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A finite element method for Dirichlet boundary control of elliptic partial differential equationsApr 22 2019This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of the domain, ... 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

A Müntz-Collocation spectral method for weakly singular volterra integral equationsApr 21 2019In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-\mu},0<\mu<1$. First we develop a family of fractional Jacobi polynomials, ... More

Super-resolution of near-colliding point sourcesApr 19 2019We consider the problem of stable recovery of sparse signals of the form $$F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C}, $$ from their spectral measurements, known in a bandwidth $\Omega$ with absolute error not exceeding ... More

Numerical Analysis of Unsteady Implicitly Constituted Incompressible Fluids: Three-Field FormulationApr 19 2019In the classical theory of fluid mechanics a linear relationship between the shear stress and the rate of strain tensor is often assumed. Even when a nonlinear relationship is assumed between the shear stress and the strain, it is typically formulated ... More

Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant ConductivityApr 18 2019In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty ... More

Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearityApr 18 2019The Strang splitting method, formally of order two, can suffer from order reduction when applied to semilinear parabolic problems with inhomogeneous boundary conditions. The recent work [L .Einkemmer and A. Ostermann. Overcoming order reduction in diffusion-reaction ... More

Quadcubic interpolation: a four-dimensional spline methodApr 18 2019We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically accessible. The specific ... 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

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

Difference Potentials Method for Models with Dynamic Boundary Conditions and Bulk-Surface ProblemsApr 17 2019In this work, we consider parabolic models with dynamic boundary conditions and parabolic bulk-surface problems in 3D. Such partial differential equations based models describe phenomena that happen both on the surface and in the bulk/domain. These problems ... More

Analysis of sparse grid multilevel estimators for multi-dimensional Zakai equationsApr 17 2019In this article, we analyse the accuracy and computational complexity of estimators for expected functionals of the solution to multi-dimensional parabolic stochastic partial differential equations (SPDE) of Zakai-type. Here, we use the Milstein scheme ... More

Modified PHT-splinesApr 17 2019The local refinement of PHT-splines (polynomial splines over hierarchical T-meshes) is achieved by a simple cross insertion, which may introduce superfluous control points or coefficients. By allowing split-in-half in mesh refinement, modified hierarchical ... More

A direct solver for the phase retrieval problem in ptychographic imagingApr 16 2019Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field diffraction patterns ... More

On isolation of singular zeros of multivariate analytic systemsApr 16 2019We give a separation bound for an isolated multiple root $x$ of a square multivariate analytic system $f$ satisfying that the deflation process applied on $f$ and $x$ terminates after only one iteration. When $x$ is only given approximately, we give a ... More

Existence results, smoothness properties and numerical methods for equations involving the generalized fractional derivatives of Caputo typeApr 16 2019In this paper, we obtain a full characterization of the solutions of equations involving the generalized Caputo fractional derivative, such as existence, uniqueness, smoothness, series expansion, etc. These results are proved by establishing an equivalence ... More

Rigorous and fully computable a posteriori error bounds for eigenfunctionsApr 16 2019Guaranteed a posteriori estimates on the error of approximate eigenfunctions in both energy and $L^2$ norms are derived for the Laplace eigenvalue problem. The problem of ill-conditioning of eigenfunctions in case of tight clusters and multiple eigenvalues ... More

Discrete Iterated Modified Projection Method for Urysohn Integral Equations with Non-smooth KernelsApr 16 2019In the present paper we consider a discrete version of the iterated modified projection method for solving a Urysohn integral equation with a kernel of the type of Green's function. For $r \geq 0,$ a space of piecewise polynomials of degree $\leq r $ ... 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

Trace operators of the bi-Laplacian and applicationsApr 16 2019We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are also relevant to describe conformity ... More

A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equationsApr 16 2019The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated pattern formation in the developing animal embryo. In this work, a second-order ... More

