Related papers: The curved Mimetic Finite Difference method: allow…
We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous…
Detecting edges is a fundamental problem in computer vision with many applications, some involving very noisy images. While most edge detection methods are fast, they perform well only on relatively clean images. Indeed, edges in such…
Two non-equidistant grid implementations of infinite range exterior complex scaling are introduced that allow for perfect absorption in the time dependent Schr\"odinger equation. Finite element discrete variables grid discretizations…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
We introduce a meshless method for solving both continuous and discrete variational formulations of a volume constrained, nonlocal diffusion problem. We use the discrete solution to approximate the continuous solution. Our method is…
Estimating the complete 3D point cloud from an incomplete one is a key problem in many vision and robotics applications. Mainstream methods (e.g., PCN and TopNet) use Multi-layer Perceptrons (MLPs) to directly process point clouds, which…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate…
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded…
Limited by the encoder-decoder architecture, learning-based edge detectors usually have difficulty predicting edge maps that satisfy both correctness and crispness. With the recent success of the diffusion probabilistic model (DPM), we…
A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each…
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…
Context. High-resolution numerical methods have been developed for nonlinear, discontinuous problems as they appear in simulations of astrophysical objects. One of the strategies applied is the concept of artificial viscosity. Aims.…
Neural implicit surfaces can be used to recover accurate 3D geometry from imperfect point clouds. In this work, we show that state-of-the-art techniques work by minimizing an approximation of a one-sided Chamfer distance. This shape metric…