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In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by…

Optimization and Control · Mathematics 2025-03-18 Michael Wiesheu , Theodor Komann , Melina Merkel , Sebastian Schöps , Stefan Ulbrich , Idoia Cortes Garcia

Future e-mobility calls for efficient electrical machines. For different areas of operation, these machines have to satisfy certain desired properties that often depend on their design. Here we investigate the use of multipatch Isogeometric…

Numerical Analysis · Mathematics 2026-04-02 Peter Gangl , Ulrich Langer , Angelos Mantzaflaris , Rainer Schneckenleitner

In this paper we investigate numerically the order of convergence of an isogeometric collocation method that builds upon the least-squares collocation method presented in [1] and the variational collocation method presented in [2]. The…

Numerical Analysis · Mathematics 2017-04-05 Monica Montardini , Giancarlo Sangalli , Lorenzo Tamellini

Isogeometric Analysis (IgA) is a versatile method for the discretization of partial differential equations on complex domains, which arise in various applications of science and engineering. Some complex geometries can be better described…

Numerical Analysis · Mathematics 2024-05-13 Alexandra Bünger , Tom-Christian Riemer , Martin Stoll

We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The…

Computational Physics · Physics 2021-01-07 Robert Cimrman , Matyáš Novák , Radek Kolman , Miroslav Tůma , Jiří Vackář

In the context of isogeometric analysis, we consider two discretization approaches that make the resulting stiffness matrix nonsymmetric even if the differential operator is self-adjoint. These are the collocation method and the…

Numerical Analysis · Mathematics 2017-05-15 Mattia Tani

We propose a compressive spectral collocation method for the numerical approximation of Partial Differential Equations (PDEs). The approach is based on a spectral Sturm-Liouville approximation of the solution and on the collocation of the…

Numerical Analysis · Mathematics 2018-10-18 Simone Brugiapaglia

The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced…

Numerical Analysis · Mathematics 2022-10-04 Jon Vegard Venås , Trond Kvamsdal

We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the…

Numerical Analysis · Mathematics 2020-07-15 Abele Simona , Luca Bonaventura , Carlo de Falco , Sebastian Schöps

This paper presents a brand new methodology to deal with isotopic fine structure calculations. By using the Poisson approximation in an entirely novel way, we introduce mathematical elegance into the discussion on the trade-off between…

Chemical Physics · Physics 2014-10-28 Mateusz Krzysztof Łącki , Anna Gambin

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the…

Numerical Analysis · Mathematics 2020-01-30 Jochen Hinz , Andrzej Jaeschke , Matthias Möller , Cornelis Vuik

Isogeometric analysis (IGA) enables exact representations of computational geometries and higher-order approximation of PDEs. In non-smooth domains, however, singularities near corners limit the effectiveness of IGA, since standard methods…

Numerical Analysis · Mathematics 2025-05-16 Thomas Apel , Philipp Zilk

Isogeometric analysis (IGA) is a numerical method that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a NURBS…

Numerical Analysis · Mathematics 2023-10-04 Somayeh Kargaran , Bert Jüttler , Thomas Takacs

One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…

Numerical Analysis · Mathematics 2015-02-13 Michel Bercovier , Ilya Soloveichik

The aim of this paper is to analyze from a mathematical perspective some existing schemes to partition a molecular density into several atomic contributions, with a specific focus on Iterative Stockholder Atom (ISA) methods. We provide a…

Numerical Analysis · Mathematics 2022-05-11 Robert Benda , Eric Cancès , Virginie Ehrlacher , Benjamin Stamm

We introduce a novel quadrature strategy for Isogeometric Analysis (IgA) boundary element discretizations, specifically tailored to collocation methods. Thanks to the dimensionality reduction and the natural handling of unbounded domains,…

Numerical Analysis · Mathematics 2025-11-25 Cesare Bracco , Francesco Patrizi , Alessandra Sestini

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

We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only require two…

Numerical Analysis · Mathematics 2017-11-22 Quanling Deng , Michael Bartoň , Vladimir Puzyrev , Victor Calo

The strong-form asymmetric kernel-based collocation method, commonly referred to as the Kansa method, is easy to implement and hence is widely used for solving engineering problems and partial differential equations despite the lack of…

Numerical Analysis · Mathematics 2018-01-03 Ka-Chun Cheung , Leevan Ling , Robert Schaback

We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time…

Computational Engineering, Finance, and Science · Computer Science 2024-08-19 Giulio Ferri , Josef Kiendl , Alessandro Reali , Enzo Marino