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  1. A Lightweight, Geometrically Flexible Fast Algorithm for the Evaluation of Layer and Volume Potentials

    Publication
    Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In …

  2. An O(logN) Monte Carlo method for periodic Coulomb systems

    Publication
    Efficient Monte Carlo (MC) sampling of many-body systems with long-range electrostatics is often limited by the cost of per-move energy-difference evaluation under periodic boundary …

  3. Fast Ewald Summation with Prolates for Charged Systems in the NPT Ensemble

    Publication
    We present an NPT extension of Ewald summation with prolates (ESP), a spectrally accurate and scalable particle-mesh method for molecular dynamics simulations of periodic, charged systems. Building …

  4. Space-time adaptive methods for parabolic evolution equations

    Publication
    We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two …

  5. The Helmholtz Dirichlet and Neumann problems on piecewise smooth open curves

    Publication
    A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and …

  6. Interpolative separable density fitting on adaptive real space grids

    Publication
    We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially …

  7. Fast summation of Stokes potentials using a new kernel-splitting in the DMK framework

    Publication
    Classical Ewald methods for Coulomb and Stokes interactions rely on ``kernel-splitting," using decompositions based on Gaussians to divide the resulting potential into a near field and a …

  8. A domain decomposition method for computing the scattering matrix of waveguide circuits

    Publication
    We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto …

  9. A fast spectral sum-of-Gaussians method for electrostatic summation in quasi-2D systems

    Publication
    The quasi-2D electrostatic systems, characterized by periodicity in two dimensions with a free third dimension, have garnered significant interest in many fields. We apply the sum-of …

  10. Designing objects that are invisible to electromagnetic waves

    Publication
    This article shows that it is, in principle, possible to make a dielectric rod completely invisible to an incident electromagnetic plane wave of a given frequency. Students can …

  11. Accelerating Fast Ewald Summation with Prolates for Molecular Dynamics Simulations

    Publication
    Fast Ewald summation is the most widely used approach for computing long-range Coulomb interactions in molecular dynamics (MD) simulations. While the asymptotic scaling is nearly optimal, its …

  12. An Accurate and Efficient Scheme for Function Extension on Smooth Domains

    Publication
    A new scheme is proposed to construct an (n)-times differentiable function extension of an (n)-times differentiable function defined on a smooth domain, (D,) in (d)-dimensions …

  13. A Dual-space Multilevel Kernel-splitting Framework for Discrete and Continuous Convolution

    Publication
    … is calculated using asymptotic methods. We illustrate the performance of DMK for both continuous and discrete sources with extensive numerical examples in two and three dimensions.

  14. Compressing the memory variables in constant-Q viscoelastic wave propagation via an improved sum-of-exponentials approximation

    Publication
    Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q theory, is widely …

  15. Recursive reduction quadrature for the evaluation of Laplace layer potentials in three dimensions

    Publication
    A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The …

  16. Coordinate complexification for the Helmholtz equation with Dirichlet boundary conditions in a perturbed half-space

    Publication
    We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half …

  17. Design of Perfectly Conducting Objects That Are Invisible to an Incident Plane Wave

    Publication
    This work concerns the design of perfectly conducting objects that are invisible to an incident transverse magnetic plane wave. The object in question is a finite planar waveguide …

  18. A new version of the adaptive fast Gauss transform for discrete and continuous sources

    Publication
    We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane …

  19. A fast method for imposing periodic boundary conditions on arbitrarily-shaped lattices in two dimensions

    Publication
    A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes …

  20. Approximating the Gaussian as a Sum of Exponentials and Its Applications to the Fast Gauss Transform

    Publication
    We develop efficient and accurate sum-of-exponential (SOE) approximations for the Gaussian using rational approximation of the exponential function on the negative real axis. Six digit accuracy …

  21. A stable, efficient scheme for \({C}^n\) function extensions on smooth domains in \({R}^d\)

    Publication
    A new scheme is proposed to construct a \(mathcal{C}^n\) function extension for smooth functions defined on a smooth domain \(Din mathbb{R}^d\). Unlike the PUX …

  22. Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries

    Publication
    A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary …