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Iterative Hard Thresholding for Low CP-rank Tensor ModelsAug 22 2019Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical guarantees. However, ... More
A Nonlinear Finite Element Heterogeneous Multiscale Method for the Homogenization of Hyperelastic Solids and a Novel Staggered Two-Scale Solution AlgorithmAug 22 2019In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM in a Lagrangean ... More
`Regression Anytime' with Brute-Force SVD TruncationAug 22 2019We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, ... More
Galerkin-collocation approximation in time for the wave equation and its post-processingAug 22 2019We introduce and analyze a class of Galerkin-collocation discretization schemes in time for the wave equation. Its conceptual basis is the establishment of a direct connection between the Galerkin method for the time discretization and the classical collocation ... More
Extended Galerkin MethodAug 22 2019A general framework, known as extended Galerkin method, is presented in this paper for the derivation and analysis of many different types of finite element methods (including various discontinuous Galerkin methods). For second order elliptic equation, ... More
Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal $hp$ approximation estimates in $H(\mathrm{div})$Aug 22 2019Given an arbitrary function in H(div), we show that the error attained by the global-best approximation by H(div)-conforming piecewise polynomial Raviart-Thomas-N\'ed\'elec elements under additional constraints on the divergence and normal flux on the ... More
Perturbations of CUR DecompositionsAug 21 2019The CUR decomposition is a factorization of a low-rank matrix obtained by selecting certain column and row submatrices of it. We perform a thorough investigation of what happens to such decompositions in the presence of noise. Since CUR decompositions ... More
Adaptive Morley FEM for the von Kármán equations with optimal convergence ratesAug 21 2019The adaptive nonconforming Morley finite element method (FEM) approximates a regular solution to the von K\'{a}rm\'{a}n equations with optimal convergence rates for sufficiently fine triangulations and small bulk parameter in the D\"orfler marking. This ... More
Minimal residual multistep methods for large stiff non-autonomous linear problemsAug 21 2019The purpose of this work is to introduce a new idea of how to avoid the factorization of large matrices during the solution of stiff systems of ODEs. Starting from the general form of an explicit linear multistep method we suggest to adaptively choose ... More
Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilationAug 21 2019We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation. These systems can be written as saddle point systems with a 3x3 block structure but block ... More
Stability of the linear complementarity problem properties under interval uncertaintyAug 21 2019We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite number of solutions ... More
Data-driven model reduction, Wiener projections, and the Mori-Zwanzig formalismAug 21 2019First-principles models of complex dynamic phenomena often have many degrees of freedom, only a small fraction of which may be scientifically relevant or observable. Reduced models distill such phenomena to their essence by modeling only relevant variables, ... More
Stochastic regularity of general quadratic observables of high frequency wavesAug 20 2019We consider the wave equation with uncertain initial data and medium, when the wavelength $\varepsilon$ of the solution is short compared to the distance traveled by the wave. We are interested in the statistics for quantities of interest (QoI), defined ... More
A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary conditionAug 20 2019A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can be troublesome ... More
A Fast Integral Equation Method for the Two-Dimensional Navier-Stokes EquationsAug 20 2019The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In particular, the divergence-free condition and boundary conditions are handled ... More
Sensitivity estimation of conditional value at risk using randomized quasi-Monte CarloAug 20 2019Conditional value at risk (CVaR) is a popular measure for quantifying portfolio risk. Sensitivity analysis of CVaR is very useful in risk management and gradient-based optimization algorithms. In this paper, we study the infinitesimal perturbation analysis ... More
Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse ProblemsAug 20 2019An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element computations. The analysis ... More
Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methodsAug 19 2019In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equivalence and additive Schwarz methods. The high-order operators are applied ... More
