Related papers: Surface Eigenvalues with Lattice-Based Approximati…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the…
We present a meshfree collocation scheme to discretize intrinsic surface differential operators over scalar fields on smooth curved surfaces with given normal vectors and a non-intersecting tubular neighborhood. The method is based on…
We present new examples of complete embedded self-similar surfaces under mean curvature by gluing a sphere and a plane. These surfaces have finite genus and are the first examples of self-shrinkers in $\mathbb R^3$ that are not rotationally…
Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…
We develop a stabilized discrete Laplace-Beltrami operator that is used to compute an approximate mean curvature vector which enjoys convergence of order one in L2. The stabilization is of gradient jump type and we consider both standard…
This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be…
The boundary integral equation method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of…
The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions and holomorphic $s$-differentials satisfy certain consistency conditions on closed hyperbolic surfaces. These consistency conditions can be…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
As 3D scanning devices and depth sensors mature, point clouds have attracted increasing attention as a format for 3D object representation, with applications in various fields such as tele-presence, navigation and heritage reconstruction.…
Real-time fluid and aeroacoustic simulation on complex surfaces can have interactive applications - from globe-based weather visualizations to immersive computer games with physically accurate wind and sound. However, conventional…
For $2\leq p<4$, we study the $L^p$ norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact $2$-dimensional Riemannian manifolds. Burq, G\'erard, and Tzvetkov \cite{BurqGerardTzvetkov2007restrictions}, and…
In the following work, we obtain a lower bound for the first Neumann eingevalue of the drift Laplacian $\Delta^{\varphi}$ for a family of properly embedded $[\varphi,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^3$ with concave function…
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented by point clouds, eliminating the need for a global…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
This paper introduces a new mathematical and numerical framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally, those metrics are defined over the infinite dimensional…
We introduce the discrete poly-Laplace operator on a subgraph with Dirichlet boundary condition. We obtain upper and lower bounds for the sum of the first $k$ Dirichlet eigenvalues of the poly-Laplace operators on a finite subgraph of…
This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…