Related papers: High-order numerical integration on regular embedd…
Zeroth-order optimization addresses problems where gradient information is inaccessible or impractical to compute. While most existing methods rely on first-order approximations, incorporating second-order (curvature) information can, in…
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
We present new higher-order quadratures for a family of boundary integral operators re-derived using the approach introduced in [Kublik, Tanushev, and Tsai - J. Comp. Phys. 247: 279-311, 2013]. In this formulation, a boundary integral over…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve…
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…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
This paper introduces a high-order accurate surface integral equation method for solving 3D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-M\"uller formulation is leveraged…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an…
Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…
We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging…
We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
Recent advances in neural implicit surfaces for multi-view 3D reconstruction primarily focus on improving large-scale surface reconstruction accuracy, but often produce over-smoothed geometries that lack fine surface details. To address…
Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is…
A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis Quadrature for Fredholm integral equations of the second kind, whose kernel is either discontinuous or not smooth along the main diagonal, is…
This paper proposes a novel higher-order multi-scale (HOMS) computational method, which is highly targeted for efficient, high-accuracy and low-computational-cost simulation of hygro-thermo-mechanical (H-T-M) coupling problems in…