Related papers: Universal Meshes: A new paradigm for computing wit…

Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…

Motivated by a wide range of real-world problems whose solutions exhibit boundary and interior layers, the numerical analysis of discretizations of singularly perturbed differential equations is an established sub-discipline within the…

Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a…

Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…

In this work, we present a boundary and hole detection approach that traverses all the boundaries of an edge-manifold triangular mesh, irrespectively of the presence of singular vertices, and subsequently determines and labels all holes of…

Establishing dense correspondences between shapes is a crucial task in computer vision and graphics, while prior approaches depend on near-isometric assumptions and homogeneous subject types (i.e., only operate for human shapes). However,…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…

In the given paper the algorithm describing original and universal principles of a triangulation of a smooth molecular surface: solvent excluding solvent (SES), received by primary and secondary rolling, and solvent accessible surface (SAS)…

An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…

Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…

A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…

In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…

We describe an algorithm that allows one to find dense packing configurations of a number of congruent disks in arbitrary domains in two or more dimensions. We have applied it to a large class of two dimensional domains such as rectangles,…

Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…

Fully convolutional neural networks like U-Net have been the state-of-the-art methods in medical image segmentation. Practically, a network is highly specialized and trained separately for each segmentation task. Instead of a collection of…