Related papers: Quadrilateral Mesh Generation III: Optimizing Sing…
This paper introduces a novel method for the efficient and accurate computation of volume fractions on unstructured polyhedral meshes, where the phase boundary is an orientable hypersurface, implicitly given as the iso-contour of a…
Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces. We also study the lattice reduction technique that is employed in order to quantify the possibility of…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
This paper is the third installment in a series of papers devoted to the computation of enumerative invariants of abelian surfaces through the tropical approach. We develop a pearl diagram algorithm similar to the floor diagram algorithm…
We generalize Abel's classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold $M^d \subset X^n$ in a compact oriented Riemannian $n$--manifold, or more generally for any $d$--cycle $Z$ relative…
We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation…
While recent generative models for 2D images achieve impressive visual results, they clearly lack the ability to perform 3D reasoning. This heavily restricts the degree of control over generated objects as well as the possible applications…
We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…
Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical…
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we factorize these semigroups as products of semigroups that…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
Image segmentation plays a central role in computer vision. However, widely used evaluation metrics, whether pixel-wise, region-based, or boundary-focused, often struggle to capture the structural and topological coherence of a…
Domain discretization is considered a dominant part of solution procedures for solving partial differential equations. It is widely accepted that mesh generation is among the most cumbersome parts of the FEM analysis and often requires…
We describe an efficient algorithm which, given a principally polarized (p.p.) abelian surface $A$ over $\mathbb{Q}$ with geometric endomorphism ring equal to $\mathbb{Z}$, computes all the other p.p. abelian surfaces over $\mathbb{Q}$ that…
Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…
The difference $[L_1]-[L_2]$ of a pair of skew lines on a cubic threefold defines a vanishing cycle on the cubic surface as the hyperplane section spanned by the two lines. By deforming the hyperplane, the flat translation of such vanishing…
Dimer models provide a method of constructing noncommutative crepant resolutions of affine toric Gorenstein threefolds. In homological mirror symmetry, they can also be used to describe noncommutative Landau--Ginzburg models dual to…
We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new…
We consider Legendre-Bregman projections defined on the Hermitian matrix space and design iterative optimization algorithms based on them. A general duality theorem is established for Bregman divergences on Hermitian matrices, and it plays…
Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological features from graph data, computational aspects of metric…