Numerical construction of spherical $t$-designs by Barzilai-Borwein methodApr 16 2019A point set $\mathrm X_N$ on the unit sphere is a spherical $t$-design is equivalent to the nonnegative quantity $A_{N,t+1}$ vanished. We show that if $\mathrm X_N$ is a stationary point set of $A_{N,t+1}$ and the minimal singular value of basis matrix ... More

Multilevel Monte Carlo theta EM scheme for SDDEs with small noiseApr 16 2019In this paper, a multilevel Monte Carlo theta EM scheme is provided for stochastic differential delay equations with small noise. Under a global Lipschitz condition, the variance of two coupled paths is derived. Then, the global Lipschitz condition is ... 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 boundary integral equation approach to computing eigenvalues of the Stokes operatorApr 15 2019The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier-Stokes equations. As the Stokes operator is a fourth-order operator, computing ... 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

Strong Stability Preserving Integrating Factor Two-step Runge--Kutta MethodsApr 15 2019Problems that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this restriction if the concern is linear stability. However, where the SSP property ... More

The Numerical Study of Regularized Barycentric InterpolationApr 15 2019This paper mainly studies the numerical stability of regularized barycentric interpolation formulae.

A monotone scheme for G-equations with application to the convergence rate of robust central limit theoremApr 15 2019We propose a monotone approximation scheme for a class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization of G-distributed random variables in a sublinear expectation space. The proposed scheme is constructed ... More

Construction of complex potentials for multiply connected domainsApr 15 2019The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential --- an analytic function in an infinite multiply connected domain with a simple pole at infinity which maps the domain onto ... More

Generalized multiscale finite element method for the steady state linear Boltzmann equationApr 15 2019The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. Depending on the media and the particles to be modeled, the equation has ... More

Quasi-best approximation in optimization with PDE constraintsApr 15 2019We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we prove that the ... More

An optimal polynomial approximation of Brownian motionApr 15 2019In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. Remarkably the coefficients obtained from the expansion of Brownian motion in this polynomial basis are independent Gaussian ... More

The surrogate matrix methodology: Low-cost assembly for isogeometric analysisApr 15 2019A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed from element-scale quadrature formulas. To generate ... More

Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural NetworksApr 15 2019Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential equations (PDEs), ... More

Hölderian convergence of fractional extended nabla operator to fractional derivativeApr 15 2019In this paper, we construct the fractional extended nabla operator as fractional power of linear spline of backward difference operator. Then we prove the strong convergence of this operator to fractional derivative in a H\"older space setting. Finally ... More

Solving Differential Equation with Constrained Multilayer Feedforward NetworkApr 14 2019In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not satisfied accurately. ... More

Travel time tomography with formally determined incomplete data in 3DApr 14 2019For the first time, a globally convergent numerical method is developed and Lipschitz stability estimate is obtained for the challenging problem of travel time tomography in 3D for formally determined incomplete data. The semidiscrete case is considered ... More

Solvers and precondtioners based on Gauss-Seidel and Jacobi algorithms for non-symmetric stochastic Galerkin system of equationsApr 13 2019In this work, solvers and preconditioners based on Gauss-Seidel and Jacobi algorithms are explored for stochastic Galerkin discretization of partial differential equations (PDEs) with random input data. Gauss-Seidel and Jacobi algorithms are formulated ... 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

Physics-Informed Tolerance Allocation: A Surrogate-Based Framework for the Control of Geometric Variation on System PerformanceApr 13 2019In this paper, we present a novel tolerance allocation algorithm for the assessment and control of geometric variation on system performance that is applicable to any system of partial differential equations. In particular, we parameterize the geometric ... 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

Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputsApr 13 2019By combining a certain spatial approximation property in the spatial domain, and weighted $\ell_2$-summability of the Hermite polynomial expansion coefficients in the parametric domain obtained in [M. Bachmayr, A. Cohen, R. DeVore and G. Migliorati, ESAIM ... More

A new class of high-order methods for multirate differential equationsApr 13 2019This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step exponential integrators. ... More

