Related papers: Spectral integration of linear boundary value prob…
We derive closed-form expressions for the poles and zeros of approximate fractional integrator/differentiator filters, which correspond to spectral roll-off filters having any desired log-log slope to a controllable degree of accuracy over…
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…
We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…
We use results in [M. Crouzeix and A. Greenbaum,Spectral sets: numerical range and beyond, SIAM Jour. Matrix Anal. Appl., 40 (2019), pp. 1087-1101] to derive a variety of K-spectral sets and show how they can be used in some applications.…
A number of examples of Hamiltonian systems that are integrable by classical means are cast within the framework of isospectral flows in loop algebras. These include: the Neumann oscillator, the cubically nonlinear Schr\"odinger systems and…
A numerical study of the Einstein field equations, based on the 3+1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the…
This paper investigates the isentropic compressible Navier-Stokes equations on k-connected domains under Navier-slip boundary conditions. We study the multi-solvability of the stationary systems on general domains, which is closely related…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…
The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is…
We present a spectral element solver for the steady incompressible Navier-Stokes equations subject to a free surface. Utilizing the kinematic behaviour of the free surface boundary, an iterative pseudo-time procedure is proposed to…
Spectral embedding of graphs uses the top k non-trivial eigenvectors of the random walk matrix to embed the graph into R^k. The primary use of this embedding has been for practical spectral clustering algorithms [SM00,NJW02]. Recently,…
A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
A recently re-discovered variant of the Backus-Gilbert algorithm for spectral reconstruction enables the controlled determination of smeared spectral densities from lattice field theory correlation functions. A particular advantage of this…
Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…
We consider the Brenier-Schr{\"o}dinger problem on compact manifolds with boundary. In the spirit of a work by Arnaudon, Cruzeiro, L{\'e}onard and Zambrini, we study the kinetic property of regular solutions and obtain a link to the…
This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the…
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…
We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the…