Variance of finite difference methods for reaction networks with non-Lipschitz rate functionsAug 19 2019Parametric sensitivity analysis is a critical component in the study of mathematical models of physical systems. Due to its simplicity, finite difference methods are used extensively for this analysis in the study of stochastically modeled reaction networks. ... More
Simple formula for integration of polynomials on a simplexAug 19 2019We show that integrating a polynomial of degree t on an arbitrary simplex (with respect to Lebesgue measure) reduces to evaluating t homogeneous polynomials of degree j = 1, 2,. .. , t, each at a unique point $\xi$ j of the simplex. This new and very ... More
Computing Spectral Measures and Spectral Types: New Algorithms and ClassificationsAug 19 2019Despite new results on computing the spectrum, there has been no general method able to compute spectral measures (as given by the classical spectral theorem) of infinite-dimensional normal operators. Given a matrix representation, we show that if each ... More
Solving a fractional parabolic-hyperbolic free boundary problem which models the growth of tumor with drug application using finite difference-spectral methodAug 19 2019In this paper, a free boundary problem modelling the growth of tumor is considered. The model includes two reaction-diffusion equations modelling the diffusion of nutrient and drug in the tumor and three hyperbolic equations describing the evolution of ... More
A posteriori error analysis for a new fully-mixed isotropic discretization to the stationary Stokes-Darcy coupled problemAug 19 2019In this paper we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming finite element method on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a new robust stabilized ... More
Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivityAug 19 2019Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable ... More
Unfitted Nitsche's method for computing wave modes in topological materialsAug 19 2019In this paper, we propose an unfitted Nitsche's method for computing wave modes in topological materials. The proposed method is based on Nitsche's technique to study the performance-enhanced topological materials which have strongly heterogeneous structures ... More
A Spectral Gradient Projection Method for the Positive Semi-definite Procrustes ProblemAug 18 2019This paper addresses the positive semi-definite procrustes problem (PSDP). The PSDP corresponds to a least squares problem over the set of symmetric and semi-definite positive matrices. These kinds of problems appear in many applications such as structure ... More
On a progressive and iterative approximation method with memory for least square fittingAug 18 2019In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with three weights. ... More
On a progressive and iterative approximation method with memory for least square fittingAug 18 2019Aug 21 2019In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with three weights. ... More
Quadrature rules for $C^0$ and $C^1$ splines, a recipeAug 16 2019Closed formulae for all Gaussian or optimal, 1-parameter quadrature rules in a compact interval [a, b] with non uniform, asymmetric subintervals, arbitrary number of nodes per subinterval for the spline classes $S_{2N, 0}$ and $S_{2N+1, 1}$, i.e. even ... More
Low-rank approximation in the Frobenius norm by column and row subset selectionAug 16 2019A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset selection to $A$ ... More
A Shift Selection Strategy for Parallel Shift-Invert Spectrum Slicing in Symmetric Self-Consistent Eigenvalue ComputationAug 16 2019The central importance of large scale eigenvalue problems in scientific computation necessitates the development massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of ... More
Optimality properties of Galerkin and Petrov-Galerkin methods for linear matrix equationsAug 16 2019Galerkin and Petrov-Galerkin methods are some of the most successful solution procedures in numerical analysis. Their popularity is mainly due to the optimality properties of their approximate solution. We show that these features carry over to the (Petrov-)Galerkin ... More
An algorithm for real and complex rational minimax approximationAug 16 2019Rational minimax approximation of real functions on real intervals is an established topic, but when it comes to complex functions or domains, there appear to be no algorithms currently in use. Such a method is introduced here, the {\em AAA-Lawson algorithm,} ... More
Algorithms and Complexity for Functions on General DomainsAug 16 2019Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the approximation ... More
