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A Posteriori Error Analysis for A Class of Integral Equations and Variational Inequalities
Integral Equations Variational Inequalities
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2015/12/11
We consider elliptic and parabolic variational equations and inequalities governed by
integro-differential operators of order 2s ∈ (0,2]. Our main motivation is the pricing of European
or Amer...
Integral Motives and Special Values of Zeta Functions
Zeta Functions Integral Motives
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2015/12/10
For each ˉeld k, we deˉne a category of rationally decomposed mixed
motives with Z-coe±cients. When k is ˉnite, we show that the category is Tannakian, and we prove formulas relating the behaviour of...
Generalized Iteration Method for First-Kind Integral Equations
Generalized Iteration Method First-Kind Integral Equations
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2015/10/16
An iteration method is described to solve one-dimensional, first-kind integral equations with finite integration limits and difference kernel, K(x − x), that decays exponentially. The method re...
SPECTACLE CYCLES WITH COEFFICIENTS AND MODULAR FORMS OF HALF-INTEGRAL WEIGHT
SPECTACLE CYCLES COEFFICIENTS AND MODULAR FORMS HALF-INTEGRAL WEIGHT
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2015/10/14
In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of o...
POSET BLOCK EQUIVALENCE OF INTEGRAL MATRICES
POSET BLOCK EQUIVALENCE INTEGRAL MATRICES
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2015/9/29
Given square matrices B and B0 with a poset-indexed block structure (for which an ij block is zero unless i 1 j), when are there invertible matrices U and V with this required-zero-block structure suc...
The Embedded Boundary Integral Method (EBI) for the Incompressible Navier-Stokes equations
Embedded Boundary Integral Method (EBI) Incompressible Navier Stokes equations
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2015/7/15
We present a new method for the solution of the unsteady incompressible Navier-Stokes equations. Our goal is to achieve a robust and scalable methodology for two and three dimensional incompressible f...
Fast Algorithms for Boundary Integral Equations
Boundary integral equations Laplace equation Helmholtz equation fast algorithms fast multipole method hierarchical matrices wavelets multiscale methods multidirectional methods
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2015/7/15
This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order...
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
oundary integral equations Nystrom discretization Singular integrals Nearly singular integrals Fast solvers Laplace equation Stokes equation Navier equation Fast multipole method Fast Fourier transform
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2015/7/14
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nystro ¨m’s method for discretization, and combine it with s...
A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
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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
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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
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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
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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
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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
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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
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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...