An a posteriori verification method for generalized Hermitian eigenvalue problems in large-scale electronic state calculationsApr 13 2019An a posteriori verification method is proposed for the generalized Hermitian eigenvalue problems that appear in large-scale electronic state calculations. The method is realized by the two stage process in which the approximate solution is generated ... More

Verified partial eigenvalue computations for Hermitian generalized eigenproblems using contour integralsApr 12 2019We propose a verified computation method for partial eigenvalues of a Hermitian generalized eigenproblem. The block Sakurai-Sugiura Hankel method, a contour integral-type eigensolver, can reduce a given eigenproblem into a generalized eigenproblem of ... More

Analysis of a Legendre spectral element method (LSEM) for the two-dimensional system of a nonlinear stochastic advection-reaction-diffusion modelsApr 12 2019In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse ... More

A minimal-variable numerical method for isospectral flowsApr 12 2019In this paper we introduce a new minimal-variable, second order, numerical method to solve isospectral flows. The algorithm is shown to be isospectral for general isospectral flows and Lie-Poisson when the isospectral flow is Hamiltonian. Moreover, the ... More

Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equationsApr 12 2019In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which measurements on a coarse ... More

Real-time reconstruction of moving point/dipole wave sources from boundary measurementsApr 12 2019This paper is concerned with a reconstruction method for multiple moving point/dipole wave sources. We assume that the number, locations, and magnitudes/moments of wave sources are unknown, and consider the problem to reconstruct these parameters from ... More

Constructive a priori error estimates for a full discrete approximation of periodic solutions for the heat equationApr 12 2019We consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation with time-periodic condition.

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

Optimization of drug controlled release from multi-laminated devices based on the modified Tikhonov regularization methodApr 12 2019From the viewpoint of inverse problem, the optimization of drug release based on the multi-laminated drug controlled release devices has been regarded as the solution problem of the diffusion equation initial value inverse problem. In view of the ill-posedness ... More

Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating SphereApr 12 2019The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps, even when the ... More

Mean-field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methodsApr 11 2019In this paper we consider systems of weakly interacting particles driven by colored noise in a bistable potential, and we study the effect of the correlation time of the noise on the bifurcation diagram for the equilibrium states. We accomplish this by ... More

Mean-field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methodsApr 11 2019Apr 22 2019In this paper we consider systems of weakly interacting particles driven by colored noise in a bistable potential, and we study the effect of the correlation time of the noise on the bifurcation diagram for the equilibrium states. We accomplish this by ... More

External optimal control of fractional parabolic PDEsApr 11 2019In this paper we introduce a new notion of optimal control, or source identification in inverse, problems with fractional parabolic PDEs as constraints. This new notion allows a source/control placement outside the domain where the PDE is fulfilled. We ... More

A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous MediaApr 11 2019Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also known as monolithic ... More

Weak and approximate curvatures of a measure: a varifold perspectiveApr 11 2019By revisiting the notion of generalized second fundamental form originally introduced by Hutchinson for a special class of integral varifolds, we define a weak curvature tensor that is particularly well-suited for being extended to general varifolds of ... 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

An adaptive multilevel Monte Carlo algorithm for the stochastic drift-diffusion-Poisson systemApr 11 2019We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift-diffusion-Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the spatial dimensions, ... More

Generalized moving least squares and moving kriging least squares approximations for solving the transport equation on the sphereApr 11 2019In this work, we apply two meshless methods for the numerical solution of the time-dependent transport equation defined on the sphere in spherical coordinates. The first technique, which was introduced by Mirzaei (BIT Numerical Mathematics, 54 (4) 1041-1063, ... 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

Space-Time NURBS-Enhanced Finite Elements for Solving the Compressible Navier-Stokes EquationsApr 11 2019This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier-Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain representation. Such ... More

An Introduction to MMPDElabApr 11 2019This article presents an introduction to MMPDElab, a package written in MATLAB for adaptive mesh movement and adaptive moving mesh P1 finite element solution of second-order partial different equations having continuous solutions.

