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We study clustered multitask learning in a semiparametric setting where tasks share a latent cluster structure in their target parameters but exhibit heterogeneous, potentially infinite-dimensional nuisance components. Such heterogeneity…

Machine Learning · Statistics 2026-05-05 Hanxiao Chen , Debarghya Mukherjee

The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust…

Numerical Analysis · Mathematics 2023-01-25 Danyang Li , Quanling Deng

We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…

Numerical Analysis · Mathematics 2021-02-09 Josef Dick , Michael Gnewuch

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

Numerical Analysis · Mathematics 2025-01-30 Santiago Badia , Wei Li , Alberto F. Martín

We study the last-iterate convergence of variance reduction methods for extragradient (EG) algorithms for a class of variational inequalities satisfying error-bound conditions. Previously, last-iterate linear convergence was only known…

Optimization and Control · Mathematics 2024-01-02 Tianlong Nan , Yuan Gao , Christian Kroer

An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…

Numerical Analysis · Mathematics 2017-11-15 Cristian Barbarosie , Sérgio Lopes , Anca-Maria Toader

Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer aided design, which generates meshes that are unfitted with the described…

Numerical Analysis · Mathematics 2022-08-10 Annalisa Buffa , Ondine Chanon , Rafael Vázquez

We analyze the convergence properties of a modified barrier method for solving bound-constrained optimization problems where evaluations of the objective function and its derivatives are affected by bounded and non-diminishing noise. The…

Optimization and Control · Mathematics 2024-05-21 Shima Dezfulian , Andreas Wächter

We discuss adaptive mesh point selection for the solution of scalar IVPs. We consider a method that is optimal in the sense of the speed of convergence, and aim at minimizing the local errors. Although the speed of convergence cannot be…

Numerical Analysis · Mathematics 2018-01-09 Boleslaw Kacewicz

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…

Numerical Analysis · Mathematics 2021-12-21 Stefano Berrone , Alessandro D'Auria

In this paper, we present a NURBS-enhanced finite element method that integrates the NURBS-based boundary representation of a geometric domain into a standard finite element framework for hexahedral meshes. We decompose an open, bounded,…

Numerical Analysis · Mathematics 2026-02-02 Duygu Sap

This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…

Optimization and Control · Mathematics 2025-10-07 Shimrit Shtern , Adeolu Taiwo

This paper deals with discrete topology optimization and describes the modification of a single-objective algorithm into its multi-objective counterpart. The result is a significant increase in the optimization speed and quality of the…

Neural and Evolutionary Computing · Computer Science 2025-03-13 Petr Kadlec , Miloslav Capek

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…

Numerical Analysis · Mathematics 2020-07-24 Mehdi Elasmi , Christoph Erath , Stefan Kurz

We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neighborhood of a point at the boundary. Our…

Numerical Analysis · Mathematics 2019-06-04 Tobias Jonsson , Mats G. Larson , Karl Larsson

Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…

Computational Physics · Physics 2020-08-05 Roberto J. Cier , Thomas Poulet , Sergio Rojas , Victor M. Calo , Manolis Veveakis

In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known…

Numerical Analysis · Mathematics 2018-04-09 Daniele Boffi , Lucia Gastaldi

An adaptive isogeometric method based on $d$-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In…

Numerical Analysis · Mathematics 2016-05-04 Annalisa Buffa , Carlotta Giannelli , Philipp Morgenstern , Daniel Peterseim

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

Numerical Analysis · Mathematics 2026-01-09 Tomas Teijeiro , Pouria Behnoudfar , Jamie M. Taylor , David Pardo , Victor M. Calo

In this article we suggest two discretization methods based on isogeometric analysis (IGA) for planar linear elasticity. On the one hand, we apply the well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a…

Numerical Analysis · Mathematics 2022-04-19 Jeremias Arf , Bernd Simeon