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Jun 30, 2018
06/18

by
Elena Celledoni; Robert I. McLachlan; David I. McLaren; Brynjulf Owren; G. R. W. Quispel

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Applying Kahan's discretization to the reduced Nahm equations, we obtain two classes of integrable mappings.

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1702.00280

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2.0

Jun 29, 2018
06/18

by
Nikolaus Hansen; Anne Auger; Olaf Mersmann; Tea Tusar; Dimo Brockhoff

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COCO is a platform for Comparing Continuous Optimizers in a black-box setting. It aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. We present the rationals behind the development of the platform as a general proposition for a guideline towards better benchmarking. We detail underlying fundamental concepts of COCO such as its definition of a problem, the idea of instances, the relevance of target values, and...

Topics: Machine Learning, Artificial Intelligence, Numerical Analysis, Computing Research Repository,...

Source: http://arxiv.org/abs/1603.08785

2
2.0

Jun 29, 2018
06/18

by
Shoji Itoh; Masaaki Sugihara

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An improved preconditioned conjugate gradient squared (PCGS) algorithm has recently been proposed, and it performs much better than the conventional PCGS algorithm. In this paper, the improved PCGS algorithm is verified as a coordinative to the left-preconditioned system, and it has the advantages of both the conventional and the left-PCGS; this is done by comparing, analyzing, and executing numerical examinations of various PCGS algorithms, including another improved one. We show that the...

Topics: Numerical Analysis, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1603.00176

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3.0

Jun 28, 2018
06/18

by
Will Pazner; Andrew Nonaka; John Bell; Marcus Day; Michael Minion

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We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a multi-implicit spectral deferred correction (MISDC) strategy that iteratively couples advection, diffusion, and reactions evolving subject to a constraint. Our new approach overcomes a stability limitation of our previous second-order method encountered when trying to incorporate higher-order polynomial...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1512.06459

3
3.0

Jun 30, 2018
06/18

by
Federico Piazzon

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We introduce numerical methods for the approximation of the main (global) quantities in Pluripotential Theory as the \emph{extremal plurisubharmonic function} $V_E^*$ of a compact $\mathcal L$-regular set $E\subset \C^n$, its \emph{transfinite diameter} $\delta(E),$ and the \emph{pluripotential equilibrium measure} $\mu_E:=\ddcn{V_E^*}.$ The methods rely on the computation of a \emph{polynomial mesh} for $E$ and numerical orthonormalization of a suitable basis of polynomials. We prove the...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1704.03411

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4.0

Jun 30, 2018
06/18

by
Konstantin Avrachenkov; Philippe Jacquet; Jithin Sreedharan

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Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper we develop efficient distributed algorithms to detect, with higher resolution, closely situated eigenvalues and corresponding eigenvectors of symmetric graph matrices. We model the system of graph spectral computation as physical systems with Lagrangian and...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1704.00941

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3.0

Jun 30, 2018
06/18

by
Ajinkya Kadu; Tristan van Leeuwen; K. Joost Batenburg

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This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We represent the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimization problem in terms of the background and coefficients for the level-set function. To constrain the...

Topics: Computational Engineering, Finance, and Science, Numerical Analysis, Computing Research Repository

Source: http://arxiv.org/abs/1704.00568

2
2.0

Jun 29, 2018
06/18

by
Wei Jiang; Jie Liu; Qing Huo Liu

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Based on the idea of the Abelian group theory in mathematics,this paper finds a sufficient condition of having independent TE and TM modes in a waveguide filled with homogenous anisotropic lossless medium. For independent TE modes, we prove the nonzero cut-off wavenumbers obtained from longitudinal scalar magnetic field stimulation and transverse vector electric field stimulation are same in theory. For independent TM modes, we also prove the nonzero cut-off wavenumbers obtained from...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1603.06439

2
2.0

Jun 30, 2018
06/18

by
Yoshihito Kazashi

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Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assumed to be given by an exponential of a Gaussian random field that is represented by a series expansion of some system of functions. Graham et al. [16] developed a lattice-based QMC theory for this problem and established a quadrature error decay rate $\approx 1$ with respect to the number of quadrature points. The key...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1701.05974

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3.0

Jun 30, 2018
06/18

by
Wilhelmiina Hämäläinen

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Fisher's exact test is often a preferred method to estimate the significance of statistical dependence. However, in large data sets the test is usually too worksome to be applied, especially in an exhaustive search (data mining). The traditional solution is to approximate the significance with the $\chi^2$-measure, but the accuracy is often unacceptable. As a solution, we introduce a family of upper bounds, which are fast to calculate and approximate Fisher's $p$-value accurately. In addition,...

