相关论文: Law of Localised Fine Structure with application i…

In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This…

The use of discrete material representation in numerical models is advantageous due to the straightforward way it takes into account material heterogeneity and randomness, and the discrete and orientated nature of cracks. Unfortunately, it…

In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian in two dimensions. An isogeometric collocation method is developed to discretize the fractional Laplacian and applied to the fractional Poisson…

Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…

We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…

In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the…

The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional…

We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…

We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…

In this paper, we present a method using AI techniques to solve a case of pure mathematics applications for finding narrow admissible tuples. The original problem is formulated into a combinatorial optimization problem. In particular, we…

We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e., vector-valued mapped…

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…

In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…