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Randomized algorithms for low-rank tensor decompositions in the Tucker formatMay 17 2019Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized matrix methods ... More

Majorization bounds for Ritz values of Rayleigh quotients of self-adjoint matricesMay 16 2019In this work we obtain a priori, a posteriori and mixed type upper bounds for the absolute change in Ritz values of Rayleigh quotients of self-adjoint matrices in terms of submajorization relations. Some of our results solve recent conjectures by Knyazev, ... More

Multigrid-reduction-in-time for Eddy Current problemsMay 16 2019Parallel-in-time methods have shown success for reducing the simulation time of many time-dependent problems. Here, we consider applying the multigrid-reduction-in-time (MGRIT) algorithm to a voltage-driven eddy current model problem.

A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimesMay 16 2019An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell interface a multiscale ... More

On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision ArithmeticMay 14 2019We consider three mathematically equivalent variants of the conjugate gradient (CG) algorithm and how they perform in finite precision arithmetic. It was shown in [{\em Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences}, Lin.~Alg.~Appl., ... More

A projection algorithm on the set of polynomials with two boundsMay 14 2019The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer. Algorithms, 76(3), ... More

A projection algorithm on the set of polynomials with two boundsMay 14 2019May 17 2019The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer. Algorithms, 76(3), ... More

Wilkinson's bus: Weak condition numbers, with an application to singular polynomial eigenproblemsMay 14 2019We propose a new approach to the theory of conditioning for numerical analysis problems for which both classical and stochastic perturbation theory fail to predict the observed accuracy of computed solutions. To motivate our ideas, we present examples ... More

Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizationsMay 14 2019This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their in-plane and out-of-plane ... More

Synthetic aperture imaging with intensity-only dataMay 13 2019We consider imaging the reflectivity of scatterers from intensity-only data recorded by a single moving transducer that both emits and receives signals, forming a synthetic aperture. By exploiting frequency illumination diversity, we obtain multiple intensity ... More

Fast Proper Orthogonal Decomposition Using Improved Sampling and Iterative Techniques for Singular Value DecompositionMay 13 2019Proper Orthogonal Decomposition (POD), also known as Principal component analysis (PCA), is a dimensionality reduction technique used to capture the energetically dominant features of datasets, known as eigenfeatures or POD modes. These modes can be obtained ... More

A Cone-Beam X-Ray CT Data Collection Designed for Machine LearningMay 12 2019Unlike previous works, this open data collection consists of X-ray cone-beam (CB) computed tomography (CT) datasets specifically designed for machine learning applications and high cone-angle artefact reduction. Forty-two walnuts were scanned with a laboratory ... More

Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse ProblemsMay 12 2019Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on certain parameters ... More

A stable semi-implicit algorithmMay 11 2019When the singular values of the evolution operator are all smaller or all greater than one, stable integration algorithms are obtained either by explicit or implicit methods. When the singular spectrum mixes greater and smaller than one values, neither ... More

Hyperparameter Estimation in Bayesian MAP Estimation: Parameterizations and ConsistencyMay 10 2019The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows for principled learning of hyperparameters. The posterior distribution may ... More

Solving Irregular and Data-enriched Differential Equations using Deep Neural NetworksMay 10 2019Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental features in numerical ... More

A Subspace Framework for ${\mathcal H}_\infty$-Norm MinimizationMay 10 2019We deal with the minimization of the ${\mathcal H}_\infty$-norm of the transfer function of a parameter-dependent descriptor system over the set of admissible parameter values. Subspace frameworks are proposed for such minimization problems where the ... More

Non-Conforming Mesh Refinement for High-Order Finite ElementsMay 10 2019We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral ... More

SABER: A Systems Approach to Blur Estimation and Reduction in X-ray ImagingMay 10 2019Blur in X-ray radiographs not only reduces the sharpness of image edges but also reduces the overall contrast. The effective blur in a radiograph is the combined effect of blur from multiple sources such as the detector panel, X-ray source spot, and system ... More

On Topologically Controlled Model Reduction for Discrete-Time SystemsMay 10 2019In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra ... More

A survey of computational frameworks for solving the acoustic inverse problem in three-dimensional photoacoustic computed tomographyMay 09 2019Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging technique that holds great promise for biomedical imaging. PACT is a hybrid imaging method that can exploit the strong endogenous contrast of optical ... More

Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methodsMay 09 2019We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication in the Fourier ... More

An Efficient and high accuracy finite-difference scheme for the acoustic wave equation in 3D heterogeneous mediaMay 09 2019Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work, we employed the combined scheme and developed a new ... More

Approximating cube roots of integers, after Heron's Metrica III.20May 09 2019Heron, in Metrica III.20-22, is concerned with the the division of solid figures - pyramids, cones and frustra of cones - to which end there is a need to extract cube roots. We report here on some of our findings on the conjecture by Taisbak in C.M.Taisbak, ... More

Projections onto the canonical simplex with additional linear inequalitiesMay 09 2019We consider projections onto the canonical simplex with additional linear inequalities. We mention three cases in the fields of distributionally robust optimization and accuracy at the top where such projections arise. For these specific examples we write ... More

Variational training of neural network approximations of solution maps for physical modelsMay 07 2019A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and train the network variationally ... More

The algorithm for the recovery of integer vector via linear measurementsMay 07 2019In this paper we continue the studies on the integer sparse recovery problem that was introduced in \cite{FKS} and studied in \cite{K},\cite{KS}. We provide an algorithm for the recovery of an unknown sparse integer vector for the measurement matrix described ... More

Multifidelity probability estimation via fusion of estimatorsMay 07 2019This paper develops a multifidelity method that enables estimation of failure probabilities for expensive-to-evaluate models via information fusion and importance sampling. The presented general fusion method combines multiple probability estimators with ... More

Computation of Circular Area and Spherical Volume Invariants via Boundary IntegralsMay 06 2019We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume integrals as line and ... More

New communication hiding conjugate gradient variantsMay 04 2019The conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures due to the two global reductions required each iteration. In this paper, we introduce a new communication hiding conjugate gradient variant, which requires ... More

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural NetworksMay 03 2019One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and the dynamically ... More

Algorithms and Complexity for some Multivariate ProblemsMay 03 2019We study multivariate problems like function approximation, numerical integration, global optimization and dispersion. We obtain new results on the information complexity $n(\varepsilon,d)$ of these problems. The information complexity is the amount of ... More

Stability-preserving model order reduction for linear stochastic Galerkin systemsMay 03 2019Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a larger linear dynamical ... More

Extending discrete exterior calculus to a fractional derivativeMay 02 2019Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the dense matrices ... More

A Note on Adjoint Linear AlgebraMay 02 2019A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector, matrix-vector, ... More

An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusionMay 01 2019We propose and analyse the properties of a new class of models for the electromechanics of the cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so ... More

High-performance sampling of generic Determinantal Point ProcessesMay 01 2019Determinantal Point Processes (DPPs) were introduced by Macchi as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a recommender ... More

Optimal robustness of port-Hamiltonian systemsApr 30 2019We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked ... More

Deflation for semismooth equationsApr 30 2019Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea is the combination ... More

Fast Mesh Refinement in Pseudospectral Optimal ControlApr 29 2019Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as ... More

Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systemsApr 29 2019For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the differential ... More

Stability of stochastic impulsive differential equations: integrating the cyber and the physical of stochastic systemsApr 29 2019According to Newton's second law of motion, we humans describe a dynamical system with a differential equation, which is naturally discretized into a difference equation whenever a computer is used. The differential equation is the continuous-time model ... More

Stability conditions of an ODE arising in human motion and its numerical simulationApr 28 2019This paper discusses the stability of an equilibrium point of an ordinary differential equation (ODE) arising from a feed-forward position control for a musculoskeletal system. The studied system has a link, a joint and two muscles with routing points. ... More

A new object-oriented framework for solving multiphysics problems via combination of different numerical methodsApr 28 2019Many interesting phenomena are characterized by the complex interaction of different physical processes, each often best modeled numerically via a specific approach. In this paper, we present the design and implementation of an object-oriented framework ... More

Multilevel adaptive sparse Leja approximations for Bayesian inverse problemsApr 27 2019Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations, deterministic ... More

