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A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
2015/7/14
This paper is concerned with the fast computation of Fourier integral operators of the general form Rd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
FAST COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators generalized Radon transform separated representation nonuniform fast Fourier transform matrix approximation operator compression randomized algorithms reflection seismology
2015/7/14
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation, general hyperbolic equations, an...
Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions
Second kind integral equation Dirichlet problem Biharmonic equation
2015/7/14
A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on th...
FAST WAVE COMPUTATION VIA FOURIER INTEGRAL OPERATORS
Wave equations Fourier integral operators discrete symbol calculus random sampling separated approximation multiscale computations
2015/7/14
This paper presents a numerical method for “time upscaling” wave equations, i.e., performing time steps not limited by the Courant-FriedrichsLewy (CFL) condition. The proposed method leverages recent ...
A MULTISCALE BUTTERFLY ALGORITHM FOR MULTIDIMENSIONAL FOURIER INTEGRAL OPERATORS
Fourier integral operators the butterfly algorithm hierarchical decomposition separated representation
2015/7/14
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = Rd a(x, ξ)e2πıΦ(x,ξ)f (ξ)dξ, where Φ(x, ξ) is a phase funct...
Hierarchical Interpolative Factorization for Elliptic Operators:Integral Equations
Hierarchical Interpolative Factorization Elliptic Operators Integral Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions.This factorization takes the form of an...
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost
electron repulsion integral tensor tensor hypercontraction format cubic scaling cost
2015/7/14
Electron repulsion integral tensor has ubiquitous applications in quantum chemistry calculations. In this work, we propose an algorithm which compresses the electron repulsion tensor into the tensor h...
A TECHNIQUE FOR UPDATING HIERARCHICAL SKELETONIZATION-BASED FACTORIZATIONS OF INTEGRAL OPERATORS
factorization updating local perturbations hierarchical factorizations integral equations
2015/7/14
We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geo...
THE INTEGRAL K-THEORETIC NOVIKOV CONJECTURE FOR GROUPS WITH FINITE ASYMPTOTIC DIMENSION
K-THEORETIC integral
2015/7/7
The goal of this paper is to apply the techniques developed by the first author
in [3] to verify the integral Novikov conjecture for groups with finite asymptotic
dimension as defi...
A recent body of work introduced new tight-frames of curvelets [3, 4] to address key problems in approximation theory and image processing. This paper shows that curvelets essentially provide optimall...
Fast Computation of Fourier Integral Operators
Fourier integral operators generalized Radon transform separated representation nonuniform fast Fourier transform matrix approximation operator compression randomized algorithms reflection seismology
2015/6/17
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations....
A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
Fourier integral operators the butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
2015/6/17
This paper is concerned with the fast computation of Fourier integral operators of the general form RRd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations
Integral monte carlo method the worm simulation lattice model the continuous spatial multibody system thermodynamics
2014/12/20
We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. ...
Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations
Worm algorithm quantum multibody system thermodynamic properties continuous space
2014/12/20
A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The a...
Dilute Bose gas with correlated disorder: a path integral Monte Carlo study
Dilute bose gas thermodynamics integral monte carlo method the continuous space superfluids quantum
2014/12/19
We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disord...