Variational Multi-Task MRI Reconstruction: Joint Reconstruction, Registration and Super-ResolutionAug 16 2019Motion degradation is a central problem in Magnetic Resonance Imaging (MRI). This work addresses the problem of how to obtain higher quality, super-resolved motion-free, reconstructions from highly undersampled MRI data. In this work, we present for the ... More
Matrix Lie Maps and Neural Networks for Solving Differential EquationsAug 16 2019The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It can be used ... More
Hermite Interpolation and data processing errors on Riemannian matrix manifoldsAug 16 2019The main contribution of this paper is twofold: On the one hand, a general framework for performing Hermite interpolation on Riemannian manifolds is presented. The method is applicable, if algorithms for the associated Riemannian exponential and logarithm ... More
An efficient implementation of mass conserving characteristic-based schemes in 2D and 3DAug 16 2019In this paper, we develop the ball-approximated characteristics (B-char) method, which is an algorithm for efficiently implementing characteristic-based schemes in 2D and 3D. Core to the implementation of numerical schemes is the evaluation of integrals, ... More
Analysis of the spectral symbol function for spectral approximation of a differential operatorAug 15 2019Given a differential operator $\mathcal{L}$ along with its own eigenvalue problem $\mathcal{L}u = \lambda u$ and an associated algebraic equation $\mathcal{L}^{(n)} \mathbf{u}_n = \lambda\mathbf{u}_n$ obtained by means of a discretization scheme (like ... More
On boundedness and growth of unsteady solutions under the double porosity/permeability modelAug 15 2019There is a recent surge in research activities on modeling the flow of fluids in porous media with complex pore-networks. A prominent mathematical model, which describes the flow of incompressible fluids in porous media with two dominant pore-networks ... More
Safe global optimization of expensive noisy black-box functions in the $δ$-Lipschitz frameworkAug 15 2019In this paper, the problem of safe global maximization (it should not be confused with robust optimization) of expensive noisy black-box functions satisfying the Lipschitz condition is considered. The notion "safe" means that the objective function $f(x)$ ... More
T-IFISS: a toolbox for adaptive FEM computationAug 15 2019T-IFISS is a finite element software package for studying finite element solution algorithms for deterministic and parametric elliptic partial differential equations. The emphasis is on self-adaptive algorithms with rigorous error control using a variety ... More
Space-Time Nonlinear Upscaling Framework Using Non-local Multi-continuum ApproachAug 15 2019In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale coefficients. ... More
Weak imposition of Signorini boundary conditions on the boundary element methodAug 15 2019We derive and analyse a boundary element formulation for boundary conditions involving inequalities. In particular, we focus on Signorini contact conditions. The Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed ... More
Mean-field limit and numerical analysis for Ensemble Kalman Inversion: linear settingAug 15 2019Ensemble Kalman inversion (EKI) is a method introduced in [14] to find samples from the target posterior distribution in the Bayesian formulation. As a deviation from Ensemble Kalman filter [6], it introduces a pseudo-time along which the particles sampled ... More
Mean-field limit and numerical analysis for Ensemble Kalman Inversion: linear settingAug 15 2019Aug 16 2019Ensemble Kalman inversion (EKI) is a method introduced in [14] to find samples from the target posterior distribution in the Bayesian formulation. As a deviation from Ensemble Kalman filter [6], it introduces a pseudo-time along which the particles sampled ... More
Substructured Two-level and Multilevel Domain Decomposition MethodsAug 15 2019Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its ... More
Ensemble Kalman filter for multiscale inverse problemsAug 15 2019We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and allows to recover ... More
Stability of explicit Runge-Kutta methods for high order finite element approximation of linear parabolic equationsAug 14 2019We study the stability of explicit Runge-Kutta methods for high order Lagrangian finite element approximation of linear parabolic equations and establish bounds on the largest eigenvalue of the system matrix which determines the largest permissible time ... More
Data-Driven Correction Reduced Order Models for the Quasi-Geostrophic Equations: A Numerical InvestigationAug 14 2019This paper investigates the recently introduced data-driven correction reduced order model (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. The DDC-ROM uses available data to model the correction term that is generally used to ... More
