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We develop and assess an optimization-based approach to parametric geometry reduction. Given a family of parametric domains, we aim to determine a parametric diffeomorphism $\Phi$ that maps a fixed reference domain $\Omega$ into each…

Numerical Analysis · Mathematics 2022-11-21 Tommaso Taddei

This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\Omega \subset \mathbb{R}^3$. The computational domain or surface considered…

Numerical Analysis · Mathematics 2019-04-05 Stephen Edward Moore

Integrated Gradients (IG) is a commonly used feature attribution method for deep neural networks. While IG has many desirable properties, the method often produces spurious/noisy pixel attributions in regions that are not related to the…

Computer Vision and Pattern Recognition · Computer Science 2021-06-21 Andrei Kapishnikov , Subhashini Venugopalan , Besim Avci , Ben Wedin , Michael Terry , Tolga Bolukbasi

In this paper, we focus on the reduced basis methodology in the context of non-linear non-affinely parametrized partial differential equations in which affine decomposition necessary for the reduced basis methodology are not obtained [4,…

Analysis of PDEs · Mathematics 2015-04-24 Cécile Daversin , Christophe Prud'Homme

In this paper, with the parametric symmetric coercive elliptic boundary value problem as an example of the primal-dual variational problems satisfying the strong duality, we develop primal-dual reduced basis methods (PD-RBM) with robust…

Numerical Analysis · Mathematics 2020-09-18 Shun Zhang

Subsea umbilical and power cables contain a large number of contact interfaces between different geometries and materials. These complex interactions rise significant challenges for accurately considering contact surface properties by using…

Numerical Analysis · Mathematics 2025-07-02 Tianjiao Dai , Shuo Yang , Xing Jin , Svein Sævik , Jiaxuan Zhang , Jun Wu , Naiquan Ye

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field…

Numerical Analysis · Mathematics 2018-04-17 Peng Yu , Cosmin Anitescu , Satyendra Tomar , Stéphane Bordas , Pierre Kerfriden

We introduce a three-dimensional (3D) fully tensor train (TT)-assembled isogeometric analysis (IGA) framework, TT-IGA, for solving partial differential equations (PDEs) on complex geometries. Our method reformulates IGA discrete operators…

Numerical Analysis · Mathematics 2025-09-17 Quoc Thai Tran , Duc P. Truong , Kim Ø. Rasmussen , Boian Alexandrov

The paper is concerned with space-time IgA approximations of parabolic initial-boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of IgA approximations and investigate their…

Numerical Analysis · Mathematics 2018-02-20 Ulrich Langer , Svetlana Matculevich , Sergey Repin

We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational…

Numerical Analysis · Mathematics 2021-08-26 Masoud Behzadinasab , Georgios Moutsanidis , Nathaniel Trask , John T. Foster , Yuri Bazilevs

This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a…

Numerical Analysis · Mathematics 2020-10-27 Alessia Patton , Pablo Antolin , Josef Kiendl , Alessandro Reali

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric…

Numerical Analysis · Mathematics 2026-05-01 Guilherme Henrique Teixeira , Nepomuk Krenn , Peter Gangl , Benjamin Marussig

Implicit Neural Representations (INRs) have emerged as a powerful tool for geometric representation, yet their suitability for physics-based simulation remains underexplored. While metrics like Hausdorff distance quantify surface…

Computational Engineering, Finance, and Science · Computer Science 2026-02-03 Samundra Karki , Adarsh Krishnamurthy , Baskar Ganapathysubramanian

This contribution presents a model order reduction strategy for fast parametric modelling of problems with cracks formulated on spline discretizations. In the context of damage detection, parametric reduced order models (ROMs) are well…

Computational Engineering, Finance, and Science · Computer Science 2026-03-30 Margarita Chasapi

We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…

Numerical Analysis · Mathematics 2024-10-04 Ngoc Cuong Nguyen

Isogeometric Analysis (IGA) is a recently introduced computational approach intended to breach the gap between the Finite Element Analysis and the Computer Aided Design worlds. In this work, we apply it to numerically simulate thermal…

Numerical Analysis · Mathematics 2018-12-05 Alexander Shamanskiy , Bernd Simeon

Model order reduction methods are a powerful tool to drastically reduce the computational effort of problems which need to be evaluated repeatedly, i.e., when computing the same system for various parameter values. When applying a reduced…

Computational Engineering, Finance, and Science · Computer Science 2024-10-21 Anna Ziegler , Sebastian Schöps

In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…

Numerical Analysis · Mathematics 2022-04-28 Wei Huang , Michael Multerer

In this paper, a novel isogeometric method for Biot's consolidation model is constructed and analyzed, using a four-field formulation where the unknown variables are the solid displacement, solid pressure, fluid flux, and fluid pressure.…

Numerical Analysis · Mathematics 2025-02-14 Hanyu Chu , Luca Franco Pavarino

The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness…

Computational Engineering, Finance, and Science · Computer Science 2022-01-19 A. Borković , B. Marussig , G. Radenković