Related papers: Spectral Methods for Numerical Relativity. The Ini…
The inhomogeneous Zerilli equation is solved in time-domain numerically with the Chebyshev spectral collocation method to investigate a radial-infall of the point particle towards a Schwarzschild black hole. Singular source terms due to the…
Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional…
In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In these methods, the underlying PDEs are numerically solved at a…
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…
We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs). The method transforms the IHOCs into finite-horizon optimal…
We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
Construction of astrophysically realistic initial data remains a central problem when modelling the merger and eventual coalescence of binary black holes in numerical relativity. The objective of this paper is to provide astrophysically…
Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…
The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for…
This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…
The recently introduced Spatial Spectral Compressive Spectral Imager (SSCSI) has been proposed as an alternative to carry out spatial and spectral coding using a binary on-off coded aperture. In SSCSI, the pixel pitch size of the coded…
This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free…
We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). The finite difference formulation has been used for temporal discretization, whereas, the space…
Nowadays, the number of emerging embedded systems rapidly grows in many application domains, due to recent advances in artificial intelligence and internet of things. The main inherent specification of these application-specific systems is…