Joint phase reconstruction and magnitude segmentation from velocity-encoded MRI dataAug 14 2019Velocity-encoded MRI is an imaging technique used in different areas to assess flow motion. Some applications include medical imaging such as cardiovascular blood flow studies, and industrial settings in the areas of rheology, pipe flows, and reactor ... More
Accuracy Controlled Structure-Preserving ${\cal H}^2$-Matrix-Matrix Product in Linear Complexity with Change of Cluster BasesAug 14 2019${\cal H}^2$-matrix constitutes a general mathematical framework for efficient computation of both partial-differential-equation and integral-equation-based operators. Existing linear-complexity ${\cal H}^2$ matrix-matrix product (MMP) algorithm lacks ... More
Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibilityAug 14 2019We consider Galerkin approximations of holomorphic Fredholm operator eigenvalue problems for which the operator values don't have the structure "coercive+compact". In this case the regularity (in sense of [O. Karma, Numer. Funct. Anal. Optim. 17 (1996)]) ... More
An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditionsAug 14 2019The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase-flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation were proposed ... More
Pair correlation for Dedekind zeta functions of abelian extensionsAug 13 2019Here we study problems related to the proportions of zeros, especially simple and distinct zeros on the critical line, of Dedekind zeta functions. We obtain new bounds on a counting function that measures the discrepancy of the zeta functions from having ... More
Resolution analysis of inverting the generalized Radon transform from discrete data in $\mathbb R^3$Aug 13 2019A number of practically important imaging problems involve inverting the generalized Radon transform (GRT) $\mathcal R$ of a function $f$ in $\mathbb R^3$. On the other hand, not much is known about the spatial resolution of the reconstruction from discretized ... More
Efficient Parallel-in-Time Solution of Time-Periodic Problems Using a Multi-Harmonic Coarse Grid CorrectionAug 13 2019This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of (nonlinear) time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential computations via parallelization ... More
On the fixed volume discrepancy of the Fibonacci sets in the integral normsAug 13 2019This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Fibonacci point set in the unit square. It was observed recently that this new characteristic allows us to obtain optimal rate of dispersion ... More
Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric MeshesAug 13 2019We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lam\'e system of linear elasticity in polyhedral domains in $\mathbb{R}^3$. In order to resolve possible corner, edge, and corner-edge singularities, anisotropic geometric ... More
Numerical benchmarking of fluid-rigid body interactionsAug 13 2019We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A number of different problems are defined for both two and three spatial ... More
Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin SchemesAug 13 2019For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach to construct entropy conservative semidiscretisations by adding suitable ... More
THINC-scaling scheme that unifies VOF and level set methodsAug 13 2019We present a novel interface-capturing scheme, THINC-scaling, to unify the VOF (volume of fluid) and the level set methods, which have been developed as two completely different approaches widely used in various applications. The THINC-scaling scheme ... More
An Auxiliary Space Preconditioner for Fractional Laplacian of Negative OrderAug 13 2019Coupled multiphysics problems often give rise to interface conditions naturally formulated in fractional Sobolev spaces. Here, both positive and negative fractionality are common. When designing efficient solvers for discretizations of such problems it ... More
An energy consistent discretization of the nonhydrostatic equations in primitive variablesAug 12 2019We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. ... More
Naturally curved quadrilateral mesh generation using an adaptive spectral element solverAug 12 2019We describe an adaptive version of a method for generating valid naturally curved quadrilateral meshes. The method uses a guiding field, derived from the concept of a cross field, to create block decompositions of multiply connected two dimensional domains. ... More
A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimatesAug 12 2019A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on ... More
Tensor-based EDMD for the Koopman analysis of high-dimensional systemsAug 12 2019Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory -- with extended dynamic mode decomposition (EDMD) being a cornerstone of the field. On the other hand, low-rank tensor product approximations ... More
