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We use the alternating direction method to simulate implicit dynamics. ur spatial discretization uses isogeometric analysis. Namely, we simulate a (hyperbolic) wave propagation problem in which we use tensor-product B-splines in space and…

Numerical Analysis · Mathematics 2019-11-20 Marcin Los , Pouria Behnoudfar , Maciej Paszynski , Victor Manuel Calo

We decrease the $rms$ mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately…

Differential Geometry · Mathematics 2018-03-28 Daud Ahmad , Bilal Masud

In this paper we present an algorithm to reduce the area of a surface spanned by a finite number of boundary curves by initiating a variational improvement in the surface. The ansatz we suggest consists of original surface plus a…

Differential Geometry · Mathematics 2014-02-24 Daud Ahmad , Bilal Masud

In this paper, we develop and study approximately smooth basis constructions for isogeometric analysis over two-patch domains. One key element of isogeometric analysis is that it allows high order smoothness within one patch. However, for…

Numerical Analysis · Mathematics 2021-08-04 Pascal Weinmüller , Thomas Takacs

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…

Computational Engineering, Finance, and Science · Computer Science 2017-09-19 Zeger Bontinck , Jacopo Corno , Herbert De Gersem , Stefan Kurz , Andreas Pels , Sebastian Schöps , Felix Wolf , Carlo de Falco , Jürgen Dölz , Rafael Vázquez , Ulrich Römer

In this paper we develop an isogeometric B\'ezier dual mortar method for the biharmonic problem on multi-patch domains. The well-posedness of the discrete biharmonic problem requires a discretization with $C^1$ continuous basis functions.…

Numerical Analysis · Mathematics 2025-10-20 Di Miao , Michael A. Scott , Michael J. Borden , Derek C. Thomas , Zhihui Zou

This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…

Numerical Analysis · Mathematics 2024-11-26 Mengjia Bai , Jingrun Chen , Rui Du , Zhiwei Sun

Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…

Statistics Theory · Mathematics 2022-05-31 Edgar Dobriban

A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…

Numerical Analysis · Mathematics 2026-03-05 Nicholas J. E. Richardson , Noah Marusenko , Michael P. Friedlander

As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…

Numerical Analysis · Mathematics 2018-09-21 Nicola A. Nodargi

Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…

Numerical Analysis · Mathematics 2021-02-08 Carolina Vittoria Beccari , Giulio Casciola

We present a mass lumping approach based on an isogeometric Petrov-Galerkin method that preserves higher-order spatial accuracy in explicit dynamics calculations irrespective of the polynomial degree of the spline approximation. To…

Computational Engineering, Finance, and Science · Computer Science 2023-09-29 Thi-Hoa Nguyen , René R. Hiemstra , Sascha Eisenträger , Dominik Schillinger

In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…

Optimization and Control · Mathematics 2013-05-16 Amos Uderzo

We introduce finite mixtures of Ising models as a novel approach to study multivariate patterns of associations of binary variables. Our proposed models combine the strengths of Ising models and multivariate Bernoulli mixture models. We…

Methodology · Statistics 2023-05-02 Zhen Miao , Yen-Chi Chen , Adrian Dobra

Inhomogeneous essential boundary conditions can be appended to a well-posed PDE to lead to a combined variational formulation. The domain of the corresponding operator is a Sobolev space on the domain $\Omega$ on which the PDE is posed,…

Numerical Analysis · Mathematics 2023-07-11 Rob Stevenson

We consider a cut isogeometric method, where the boundary of the domain is allowed to cut through the background mesh in an arbitrary fashion for a second order elliptic model problem. In order to stabilize the method on the cut boundary we…

Numerical Analysis · Mathematics 2018-04-17 Daniel Elfverson , Mats G. Larson , Karl Larsson

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…

Computational Physics · Physics 2014-04-22 A. B. Stamm , B. A. Shadwick , E. G. Evstatiev

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…

Optimization and Control · Mathematics 2020-07-23 Boris S. Mordukhovich , Pedro Pérez-Aros

In this paper, we develop multigrid solvers for the biharmonic problem in the framework of isogeometric analysis (IgA). In this framework, one typically sets up B-splines on the unit square or cube and transforms them to the domain of…

Numerical Analysis · Mathematics 2019-06-18 Jarle Sogn , Stefan Takacs

We prove $p$-robust approximation error estimates for $H^2$-conforming isogeometric discretizations over planar multi-patch domains. Possible applications are fourth order boundary value problems, like the biharmonic equation or…

Numerical Analysis · Mathematics 2026-05-14 Fatima Hasanova , Stefan Takacs , Thomas Takacs