Topics: Computation, Numerical Analysis, Computing Research Repository, Statistics

Source: http://arxiv.org/abs/1405.1250

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7.0

Jun 28, 2018
06/18

by
Huikang Liu; Weijie Wu; Anthony Man-Cho So

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A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel manifold, which are known to converge globally under mild conditions. To determine the convergence rate of these methods, we give an explicit estimate of the exponent in a Lojasiewicz inequality for the (non-convex) set of critical points of the aforementioned...

Topics: Numerical Analysis, Learning, Optimization and Control, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1510.01025

2
2.0

Jun 30, 2018
06/18

by
Min Hyung Cho; Jingfang Huang; Dangxing Chen; Wei Cai

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In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key compression step in the H-FMM is based on a fact that the multipole expansion for the sources of the free-space Green's function can be used also to compress the far field of the sources of the layered-media or domain Green's function, and a similar result exists...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1703.09136

3
3.0

Jun 29, 2018
06/18

by
Simon Hubbert; Jeremy Levesley

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In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite smoothness. In this paper we deliver a first error estimates for the multilevel algorithm using analytic basis functions. The estimate has two parts, one involving the convergence of a low degree polynomial truncation term and one involving the control of...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.02457

3
3.0

Jun 30, 2018
06/18

by
Andreas Buhr; Christian Engwer; Mario Ohlberger; Stephan Rave

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The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of an a posteriori error estimator to reliably estimate the error introduced by the reduction process. However, straightforward implementations of standard residual based estimators show poor numerical stability, rendering them unusable if high accuracy is...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1407.8005

Using stiffness matrix and lumped-mass representation specified number of natural frequencies are obtained using inverse iteration method. Mode shapes for each frequency are also obtained. These frequencies and mode shapes can be found in reasonable periods of computer time utilizing this code.

Topics: NASA Technical Reports Server (NTRS), CDC 6000 SERIES COMPUTERS, COMPUTER PROGRAMS, FORTRAN, IBM...

3
3.0

Jun 30, 2018
06/18

by
Simon N. Chandler-Wilde; David P. Hewett

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We consider time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens. In contrast to previous studies, in which the domain occupied by the screen is assumed to be Lipschitz or smoother, we consider screens occupying an arbitrary bounded open set in the plane. Thus our study includes cases where the closure of the domain occupied by the screen has larger planar Lebesgue measure than the screen, as can happen, for example, when the screen has a fractal...

Topics: Mathematics, Numerical Analysis, Analysis of PDEs

Source: http://arxiv.org/abs/1401.2805

3
3.0

Jun 29, 2018
06/18

by
Kai Bittner; Hans Georg Brachtendorf

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New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrary to classical wavelet transforms, the algorithms are not based on filter coefficients, but on algorithms for B-spline expansions (differentiation, Oslo algorithm, etc.). Due to inherent properties of the spline wavelets, the algorithm can be modified for spline grid refinement or coarsening. The performance of the algorithms is demonstrated by numerical tests of the...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1604.07228

3
3.0

Jun 29, 2018
06/18

by
Jian Huang; Long Chen; Hongxing Rui

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An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence constraint. The nonlinear equation can be solved element-wise with a closed formulae. The linear saddle point system for the constraint is reduced into a symmetric positive definite system of Poisson type. Furthermore an empirical choice of the parameter...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1611.05576

3
3.0

Jun 29, 2018
06/18

by
Balgaisha Mukanova; Vladimir G. Romanov

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The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR) data interpretation problem is shown. The non-iterative algorithm for reconstructing the unknown source F(x) is developed. The algorithm is based on the Fourier expansion of the source F(x) and the explicit representation of the direct problem solution via...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.03555

