6 citations · 12 across the 14 of their papers we have counts for
15 papers
An adaptive delaminating Levin method in two dimensions
Shukui Chen, Kirill Serkh, James Bremer +1
We present an adaptive delaminating Levin method for evaluating bivariate oscillatory integrals over rectangular domains. Whereas previous analyses of Levin methods impose non-reso…
An adaptive Levin method for complicated domains
Shukui Chen, Kirill Serkh, James Bremer
In this paper we describe an adaptive Levin method for numerically evaluating integrals of the form over general domains that have be…
Enhancing Image Layout Control with Loss-Guided Diffusion Models
Zakaria Patel, Kirill Serkh
Diffusion models are a powerful class of generative models capable of producing high-quality images from pure noise using a simple text prompt. While most methods which introduce a…
An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion Curves
Seungbae Bang, Kirill Serkh, Oded Stein +1
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization ar…
On the Approximation of Singular Functions by Series of Non-integer Powers
Mohan Zhao, Kirill Serkh
In this paper, we describe an algorithm for approximating functions of the form over , where is some signed Radon measure, or, mor…
A Continuation Method for Fitting a Bandlimited Curve to Points in the Plane
Mohan Zhao, Kirill Serkh
In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in . The main…
On polynomial interpolation in the monomial basis
Zewen Shen, Kirill Serkh
In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde…
Phase function methods for second order inhomogeneous linear ordinary differential equations
Kirill Serkh, James Bremer
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underl…
On the adaptive Levin method
Shukui Chen, Kirill Serkh, James Bremer
The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antider…
Rapid evaluation of Newtonian potentials on planar domains
Zewen Shen, Kirill Serkh
The accurate and efficient evaluation of Newtonian potentials over general 2-D domains is important for the numerical solution of Poisson's equation and volume integral equations.…
Accelerating potential evaluation over unstructured meshes in two dimensions
Zewen Shen, Kirill Serkh
The accurate and efficient evaluation of potentials is of great importance for the numerical solution of partial differential equations. When the integration domain of the potentia…
Fast Computation of Electrostatic Potentials for Piecewise Constant Conductivities
Kyle Bower, Kirill Serkh, Spyros Alexakis +1
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ a…
A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing
Dawei Wang, Kirill Serkh, Christina Christara
This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference…
On the Evaluation of the Eigendecomposition of the Airy Integral Operator
Zewen Shen, Kirill Serkh
The distributions of the -th largest level at the soft edge scaling limit of Gaussian ensembles are some of the most important distributions in random matrix theory, and their n…
Zernike Polynomials: Evaluation, Quadrature, and Interpolation
Philip Greengard, Kirill Serkh
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications includ…