Successive Projection Algorithm Robust to OutliersAug 12 2019The successive projection algorithm (SPA) is a fast algorithm to tackle separable nonnegative matrix factorization (NMF). Given a nonnegative data matrix $X$, SPA identifies an index set $\mathcal{K}$ such that there exists a nonnegative matrix $H$ with ... More
An Adaptive $s$-step Conjugate Gradient Algorithm with Dynamic Basis UpdatingAug 12 2019The adaptive $s$-step CG algorithm is a solver for sparse, symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we improve the adaptive ... More
Solving high-dimensional nonlinear filtering problems using a tensor train decomposition methodAug 12 2019In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the NLF problem. ... More
Lectures on error analysis of interpolation on simplicial triangulations without the shape-regularity assumption and its applications to finite element methods, Part 1: two-dimensional Lagrange interpolationAug 11 2019In the error analysis of finite element methods, the shape-regularity assumption on triangulations is usually imposed to obtain anticipated error estimations. In practical computations, however, very "thin" or "degenerated" elements may appear, when we ... More
Optimal Control for Chemotaxis Systems and Adjoint-Based Optimization with Multiple-Relaxation-Time Lattice Boltzmann ModelsAug 11 2019This paper is devoted to continuous and discrete adjoint-based optimization approaches for optimal control problems governed by an important class of Nonlinear Coupled Anisotropic Convection-Diffusion Chemotaxis-type System (NCACDCS). This study is motivated ... More
Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equationAug 11 2019In this paper, we develop discontinuous Galerkin (DG) methods for the Ostrovsky-Vakhnenko (OV) equation, which yields the shock solutions and singular soliton solutions, such as peakon, cuspon and loop solitons. The OV equation has also been shown to ... More
An Asymptotically Compatible Approach For Neumann-Type Boundary Condition On Nonlocal ProblemsAug 11 2019In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter $\delta$ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for ... More
Space-time error estimates for deep neural network approximations for differential equationsAug 11 2019Over the last few years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a wide variety of computational problems including computer vision, image classification, speech recognition, natural language ... More
Numerical upscaling for heterogeneous materials in fractured domainsAug 10 2019We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The main computational ... More
An approximate factorization method for inverse acoustic scattering with phaseless near-field dataAug 10 2019This paper is concerned with the inverse acoustic scattering problem with phaseless near-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the unknown scatterer ... More
Lifting methods for manifold-valued variational problemsAug 10 2019Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum, which allows ... More
Adaptive RBF Interpolation for Estimating Missing Values in Geographical DataAug 10 2019The quality of datasets is a critical issue in big data mining. More interesting things could be mined from datasets with higher quality. The existence of missing values in geographical data would worsen the quality of big datasets. To improve the data ... More
Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated PhenomenaAug 10 2019Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science and engineering. ... More
A comparison between Caputo and Caputo-Fabrizio fractional derivatives for modelling Lotka-Volterra differential equationsAug 10 2019In this paper, we apply the concept of the fractional calculus to study three-dimensional Lotka-Volterra differential equations. Our goal is to compare the results of this system with respect to Caputo and Caputo-Fabrizio fractional derivatives. According ... More
An energy stable $C^0$ finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable densityAug 10 2019In this paper, we focus on modeling and simulation of two-phase flow with moving contact lines and variable density. A thermodynamically consistent phase-field model with General Navier Boundary Condition is developed based on the concept of quasi-incompressibility ... More
Numerical analysis for a chemotaxis-Navier-Stokes systemAug 09 2019In this paper we develop a numerical scheme for approximating a $d$-dimensional chemotaxis-Navier-Stokes system, $d=2,3$, modeling cellular swimming in incompressible fluids. This model describes the chemotaxis-fluid interaction in cases where the chemical ... More