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6.0

Jun 26, 2018
06/18

by
D. A. Bini; S. Dendievel; G. Latouche; B. Meini

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The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure. To this end, we propose some algorithms which exploit the Toeplitz structure and the properties of generators. Such algorithms allow to compute the exponential of very large matrices, which would otherwise be untreatable with standard methods. We also prove interesting decay properties of the exponential of a...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1502.07533

2
2.0

Jun 30, 2018
06/18

by
Martin Hutzenthaler; Arnulf Jentzen

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We develope a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the $ L^p $-distance between the solution process of an SDE and an arbitrary It\^o process, which we view as a perturbation of the solution process of the SDE, by the $ L^q $-distances of the differences of the local characteristics for suitable $ p, q > 0 $. As...

Topics: Probability, Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1401.0295

2
2.0

Jun 30, 2018
06/18

by
Sheng Zhang

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We prove Korn's inequalities for Naghdi and Koiter shell models defined on spaces of discontinuous piecewise functions. They are useful in study of discontinuous finite element methods for shells.

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1412.3654

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4.0

Jun 29, 2018
06/18

by
Daisuke Furihata; Mihály Kovács; Stig Larsson; Fredrik Lindgren

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We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension $d\le 3$. We discretize the equation using a standard finite element method in space and a fully implicit backward Euler method in time. By proving optimal error estimates on subsets of the probability space with arbitrarily large probability and uniform-in-time moment bounds we show that the numerical solution converges strongly to the solution as the...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1612.09459

2
2.0

Jun 30, 2018
06/18

by
Jun Hu; Rui Ma

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In this paper, a new method is proposed to produce guaranteed lower bounds for eigenvalues of general second order elliptic operators in any dimension. Unlike most methods in the literature, the proposed method only needs to solve one discrete eigenvalue problem but not involves any base or intermediate eigenvalue problems, and does not need any a priori information concerning exact eigenvalues either. Moreover, it just assumes basic regularity of exact eigenfunctions. This method is defined by...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1406.6520

3
3.0

Jun 29, 2018
06/18

by
Duangpen Jetpipattanapong; Gun Srijuntongsiri

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We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the pivots. Our method is based on the minimum degree algorithm and also considers the stability of the factors at the same time. Our experiments show that our method produces factors that are sparser than the factors computed by MA57 and are stable.

Topics: Numerical Analysis, Computing Research Repository

Source: http://arxiv.org/abs/1601.06812

3
3.0

Jun 29, 2018
06/18

by
Giacomo Dimarco; Lorenzo Pareschi

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We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full Boltzmann equation. The behavior of the schemes in the Navier-Stokes regime is also studied and compatibility conditions derived. We show that, compared to IMEX Runge-Kutta methods, the IMEX multistep schemes have several advantages due to the absence of coupling...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1603.00102

3
3.0

Jun 30, 2018
06/18

by
K. Kopotun; D. Leviatan; A. Prymak

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Several results on constrained spline smoothing are obtained. In particular, we establish a general result, showing how one can constructively smooth any monotone or convex piecewise polynomial function (ppf) (or any $q$-monotone ppf, $q\geq 3$, with one additional degree of smoothness) to be of minimal defect while keeping it close to the original function in the ${\mathbb L}_p$-(quasi)norm. It is well known that approximating a function by ppf's of minimal defect (splines) avoids introduction...

Topics: Mathematics, Numerical Analysis, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1403.7983

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5.0

Jun 27, 2018
06/18

by
Benjamin Berkels; Alexander Effland; Martin Rumpf

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The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and non-constrained relaxation of the originally...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1505.05284

3
3.0

Jun 29, 2018
06/18

by
Lorenzo Pareschi; Thomas Rey

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Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in particular for high order ones. In this paper, inspired by micro-macro decomposition methods for kinetic equations, we present a class of schemes which are capable to preserve the steady state solution and achieve high order accuracy for a class of time dependent...

