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Related papers: Layer-adapted meshes for weak boundary layers

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Transmission matrices, mapping the propagation of light from one end of the tissue to the other, form an important mathematical tool in the analysis of tissue scattering and the design of wavefront shaping systems. To understand the…

Optics · Physics 2025-04-01 Anat Levin , Marina Alterman

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…

Optimization and Control · Mathematics 2020-05-26 Parvin Nazari , Davoud Ataee Tarzanagh , George Michailidis

We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…

Numerical Analysis · Mathematics 2022-02-08 Niklas Kolbe , Nikolaos Sfakianakis

We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a…

Quantum Algebra · Mathematics 2008-12-18 Haisheng Li , Shaobin Tan , Qing Wang

Aberrations limit optical systems in many situations, for example when imaging in biological tissue. Machine learning offers novel ways to improve imaging under such conditions by learning inverse models of aberrations. Learning requires…

Optics · Physics 2021-04-30 Ivan Vishniakou , Johannes D. Seelig

We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…

Numerical Analysis · Mathematics 2017-01-24 Simon Becher

Adaptive mesh refinement is a key component of efficient unstructured space-time finite element methods. Underlying any adaptive mesh refinement scheme is, of course, a method for local refinement of simplices. However, simplex bisection…

Numerical Analysis · Mathematics 2021-08-16 David Lenz

In recent years, object detection has shown impressive results using supervised deep learning, but it remains challenging in a cross-domain environment. The variations of illumination, style, scale, and appearance in different domains can…

Computer Vision and Pattern Recognition · Computer Science 2019-08-12 Rongchang Xie , Fei Yu , Jiachao Wang , Yizhou Wang , Li Zhang

Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…

Numerical Analysis · Mathematics 2015-03-17 Weizhang Huang , Lennard Kamenski , Xianping Li

Recently, the method that learns networks layer by layer has attracted increasing interest for its ease of analysis. For the method, the main challenge lies in deriving an optimization target for each layer by inversely propagating the…

Machine Learning · Computer Science 2021-10-22 Weizhi Lu , Mingrui Chen , Kai Guo , Weiyu Li

We propose some adaptive mirror descent dethods for convex programming problems with delta-subgradients and prove some theoretical results.

Optimization and Control · Mathematics 2020-12-24 Fedor S. Stonyakin

Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a…

Graphics · Computer Science 2023-10-04 Junyi Shen

This article proposes a new layered model to represent the spectrum assignment on flexible-grid optical networks. This model can reduce the time-complexity of existing routing and spectrum assignment methods by providing a data structure…

Networking and Internet Architecture · Computer Science 2015-12-14 Aysegul Yayimli

Automatic melanoma segmentation in dermoscopic images is essential in computer-aided diagnosis of skin cancer. Existing methods may suffer from the hole and shrink problems with limited segmentation performance. To tackle these issues, we…

Computer Vision and Pattern Recognition · Computer Science 2020-01-14 Xiaoqing Guo , Zhen Chen , Yixuan Yuan

In domains where computational resources and labeled data are limited, such as in robotics, deep networks with millions of weights might not be the optimal solution. In this paper, we introduce a connectivity scheme for pyramidal…

Computer Vision and Pattern Recognition · Computer Science 2021-03-24 Henrique Siqueira , Pablo Barros , Sven Magg , Cornelius Weber , Stefan Wermter

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…

Numerical Analysis · Mathematics 2017-06-26 Brittany D. Froese , Tiago Salvador

Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of…

Numerical Analysis · Mathematics 2020-04-22 Alex Viguerie , Silvia Bertoluzza , Ferdinando Auricchio

A convection-diffusion problem with a large shift in space is considered. Numerical analysis of high order finite element methods on layer-adapted Duran type meshes, as well as on coarser Duran type meshes in places where weak layers…

Numerical Analysis · Mathematics 2023-04-25 Mirjana Brdar , Sebastian Franz , Hans-Goerg Roos

We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…

Numerical Analysis · Mathematics 2023-01-26 Peter Binev , Francesca Fierro , Andreas Veeser

A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…

Numerical Analysis · Computer Science 2016-04-04 Samir Omerović , Thomas-Peter Fries