Multilevel adaptive sparse Leja approximations for Bayesian inverse problemsApr 27 2019May 07 2019Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations, deterministic ... More

A development of Lagrange interpolation, Part I: TheoryApr 27 2019In this work, we introduce the new class of functions which can use to solve the nonlinear/linear multi-dimensional differential equations. Based on these functions, a numerical method is provided which is called the Developed Lagrange Interpolation (DLI). ... More

Convergence of Stochastic-extended Lagrangian molecular dynamics method for polarizable force field simulationApr 27 2019Extended Lagrangian molecular dynamics (XLMD) is a general method for performing molecular dynamics simulations using quantum and classical many-body potentials. Recently several new XLMD schemes have been proposed and tested on several classes of many-body ... More

Evaluating the boundary and Stieltjes transform of limiting spectral distributions for random matrices with a separable variance profileApr 26 2019We present numerical algorithms for solving two problems encountered in random matrix theory and its applications. First, we compute the boundary of the limiting spectral distribution for random matrices with a separable variance profile. Second, we evaluate ... More

Threshold shift method for reliability-based design optimizationApr 25 2019We present a novel approach, referred to as the 'threshold shift method' (TSM), for reliability based design optimization (RBDO). The proposed approach is similar in spirit with the sequential optimization and reliability analysis (SORA) method where ... More

A compact subcell WENO limiting strategy using immediate neighbors for Runge-Kutta Discontinuous Galerkin MethodsApr 25 2019A different WENO limiting strategy using immediate neighbors by dividing them into subcells for the Discontinuous Galerkin method has been proposed. In this limiter, we reconstruct the polynomial in the cell where limiting is needed, using a WENO reconstruction ... More

Low-Rank Tucker Approximation of a Tensor From Streaming DataApr 24 2019This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as the interactions ... More

Construction of the similarity matrix for the spectral clustering method: numerical experimentsApr 24 2019Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual clusters is highly ... More

Multi-modal 3D Shape Reconstruction Under Calibration Uncertainty using Parametric Level Set MethodsApr 23 2019We consider the problem of 3D shape reconstruction from multi-modal data, given uncertain calibration parameters. Typically, 3D data modalities can be in diverse forms such as sparse point sets, volumetric slices, 2D photos and so on. To jointly process ... More

Discrepancy of Digital Sequences: New Results on a Classical QMC TopicApr 23 2019The theory of digital sequences is a fundamental topic in QMC theory. Digital sequences are prototypes of sequences with low discrepancy. First examples were given by Il'ya Meerovich Sobol' and by Henri Faure with their famous constructions. The unifying ... More

Dynamic evaluation of exponential polynomial curves and surfaces via basis transformationApr 23 2019It is shown in "SIAM J. Sci. Comput. 39 (2017):B424-B441" that free-form curves used in CAGD (computer aided geometric design) can usually be represented as the solutions of linear differential systems and points and derivatives on the curves can be evaluated ... More

A theoretical and experimental investigation of a family of immersed finite element methodsApr 22 2019In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of these methods, ... More

Low-Rank Approximation from Communication ComplexityApr 22 2019In low-rank approximation with missing entries, given $A\in \mathbb{R}^{n\times n}$ and binary $W \in \{0,1\}^{n\times n}$, the goal is to find a rank-$k$ matrix $L$ for which: $$cost(L)=\sum_{i=1}^{n} \sum_{j=1}^{n}W_{i,j}\cdot (A_{i,j} - L_{i,j})^2\le ... More

A Simple Local Variational Iteration Method and Related Algorithm for Nonlinear Science and EngineeringApr 22 2019A very simple and efficient local variational iteration method for solving problems of nonlinear science is proposed in this paper. The analytical iteration formula of this method is derived first using a general form of first order nonlinear differential ... More

A convex relaxation to compute the nearest structured rank deficient matrixApr 21 2019Given an affine space of matrices $L$ and a matrix $\theta \in L$, consider the problem of finding the closest rank deficient matrix to $\theta$ on $L$ with respect to the Frobenius norm. This is a nonconvex problem with several applications in estimation ... More

Solution of Definite Integrals using Functional Link Artificial Neural NetworksApr 21 2019This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a learning algorithm, ... More