Topics: Analysis of PDEs, Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1602.02711

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5.0

Jun 30, 2018
06/18

by
Xiaofeng Yang; Alex Brylev

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In this paper, we consider numerical approximations for the model of smectic-A liquid crystal flows. The model equation, that is derived from the variational approach of the de Gennes free energy, is a highly nonlinear system that couples the incompressible Navier-Stokes equations, and two nonlinear coupled second-order elliptic equations. Based on some subtle explicit--implicit treatments for nonlinear terms, we develop a unconditionally energy stable, linear and decoupled time marching...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1701.07487

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4.0

Jun 29, 2018
06/18

by
Nicolas Crouseilles; Lukas Einkemmer; Erwan Faou

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We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov--Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher...

Topics: Physics, Numerical Analysis, Computational Physics, Mathematics

Source: http://arxiv.org/abs/1602.09062

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2.0

Jun 28, 2018
06/18

by
Duan Chen; Wei Cai; Brian Zinser; Min Hyung Cho

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In this paper, we develop an accurate and efficient Nystr\"{o}m volume integral equation (VIE) method for the Maxwell equations for large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1510.07023

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Jun 30, 2018
06/18

by
Jonathan Gustafsson; Bartosz Protas

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In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical fluid dynamics. Following a review of key mathematical properties of such solutions related to the slow decay of the velocity field at large distances from the obstacle, we develop and carefully validate a spectrally-accurate computational approach which...

Topics: Fluid Dynamics, Physics, Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1407.1731

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6.0

Jun 29, 2018
06/18

by
Eduardo Corona; Leslie Greengard; Manas Rachh; Shravan Veerapaneni

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We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1606.07428

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4.0

Jun 30, 2018
06/18

by
Majnu John; Yihren Wu

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Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it's only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential equations. In line with this very recent trend, we show how certain commonly used finite difference schemes for numerical solutions of ordinary and partial differential equations can be considered in a regression setting. Focusing on this regression framework,...

Topics: Computation, Statistics, Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1701.05609

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6.0

Jun 27, 2018
06/18

by
Cuong Ngo; Weizhang Huang

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Nonnegative directional splittings of anisotropic diffusion operators in the divergence form are investigated. Conditions are established for nonnegative directional splittings to hold in a neighborhood of an arbitrary interior point. The result is used to construct monotone finite difference schemes for the boundary value problem of anisotropic diffusion operators. It is shown that such a monotone scheme can be constructed if the underlying diffusion matrix is continuous on the closure of the...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1503.08177

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3.0

Jun 30, 2018
06/18

by
Shi Jin; Hanqing Lu; Lorenzo Pareschi

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For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that contain both uncertainties and multiple scales. Compared with previous methods for these problems, our new method use the implicit-explicit (IMEX) time discretization to gain higher order accuracy, and by using a modified diffusion operator based penalty method, a...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1703.03841

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9.0

Jun 28, 2018
06/18

by
Nick Dexter; Clayton Webster; Guannan Zhang

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This work analyzes the overall computational complexity of the stochastic Galerkin finite element method (SGFEM) for approximating the solution of parameterized elliptic partial differential equations with both affine and non-affine random coefficients. To compute the fully discrete solution, such approaches employ a Galerkin projection in both the deterministic and stochastic domains, produced here by a combination of finite elements and a global orthogonal basis, defined on an isotopic total...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1507.05545

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2.0

Jun 30, 2018
06/18

by
Richard C. Barnard; Martin Frank; Kai Krycki

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In this paper we study the sensitivities of electron dose calculations with respect to the stopping power and the transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker-Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker-Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion ($P_N$) and an HLL finite volume method....

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1410.5622

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2.0

Jun 28, 2018
06/18

by
Eskil Hansen; Erik Henningsson

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The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable criteria. In the setting of linear dissipative evolution equations we prove optimal convergence orders, simultaneously in time and space. We apply our abstract results to dimension splitting of a 2D diffusion problem, where a finite element method is used for...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1512.05931

The interactions of control system and distributed flexible structural dynamics is explored for mechanical arms. A modeling process using 4 x 4 transfer matrices is described which permits the closed loop response of many current arm configurations to be evaluated. Root locus, frequency response, modal shapes, and time impulse response have all been obtained from the digital computer implementation of this model, which is oriented to arm design and allows for easy variation of the arm...

Topics: NASA Technical Reports Server (NTRS), DYNAMIC STRUCTURAL ANALYSIS, FLEXIBLE BODIES, MECHANICAL...

