Related papers: High-Order Quadrature on Multi-Component Domains I…
Quadrature by Expansion (QBX) is a quadrature method for approximating the value of the singular integrals encountered in the evaluation of layer potentials. It exploits the smoothness of the layer potential by forming locally-valid…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules.…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources,…
We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher order image priors encode high level structural dependencies between pixels and are key to…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…