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11 papers · 2 filters
A Riemann--Hilbert approach to Jacobi operators and Gaussian quadrature
Thomas Trogdon, Sheehan Olver
The computation of the entries of Jacobi operators associated with orthogonal polynomials has important applications in numerical analysis. From truncating the operator to form a J…
Fast and Accurate Evaluation of Nonlocal Coulomb and Dipole-Dipole Interactions via the Nonuniform FFT
Shidong Jiang, Leslie Greengard, Weizhu Bao
We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the con…
Analysis of some projection method based preconditioners for models of incompressible flow
Mingchao Cai
In this paper, several projection method based preconditioners for various incompressible flow models are studied. In particular, we are interested in the theoretical analysis of a…
Metropolis Integration Schemes for Self-Adjoint Diffusions
Nawaf Bou-Rabee, Aleksandar Donev, Eric Vanden-Eijnden
We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this pr…
Efficient sum-of-exponentials approximations for the heat kernel and their applications
Shidong Jiang, Leslie Greengard, Shaobo Wang
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel…
The solution of the scalar wave equation in the exterior of a sphere
Leslie Greengard, Thomas Hagstrom, Shidong Jiang
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our form…