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In this paper, we take a step towards developing efficient hard thresholding methods for low-rank tensor recovery from memory-efficient linear measurements with tensorial structure. Theoretical guarantees for many standard iterative…

Numerical Analysis · Mathematics 2025-02-06 Shambhavi Suryanarayanan , Elizaveta Rebrova

Isogeometric Analysis is a spline-based discretization method to partial differential equations which shows the approximation power of a high-order method. The number of degrees of freedom, however, is as small as the number of degrees of…

Numerical Analysis · Mathematics 2021-04-22 Stefan Takacs

The simulation of electromagnetic devices with complex geometries and large-scale discrete systems benefits from advanced computational methods like IsoGeometric Analysis and Domain Decomposition. In this paper, we employ both concepts in…

Computational Engineering, Finance, and Science · Computer Science 2025-01-24 Mario Mally , Bernard Kapidani , Melina Merkel , Sebastian Schöps , Rafael Vázquez

In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the…

Numerical Analysis · Mathematics 2024-12-16 Xiaoxu Li , Xucheng Meng

Low-rank methods for kinetic equations have attracted increasing attention due to their effectiveness in reducing the high dimensionality of phase space. In our previous work [G. Wang & J. Hu, J. Comput. Phys. 558 (2026) 114884], we…

Numerical Analysis · Mathematics 2026-05-18 Geshuo Wang , Jingwei Hu

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

Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…

Numerical Analysis · Computer Science 2016-01-16 Christian Engwer , Andreas Nüßing

We propose a numerical scheme based on the principles of Isogeometric Analysis (IgA) for a geometrical pattern formation induced evolution of manifolds. The development is modelled by the use of the Gray-Scott equations for pattern…

Numerical Analysis · Mathematics 2019-10-29 Jochen Hinz , Joost van Zwieten , Matthias Möller , Fred Vermolen

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

Optimization and Control · Mathematics 2025-05-19 Ferdinand Vanmaele , Yara Elshiaty , Stefania Petra

This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric…

Computational Engineering, Finance, and Science · Computer Science 2019-01-04 Annalisa Buffa , Jacopo Corno , Carlo de Falco , Sebastian Schöps , Rafael Vázquez

In this paper the isogeometric Nystr\"om method is presented. It's outstanding features are: it allows the analysis of domains described by many different geometrical mapping methods in computer aided geometric design and it requires only…

Numerical Analysis · Computer Science 2015-06-15 Jürgen Zechner , Benjamin Marussig , Gernot Beer , Thomas-Peter Fries

Dynamical low-rank approximation (DLRA) is a widely used paradigm for solving large-scale matrix differential equations, as they arise, for example, from the discretization of time-dependent partial differential equations on tensorized…

Numerical Analysis · Mathematics 2025-10-23 Benjamin Carrel , Daniel Kressner , Hei Yin Lam , Bart Vandereycken

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

Machine Learning · Computer Science 2025-05-27 Habib Hajimolahoseini , Walid Ahmed , Austin Wen , Yang Liu

The paper presents the Isogeometric Boundary Element Method (IGABEM) algorithm for solving the plane strain problem of an isotropic linearly elastic matrix containing an open material surface of arbitrary shape. Theoretical developments are…

Numerical Analysis · Mathematics 2025-11-06 Rohit Satish Patil , Zhilin Han , Sofia G. Mogilevskaya

The development of materials with specific structural properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In this article, we combine shape…

Numerical Analysis · Mathematics 2021-06-01 Helmut Harbrecht , Michael Multerer , Remo von Rickenbach

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple…

Computational Geometry · Computer Science 2017-11-22 Gang Xu , Ming Li , Bernard Mourrain , Timon Rabczuk , Jinlan Xu , Stephane P. A. Bordas

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with…

Mathematical Software · Computer Science 2015-07-29 Lisandro Dalcin , Nathan Collier , Philippe Vignal , Adriano M. A. Cortes , V. M. Calo

We propose a novel approach to the analysis of programmable geometrically exact shear deformable beam systems made of shape memory polymers. The proposed method combines the viscoelastic Generalized Maxwell model with the Williams, Landel…

Computational Engineering, Finance, and Science · Computer Science 2025-03-11 Giulio Ferri , Enzo Marino

This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…

Numerical Analysis · Mathematics 2025-09-15 Gianmarco Manzini , Tommaso Sorgente

In this work a novel approach is presented for the isogeometric Boundary Element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions. In addition the…

Numerical Analysis · Computer Science 2016-08-24 Gernot Beer , Benjamin Marussig , Jürgen Zechner , Christian Dünser , Thomas-Peter Fries