Related papers: A geometric discretization and a simple implementa…
Mesh reconstruction of the cardiac anatomy from medical images is useful for shape and motion measurements and biophysics simulations to facilitate the assessment of cardiac function and health. However, 3D medical images are often acquired…
The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…
When smoothing a function $f$ via convolution with some kernel, it is often desirable to adapt the amount of smoothing locally to the variation of $f$. For this purpose, the constant smoothing coefficient of regular convolutions needs to be…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built…
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical…
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
This paper introduces a framework designed to accurately predict piecewise linear mappings of arbitrary meshes via a neural network, enabling training and evaluating over heterogeneous collections of meshes that do not share a…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
For linear elastic problems, it is well-known that mesh generation dominates the total analysis time. Different types of methods have been proposed to directly or indirectly alleviate this burden associated with mesh generation. We review…
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…
Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…
The efficient generation of meshes is an important step in the numerical solution of various problems in physics and engineering. We are interested in situations where global mesh quality and tight coupling to the physical solution is…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random…
In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics…
We develop two adaptive finite difference methods for the numerical simulation of the Willmore flow, employing the kth-order backward differentiation formula (BDFk) for time discretization, together with monitor functions for dynamic mesh…