Removal of spurious solutions encountered in Helmholtz scattering resonance computations in R^dApr 18 2019In this paper we consider a sorting scheme for the removal of spurious scattering resonant pairs in two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a Lippmann-Schwinger type of ... More

Removal of spurious solutions encountered in Helmholtz scattering resonance computations in R^dApr 18 2019May 17 2019In this paper we consider a sorting scheme for the removal of spurious scattering resonant pairs in two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a Lippmann-Schwinger type of ... More

Sensitivity Analysis for Hybrid Systems and Systems with MemoryApr 18 2019We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two (Hessenberg) ... More

An extremal problem for integer sparse recoveryApr 18 2019Motivated by the problem of integer sparse recovery we study the following question. Let $A$ be an $m \times d$ integer matrix whose entries are in absolute value at most $k$. How large can be $d=d(m,k)$ if all $m \times m$ submatrices of $A$ are non-degenerate? ... More

Improving solution accuracy and convergence for stochastic physics parameterizations with colored noiseApr 18 2019Stochastic parameterizations are used in numerical weather prediction and climate modeling to help improve the statistical distributions of the simulated phenomena. Earlier studies (Hodyss et al 2013, 2014) have shown that convergence issues can arise ... More

Towards Solving the Navier-Stokes Equation on Quantum ComputersApr 16 2019In this paper, we explore the suitability of upcoming novel computing technologies, in particular adiabatic annealing based quantum computers, to solve fluid dynamics problems that form a critical component of several science and engineering applications. ... More

The Euler-Maruyama Scheme for SDEs with Irregular Drift: Convergence Rates via Reduction to a Quadrature ProblemApr 16 2019We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a novel framework for the error analysis by reducing it to a weighted quadrature problem ... More

Approximation and Uncertainty Quantification of Stochastic Systems with Arbitrary Input Distributions using Weighted Leja InterpolationApr 16 2019Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of a stochastic system's input parameters are not normal, uniform, or closely related ones, due to ... More

An Integral Equation Method for the Cahn-Hilliard Equation in the Wetting ProblemApr 15 2019We present an integral equation approach to solve the Cahn-Hilliard equation equipped with boundary conditions that model solid surfaces with prescribed Young's angles. Discretization of the system in time using convex splitting leads to a modified biharmonic ... More

A Discussion on Solving Partial Differential Equations using Neural NetworksApr 15 2019Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are five-fold. (1) ... More

Identification of Parameters for Large-scale Models in Systems BiologyApr 15 2019Inverse problem for the identification of the parameters for large-scale systems of nonlinear ordinary differential equations (ODEs) arising in systems biology is analyzed. In a recent paper in \textit{Mathematical Biosciences, 305(2018), 133-145}, the ... More

Regularity and convergence analysis in Sobolev and Hölder spaces for generalized Whittle-Matérn fieldsApr 13 2019We analyze several Galerkin approximations of a Gaussian random field $\mathcal{Z}\colon\mathcal{D}\times\Omega\to\mathbb{R}$ indexed by a Euclidean domain $\mathcal{D}\subset\mathbb{R}^d$ whose covariance structure is determined by a negative fractional ... More

On barrier and modified barrier multigrid methods for 3d topology optimizationApr 13 2019One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum compliance ... More

L1-norm Tucker Tensor DecompositionApr 13 2019Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral entries. In this ... More

Leveraging the bfloat16 Artificial Intelligence Datatype For Higher-Precision ComputationsApr 12 2019In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks due to their ... More

The Lanczos Algorithm Under Few Iterations: Concentration and Location of the Ritz ValuesApr 12 2019We study the Lanczos algorithm where the initial vector is sampled uniformly from $\mathbb{S}^{n-1}$. Let $A$ be an $n \times n$ Hermitian matrix. We show that when run for few iterations, the output of the algorithm on $A$ is almost deterministic. For ... More

Construction of conformal maps based on the locations of singularities for improving the double exponential formulaApr 12 2019The double exponential formula, or the DE formula, is a high-precision integration formula using a change of variables called a DE transformation; whereas there is a disadvantage that it is sensitive to singularities of an integrand near the real axis. ... More

Variational integrators for stochastic dissipative Hamiltonian systemsApr 11 2019Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for the stochastic ... More

