Related papers: Towards Unstructured Mesh Generation Using the Inv…

We propose a conceptually new method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology and other applications. The method is inspired by the theory of…

An important problem in shape analysis is to match configurations of points in space filtering out some geometrical transformation. In this paper we introduce hierarchical models for such tasks, in which the points in the configurations are…

We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…

We present a multigrid algorithm for the solution of the linear systems of equations stemming from the $p-$version of the Virtual Element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed…

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction…

In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is…

In the current practices of both industry and academia, the convergence and accuracy of finite element calculations are closely related to the methods and quality of mesh generation. For years, the research on high-quality mesh generation…

In this paper, we present a feature-aware SPH method for the concurrent and automated isotropic unstructured mesh generation. Two additional objectives are achieved with the proposed method compared to the original SPH-based mesh generator…

We introduce the Probabilistic Generative Adversarial Network (PGAN), a new GAN variant based on a new kind of objective function. The central idea is to integrate a probabilistic model (a Gaussian Mixture Model, in our case) into the GAN…

A class of quasilinear singularly perturbed boundary value problems with a turning point of attractive type is considered. The problems are solved numerically by a finite-difference scheme on a special discretization mesh which is dense…

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…

In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…

We propose an end-to-end pipeline to robustly generate high-quality quadrilateral meshes for complex CAD models. An initial quad-dominant mesh is generated with frontal point insertion guided by a locally integrable cross field and a scalar…

We propose a new two-dimensional meshing algorithm called PINW able to generate meshes that accurately approximate the distance between any two domain points by paths composed only of cell edges. This technique is based on an extension of…

For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…

Let $P$ be a Poisson structure on a finite-dimensional affine real manifold. Can $P$ be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach -- with respect to all affine Poisson…

The inverse mapping of GANs'(Generative Adversarial Nets) generator has a great potential value.Hence, some works have been developed to construct the inverse function of generator by directly learning or adversarial learning.While the…

Many problems in machine learning write as the minimization of a sum of individual loss functions over the training examples. These functions are usually differentiable but, in some cases, their gradients are not Lipschitz continuous, which…

We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…