much more than the sum of their parts. The increased smoothness and accuracy of Isogeometric Analysis opens the door for improving the modeling, develop new formulations, and gain a deeper understanding of coupled problems, interfaces, and contact. Also, machine learning techniques can be expected to play an increasingly important role in their study.

This session aims at bringing together researchers working on these aspects and providing them with a forum for discussion. Possible topics to be discussed in this session are:

• Multifield & interface problems

• Multiscale problems

• Surface & edge effects

• Scaling

• Fluid-structure & soil-structure interaction

• Boundary layers

• Decohesion & fracture

• Contact, adhesion & friction

• Interfacial flows

This mini-symposium provides a platform for discussing recent progress in applying Isogeometric Analysis (IGA) to Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) in different areas, including biomedical, aerospace, manufacturing, automotive, marine, renewable enrgy, and other applications. Topics of interest include, but are not limited to, immersed and unfitted methods, ALE methods, reduced-order models, auxiliary field interaction (e.g., FSI with contact, fracture, or elasto-capillary interactions), artificial intelligence and machine learning approaches, novel iterative solution methods, software development, mesh generation and stabilized techniques. Contributions related to other coupled problems and innovative applications are also welcomed.

Significant advancements are being made as IGA transitions from academia to industry. This minisymposium will feature a broad representation of industrial results and projects in IGA, academic and industry efforts in solving complex problems in science and engineering using IGA, and large-scale, general-purpose implementations of IGA.

Computational modeling for biomedical and bioengineering applications provides a non-invasive approach to understanding the underlying mechanics of biological processes, guiding device design and treatment planning. Within this framework, Isogeometric Analysis (IGA) plays a pivotal role by streamlining complex mesh generation and geometry handling. The future of computational modeling lies in patient-specific simulations of real-world disease states, enabling simulation-assisted diagnostics, device deployment, and personalized treatment strategies. A primary challenge in this pursuit is that patient-specific phenomena involve the synergistic interplay of multiple physical and chemical processes, coupled across diverse spatial and temporal scales. Consequently, computational multiphysics modeling has emerged as a new frontier, advancing our ability to resolve physiological and pathological phenomena in realistic clinical scenarios. Progress in this field requires the integration of engineering principles across disciplines, necessitating research efforts that extend beyond current multiscale computational mechanics. This minisymposium aims to bring together researchers from various domains to discuss the state-of-the-art and future directions in isogeometric analysis for biomedical applications. We invite both fundamental and applied contributions on a wide range of topics, focusing on theoretical and computational approaches to modeling these complex environments.

Over the past two decades, significant advances in isogeometric analysis (IGA) have progressively bridged the longstanding gap between computer-aided design (CAD) systems and finite element analysis (FEA) software.  This convergence has enabled a more seamless integration of design and analysis processes, offering distinct advantages for design optimization.  By leveraging IGA, designers and engineers can directly incorporate precise CAD geometry into simulation workflows, enhancing the accuracy and efficiency of size, shape, and topology optimization, as well as explicitly accounting for material and geometric uncertainty.

Despite these advances, IGA-based design optimization continues to face important challenges.  Maintaining smooth, accurate, and flexible geometric representations throughout the optimization process - particularly under complex design changes or significant uncertainty - remains nontrivial.  In addition, the computational cost and algorithmic complexity associated with scalable IGA formulations and their integration into existing optimization workflows call for further methodological development.

The objective of this mini-symposium is to bring together experts in computer-aided geometric design, numerical analysis, design optimization, and uncertainty quantification to discuss recent advances, open challenges, and emerging opportunities in IGA-based optimization.  Emphasis will be placed on shape and topology optimization, robust and stochastic design methodologies, optimization under uncertainty, and the growing role of AI/ML-assisted techniques for surrogate modeling, reduced-order modeling, and data-driven design within IGA-based optimization, along with practical applications that highlight the potential of IGA to transform next-generation design and analysis workflows.

Boundary Element Methods (BEM) have long provided engineers with an effective alternative to Finite Element Methods for specific classes of problems, such as those involving unbounded domains—common in acoustic scattering—or discontinuous and singular fields, as encountered in fracture mechanics. The advent of the isogeometric analysis (IgA) paradigm has recently renewed interest in BEM; see, for example, [1] for recent developments and [2] for a general introduction. BEMs are based on a boundary integral formulation, which can be derived whenever the fundamental solution of the associated differential operator is available. As a result, only a discretization of the domain boundary is required, significantly simplifying mesh generation—particularly within the IgA framework, where an exact CAD representation of the boundary is readily available. In IgA, computational domain boundaries are described parametrically using Non-Uniform Rational B-Splines (NURBS), the standard representation in CAD systems. The same NURBS basis is employed to construct the approximation spaces for the boundary integral equations, leading to a seamless integration between geometry and analysis. This approach enables the use of approximation spaces that are more regular and flexible than those of traditional methods, for instance by allowing spline functions with variable inter-element continuity.

The Isogeometric Boundary Element Method (IgA-BEM) has demonstrated promising results across a wide range of applications, including acoustics, potential flow, electromagnetic scattering, elastostatics, and steady incompressible flow. Collocation-based IgA-BEM formulations have been successfully applied to numerous two- and three-dimensional problems, while more recently, conforming Galerkin IgA-BEM approaches have also been developed and employed for three-dimensional applications.

The objective of this mini-symposium is to present recent advances and ongoing developments in IgA-BEM, encompassing both theoretical contributions and implementation-related aspects, such as computational efficiency, versatility, and adaptivity.

REFERENCES

[1] C. Manni, H. Speleers, eds. Geometric Challenges in Isogeometric Analysis. Vol. 49. Springer Nature, 2022.
[2] G. Beer, B. Marussig, C. Dünser: The Isogeometric Boundary Element Method, Springer, 2020.