Reducing Communication in Algebraic Multigrid with Multi-step Node Aware CommunicationApr 11 2019Algebraic multigrid (AMG) is often viewed as a scalable $\mathcal{O}(n)$ solver for sparse linear systems. Yet, parallel AMG lacks scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid ... More

Reducing Communication in Algebraic Multigrid with Multi-step Node Aware CommunicationApr 11 2019Apr 24 2019Algebraic multigrid (AMG) is often viewed as a scalable $\mathcal{O}(n)$ solver for sparse linear systems. Yet, parallel AMG lacks scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid ... More

Probabilistic Permutation Synchronization using the Riemannian Structure of the Birkhoff PolytopeApr 11 2019We present an entirely new geometric and probabilistic approach to synchronization of correspondences across multiple sets of objects or images. In particular, we present two algorithms: (1) Birkhoff-Riemannian L-BFGS for optimizing the relaxed version ... More

A Kaczmarz Algorithm for Solving Tree Based Distributed Systems of EquationsApr 11 2019The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a modified Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e. the equations within the system are distributed ... More

Deep learning as optimal control problems: models and numerical methodsApr 11 2019We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the ... More

Fatigue design load calculations of the offshore NREL 5MW benchmark turbine using quadrature rule techniquesApr 11 2019A novel approach is proposed to reduce, compared to the conventional binning approach, the large number of aeroelastic code evaluations that are necessary to obtain equivalent loads acting on wind turbines. These loads describe the effect of long-term ... More

A Reduced Basis Method For Fractional Diffusion Operators IApr 11 2019We propose and analyze new numerical methods to evaluate fractional norms and apply fractional powers of elliptic operators. By means of a reduced basis method, we project to a small dimensional subspace where explicit diagonalization via the eigensystem ... More

Error indicator for the incompressible Darcy flow problems using Enhanced Velocity Mixed Finite Element MethodApr 11 2019In the flow and transport numerical simulation, mesh adaptivity strategy is important in reducing the usage of CPU time and memory. The refinement based on the pressure error estimator is commonly-used approach without considering the flux error which ... More

On the segmentation of astronomical images via level-set methodsApr 09 2019Astronomical images are of crucial importance for astronomers since they contain a lot of information about celestial bodies that can not be directly accessible. Most of the information available for the analysis of these objects starts with sky explorations ... More

On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt methodApr 09 2019This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential equation. The learning ... More

Developable surface patches bounded by NURBS curvesApr 09 2019In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. The ... More

A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS $L^{2}$ spacesApr 09 2019We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as "the" Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral ... More

Modeling a Hidden Dynamical System Using Energy Minimization and Kernel Density EstimatesApr 08 2019In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined by an underlying ... More

Desaturating EUV observations of solar flaring stormsApr 08 2019Image saturation has been an issue for several instruments in solar astronomy, mainly at EUV wavelengths. However, with the launch of the Atmospheric Imaging Assembly (AIA) as part of the payload of the Solar Dynamic Observatory (SDO) image saturation ... More

Implicit-Explicit multistep methods for hyperbolic systems with multiscale relaxationApr 08 2019We consider the development of high order space and time numerical methods based on Implicit-Explicit (IMEX) multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which the convection ... More

Sparse Identification of Truncation ErrorsApr 07 2019This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation errors, for ... More

Sparse Identification of Truncation ErrorsApr 07 2019Apr 18 2019This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation errors, for ... More

Phase field modelling of crack propagation in functionally graded materialsApr 07 2019We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case studies are addressed ... More

Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex OptimizationApr 06 2019Backtracking line-search is an old yet powerful strategy for finding better step size to be used in proximal gradient algorithms. The main principle is to locally find a simple convex upper bound of the objective function, which in turn controls the step ... More

Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavitiesApr 06 2019We derive Euler-Lagrange equations for ``the full topology optimization'' of the decay rate of eigenoscillations in 3d lossy optical cavities. The approach is based on the notion of Pareto optimal frontier and on the multi-parameter perturbation theory ... More

A Flexible, Parallel, Adaptive Geometric Multigrid method for FEMApr 05 2019We present data structures and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by using ... More