An Adaptive ALE Scheme for Non-Ideal Compressible-Fluid Dynamics over Dynamic Unstructured MeshesAug 09 2019This paper investigates the application of mesh adaptation techniques in the Non-Ideal Compressible Fluid Dynamic (NICFD) regime, a region near the vapor-liquid saturation curve where the flow behavior significantly departs from the ideal gas model, as ... More
On the smallest eigenvalue of finite element equations with meshes without regularity assumptionsAug 09 2019A lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes without any regularity assumptions. The bound has the same form as the one by Graham and McLean [SIAM J. Numer. Anal., 44 (2006), ... More
A posteriori error estimates for the mortar staggered DG methodAug 09 2019Two residual-type error estimators for the mortar staggered discontinuous Galerkin discretizations of second order elliptic equations are developed. Both error estimators are proved to be reliable and efficient. Key to the derivation of the error estimator ... More
Viscoelastic flows with conservation lawsAug 09 2019We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of quasilinear PDEs ... More
Galerkin Approximation In Banach and Hilbert SpacesAug 09 2019In this paper we study the conforming Galerkin approximation of the problem: find u $\in$ U such that a(u, v) = L, v for all v $\in$ V, where U and V are Hilbert or Banach spaces, a is a continuous bilinear or sesquilinear form and L $\in$ V a given data. ... More
A second-order face-centred finite volume method for elliptic problemsAug 08 2019A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). ... More
3D Compton scattering imaging: study of the spectrum and contour reconstructionAug 08 20193D Compton scattering imaging is an upcoming concept focusing on exploiting the photons scattered, following on from the so-called Compton effect, by the atomic structure of an object under study. This phenomenon rules the collision of particles with ... More
Hiddenly Hermitian quantum models: The concept of perturbationsAug 08 2019In conventional Schr\"{o}dinger representation the unitarity of the evolution of bound states is guaranteed by the Hermiticity of the Hamiltonian. A non-unitary isospectral simplification of the Hamiltonian, $\mathfrak{h} \to H=\Omega\,\mathfrak{h}\,\Omega ... More
A conjugate-gradient-type rational Krylov subspace method for ill-posed problemsAug 08 2019Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarised as minimising the residuum over a suitable Krylov subspace. It is shown that using the same idea for ... More
Sparse $\ell^q$-regularization of inverse problems with deep learningAug 08 2019We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transforms, we train an encoder-decoder network $D \circ E$ with $E$ acting as a nonlinear ... More
A phase field approach for damage propagation in periodic microstructured materialsAug 08 2019In the present work, the evolution of damage in periodic composite materials is investigated through a novel finite element-based multiscale computational approach. The methodology is developed by means of the original combination of homogenization methods ... More
Contributed Discussion of "A Bayesian Conjugate Gradient Method"Aug 08 2019We would like to congratulate the authors of "A Bayesian Conjugate Gradient Method" on their insightful paper, and welcome this publication which we firmly believe will become a fundamental contribution to the growing field of probabilistic numerical ... More
An explicit numerical algorithm to the solution of Volterra integral equation of the second kindAug 07 2019This paper considers a numeric algorithm to solve the equation \begin{align*} y(t)=f(t)+\int^t_0 g(t-\tau)y(\tau)\,d\tau \end{align*} with a kernel $g$ and input $f$ for $y$. In some applications we have a smooth integrable kernel but the input $f$ could ... More
Faster Tensor Train Decomposition for Sparse DataAug 07 2019In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to harness the notorious ... More
Well-posedness study of a non-linear hyperbolic-parabolic coupled system applied to image speckle reductionAug 07 2019Aug 12 2019In this article, we consider a non-linear hyperbolic-parabolic coupled system based on telegraph diffusion framework applied to image despeckling. A separate equation is used to calculate the edge variable, which improves the quality of the despeckled ... More
Well-posedness study of a non-linear hyperbolic-parabolic coupled system applied to image speckle reductionAug 07 2019In this article, we consider a non-linear hyperbolic-parabolic coupled system based on telegraph diffusion framework applied to image despeckling. A separate equation is used to calculate the edge variable, which improves the quality of the despeckled ... More
Multiply Periodic SplinesAug 07 2019Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process. Usually many NURBS ... More