Exact sequences on Powell-Sabin splitsApr 10 2019We construct smooth finite elements spaces on Powell-Sabin triangulations that form an exact sequence. The first space of the sequence coincides with the classical $C^1$ Powell-Sabin space, while the others form stable and divergence-free yielding pairs ... More

New numerical algorithm for deflation of infinite and zero eigenvalues and full solution of quadratic eigenvalue problemsApr 10 2019This paper presents a new method for computing all eigenvalues and eigenvectors of quadratic matrix pencil. It is an upgrade of the quadeig algorithm by Hammarling, Munro and Tisseur, which attempts to reveal and remove by deflation certain number of ... More

Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy dataApr 10 2019While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome ... More

On multiple solutions to the steady flow of incompressible fluids subject to do-nothing or constant traction boundary conditions on artificial boundariesApr 09 2019The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they do not facilitate ... 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

The Hellan-Herrmann-Johnson Method for Nonlinear ShellsApr 09 2019In this paper we derive a new finite element method for nonlinear shells. The Hellan-Herrmann-Johnson (HHJ) method is a mixed finite element method for fourth order Kirchhoff plates. It uses convenient Lagrangian finite elements for the vertical deflection, ... More

On high-order multilevel optimization strategiesApr 09 2019We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently proposed in the literature. ... 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

Robust Design Optimization for Egressing Pedestrians in Unknown EnvironmentsApr 09 2019In this paper, we deal with a size-variable group of pedestrians moving in a unknown confined environment and searching for an exit. Pedestrian dynamics are simulated by means of a recently introduced microscopic (agent-based) model, characterized by ... More

Inversion of multi-configuration complex EMI data with Minimum Gradient Support regularizationApr 09 2019Frequency-domain electromagnetic instruments allow, also because of their handy sizes, the collection of data in different configuration, i.e. varying the inter-coil spacing, the frequency, and the height above the ground. This makes these tools very ... More

A uniformly and optimally accurate method for the Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regimeApr 09 2019We present a uniformly and optimally accurate numerical method for solving the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters $0<\epsilon\le1$ and $0<\gamma\le 1$, which are inversely proportional to the plasma frequency and 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

Generalized Gaussian belief propagation solversApr 08 2019In this paper, we argue for the utility of deterministic inference in the classical problem of numerical linear algebra, that of solving a linear system. We show how the Gaussian belief propagation solver can be modified to handle non-symmetric positive ... 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

Numerical solution of scattering problems using a Riemann--Hilbert formulationApr 07 2019A fast and accurate numerical method for the solution of scalar and matrix Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as Riemann--Hilbert problems on the real line, and a numerical approach developed for these problems ... 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

IDENT: Identifying Differential Equations with Numerical Time evolutionApr 06 2019Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying coefficients add complexity ... 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

Low-Rank Approximability and Entropy Area Laws for PDEsApr 06 2019We show how local interactions in a partial differential equation (PDE) model lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the ... More

Low-Rank Approximability and Entropy Area Laws for PDEsApr 06 2019Apr 11 2019We show how local interactions in a partial differential equation (PDE) model lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the ... 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

Practical rare event sampling for extreme mesoscale weatherApr 06 2019Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here we present a new rare event sampling ... More

Spectral parameter power series representation for solutions of linear system of two first order differential equationsApr 06 2019A representation in the form of spectral parameter power series (SPPS) is given for a general solution of a one dimension Dirac system containing arbitrary matrix coefficient at the spectral parameter, \[ B \frac{dY}{dx} + P(x)Y = \lambda R(x)Y,\] where ... More

Numerical solutions of the generalized equal width wave equation using Petrov Galerkin methodApr 06 2019In this article we consider a generalized equal width wave (GEW) equation which is a significant nonlinear wave equation as it can be used to model many problems occurring in applied sciences. As the analytic solution of the (GEW) equation of this kind ... More

Numerical approximation of the generalized regularized long wave equation using Petrov-Galerkin finite element methodApr 06 2019The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion-acoustic and magnetohydrodynamic waves in plasma, nonlinear transverse waves in shallow water and phonon packets in nonlinear ... More