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3.0

Jun 29, 2018
06/18

by
Lise-Marie Imbert-Gerard; Leslie Greengard

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The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning to com- putational physics. Here, we present a high-order accurate pseudo-spectral approach, applicable to closed surfaces of genus one in three dimensional space, with a view toward applications in plasma physics and fluid dynamics.

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1608.04436

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5.0

Jun 30, 2018
06/18

by
Matania Ben-Artzi; Guy Katriel

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The biharmonic operator plays a central role in a wide array of physical models, notably in elasticity theory and the streamfunction formulation of the Navier-Stokes equations. The need for corresponding numerical simulations has led, in recent years, to the development of a discrete biharmonic calculus. The primary object of this calculus is a high-order compact discrete biharmonic operator (DBO). The numerical results have been remarkably accurate, and have been corroborated by some rigorous...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1702.08179

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3.0

Jun 29, 2018
06/18

by
Igor Ostanin; Ivan Tsybulin; Mikhail Litsarev; Ivan Oseledets; Denis Zorin

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The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a topological derivative. The numerical solution of the elasticity boundary value problem at every iteration is performed with the boundary element formulation and the kernel-independent fast multipole method. Providing excellent single node performance, scalable...

Topics: Optimization and Control, Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1612.04082

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3.0

Jun 28, 2018
06/18

by
Jiayu Han; Yidu Yang

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In this paper we develop an $H^m$-conforming ($m\ge1$) spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We construct a set of basis functions on the interval $[-1,1]$ that is made up of the generalized Jacobi polynomials (GJPs) and the nodal basis functions. So the basis functions on multi-dimensional rectangles consist of the tensorial product of the basis functions on the interval $[-1,1]$. Then we construct the spectral...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1512.06659

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2.0

Jun 30, 2018
06/18

by
Fardin Saedpanah

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We study a second order hyperbolic initial-boundary value partial differential equation with memory, that results in an integro-differential equation with a convolution kernel. The kernel is assumed to be either smooth or no worse than weakly singular, that arise, e.g. in linear and fractional order viscoelasticity. Existence and uniqueness of the spatial local and global Galerkin approximation of the problem is proved by means of Picard iteration. Then spatial finite element approximation of...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1401.7213

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2.0

Jun 30, 2018
06/18

by
Erich Novak; Daniel Rudolf

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We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this problem is intractable while for other parameters the problem is tractable and the complexity is only polynomial in the dimension for every fixed $\varepsilon>0$. For randomized algorithms we completely characterize the set of parameters that lead to easy or...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1402.5011

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5.0

Jun 29, 2018
06/18

by
M. J. Kronenburg

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Toom-Cook multiprecision multiplication is a well-known multiprecision multiplication method, which can make use of multiprocessor systems. In this paper the Toom-Cook complexity is derived, some explicit proofs of the Toom-Cook interpolation method are given, the even-odd method for interpolation is explained, and certain aspects of a 32-bit C++ and assembler implementation, which is in development, are discussed. A performance graph of this implementation is provided. The Toom-Cook method can...

Topics: Numerical Analysis, Computing Research Repository

Source: http://arxiv.org/abs/1602.02740

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Jun 30, 2018
06/18

by
Christian Irrgeher; Peter Kritzer; Gunther Leobacher; Friedrich Pillichshammer

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We study integration in a class of Hilbert spaces of analytic functions defined on the $\mathbb{R}^s$. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite integration rules and show that the error of our algorithms decays exponentially fast. Furthermore, we give necessary and sufficient conditions under which we achieve exponential convergence with weak, polynomial, and strong polynomial tractability.

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1403.5102

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5.0

Jun 30, 2018
06/18

by
Bryan Quaife; George Biros

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We construct a high-order adaptive time stepping scheme for vesicle suspensions with viscosity contrast. The high-order accuracy is achieved using a spectral deferred correction (SDC) method, and adaptivity is achieved by estimating the local truncation error with the numerical error of physically constant values. Numerical examples demonstrate that our method can handle suspensions with vesicles that are tumbling, tank-treading, or both. Moreover, we demonstrate that a user-prescribed...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1409.0212