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Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…
Curvature has received increased attention as an important alternative to length based regularization in computer vision. In contrast to length, it preserves elongated structures and fine details. Existing approaches are either inefficient,…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…
Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the…
We study mechanical structures composed of spatial four-bar linkages that are bistable, that is, they allow for two distinct configurations. They have an interpretation as quad nets in the Study quadric which can be used to prove existence…
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
This paper proposes a practical and efficient solution for computing convolutions using hybrid dealiasing. It offers an alternative to explicit or implicit dealiasing and includes an optimized hyperparameter tuning algorithm that uses…
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace…
A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In…
The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires O(L^2) circuit…
We present a comprehensive and self-contained simplified review of the quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%,…