Related papers: Integration over curves and surfaces defined by th…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains. In this paper, the conjugate function method is extended to cover conformal mappings between Riemannian…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
We investigate the approximation of weighted integrals over $\mathbb{R}^d$ for integrands from weighted Sobolev spaces of mixed smoothness. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to $n$…
Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We…
In this paper, we propose to use the HLL finite volume scheme combined with implicit techniques for modelling the coupled surface and subsurface water flows. In our approach, we used the shallow water equations modelling surface water flow…
We present a numerical method for computing the single layer (Stokeslet) and double layer (stresslet) integrals in Stokes flow. The method applies to smooth, closed surfaces in three dimensions, and achieves high accuracy both on and near…
This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
Boundary integral equation methods are widely used in the solution of many partial differential equations. The kernels that appear in these surface integrals are nearly singular when evaluated near the boundary, and straightforward…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
In these notes we discuss some relations between complex analysis (derivatives of Cauchy integrals) and curvatures of curves and surfaces. In higher dimensions the Cauchy integrals are based on generalizations of complex analysis using…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…