Related papers: On the Division Problem for the Wave Maps Equation

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any nonrelativistic effective theory of point particles on the lattice. In the…

In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…

We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…

We introduce a new sphericalization mapping for metric spaces that is applicable in very general situations, including totally disconnected fractal type sets. For an unbounded complete metric space which is uniformly perfect at a base point…

The problem of quantizing a particle on a 2-sphere has been treated by numerous approaches, including Isham's global method based on unitary representations of a symplectic symmetry group that acts transitively on the phase space. Here we…

We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…

This paper focuses on scattered data fitting problems on spheres. We study the approximation performance of a class of weighted spectral filter algorithms, including Tikhonov regularization, Landaweber iteration, spectral cut-off, and…

This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…

This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish the stability and convergence of a semi-implicit time-stepping…

This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…

We define distributions on an abstract measure space endowed with a sequence of partitions, and introduce analogues of Besov spaces with negative smoothness in this setting. In particular, we describe these spaces of distributions using…

In this paper we consider a novel partitioned framework for distributed optimization in peer-to-peer networks. In several important applications the agents of a network have to solve an optimization problem with two key features: (i) the…

We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…

Meta-atoms, nano-antennas, plasmonic particles and other small scatterers are commonly modeled in terms of their modes. However these modal solutions are seldom determined explicitly, due to the conceptual and numerical difficulties in…

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…

We apply the cell merging method to a model shallow water problem with a permeable boundary. We use a cut cell approach which is more easily and systematically scalable with different shapes of boundaries. The novel cell merging method…

This paper constructs the first quantum algorithm for wavelet packet transforms with a "parabolic scaling" tree structure, sometimes called wave atom transforms. Classically, wave atoms are used to construct sparse representations of…

We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…

A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…

The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…