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Robust linear domain decomposition schemes for reduced non-linear fracture flow modelsJun 13 2019In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we reformulate the ... More

Post-Processing of High-Dimensional DataJun 13 2019Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high degree in some ... More

A stabilized DG cut cell method for discretizing the linear transport equationJun 13 2019We present new stabilization terms for solving the linear transport equation on a cut cell mesh using the discontinuous Galerkin (DG) method in two dimensions with piecewise linear polynomials. The goal is to allow for explicit time stepping schemes, ... More

Non-convex optimization via strongly convex majoirziation-minimizationJun 13 2019In this paper, we introduce a class of nonsmooth nonconvex least square optimization problem using convex analysis tools and we propose to use the iterative minimization-majorization (MM) algorithm on a convex set with initializer away from the origin ... More

Fast, reliable and unrestricted iterative computation of Gauss--Hermite and Gauss--Laguerre quadraturesJun 12 2019Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and they are fast ... More

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAMJun 12 2019The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper ... More

Conditional Monte Carlo for Reaction NetworksJun 12 2019Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of differential equations. ... More

Model Order Reduction by Proper Orthogonal DecompositionJun 12 2019We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from the infinite-dimensional ... More

Convergence of second-order, entropy stable methods for multi-dimensional conservation lawsJun 12 2019High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space dimensions. ... More

Torus computed tomographyJun 12 2019We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization ... More

Desingularization of matrix equations employing hypersingular integrals in boundary element methods using double nodesJun 12 2019In boundary element methods, the method of using double nodes at corners is a useful approach to uniquely define the normal direction of boundary elements. However, matrix equations constructed by conventional boundary integral equations (CBIE) become ... More

An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximationJun 12 2019We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness ... More

On regularization for a convolutional kernel in neural networksJun 12 2019Convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around ... More

The NMF problem and lattice-subspacesJun 11 2019Suppose that $A$ is a nonnegative $n\times m$ real matrix. The NMF problem is the determination of two nonnegative real matrices $F$, $V$ so that $A=FV$ with intermediate dimension $p$ smaller than $min\{ n,m\}$. In this article we present a general mathematical ... More

Mathematical and numerical analysis of a nonlocal Drude model in nanoplasmonicsJun 11 2019In this paper, we consider the frequency-domain Maxwell's equations coupled to a nonlocal Drude model which describes the nonlocal optical response in metallic nanostructures. We prove the existence and uniqueness of weak solutions to the coupled equations. ... More

Joint 3D Localization and Classification of Space Debris using a Multispectral Rotating Point Spread FunctionJun 11 2019We consider the problem of joint three-dimensional (3D) localization and material classification of unresolved space debris using a multispectral rotating point spread function (RPSF). The use of RPSF allows one to estimate the 3D locations of point sources ... More

Phase-field material point method for dynamic brittle fracture with isotropic and anisotropic surface energyJun 11 2019A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly defined crack density ... More

Residual estimates for post-processors in elliptic problemsJun 11 2019In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `tweaks' a wide variety of existing post-processing techniques to enable efficient ... More

Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimatorJun 11 2019In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing the fracture ... More

Generalized Langevin equations for systems with local interactionsJun 11 2019We present a new method to approximate the Mori-Zwanzig (MZ) memory integral in generalized Langevin equations (GLEs) describing the evolution of observables in high-dimensional nonlinear systems with local interactions. Building upon the Faber operator ... More

Hierarchical multiscale finite element method for multi-continuum mediaJun 11 2019Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum technique, where ... More

Polynomial root clustering and explicit deflationJun 11 2019We seek complex roots of a univariate polynomial $P$ with real or complex coefficients. We address this problem based on recent algorithms that use subdivision and have a nearly optimal complexity. They are particularly efficient when only roots in a ... More

Behavioral Switching Loss Modeling of Inverter ModulesJun 11 2019This paper presents a new behavioral model for switching power loss evaluation in phase-shifted full-bridge inverter Power Modules (PoMs). The proposed model has been identified by means of a Genetic Programming (GP) algorithm combined with a Multi-Objective ... More

Numerical computations of split Bregman method for fourth order total variation flowJun 11 2019The split Bregman framework for Osher-Sol\'e-Vese (OSV) model and fourth order total variation flow are studied. We discretize the problem by piecewise constant function and compute $\nabla(-\Delta_{\mathrm{av}})^{-1}$ approximately and exactly. Furthermore, ... More

Low Rank Approximation at Sublinear Cost by Means of Subspace SamplingJun 11 2019Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with LRA can be performed at sub-linear cost, that is, by using much fewer arithmetic operations ... More

Low Rank Approximation Directed by Leverage Scores and Computed at Sub-linear CostJun 10 2019Low rank approximation (LRA) of a matrix is a major subject of matrix and tensor computations and data mining and analysis. It is desired (and even imperative in applications to Big Data) to solve the problem at sub-linear cost, involving much fewer memory ... More

Analysis Of Momentum MethodsJun 10 2019Gradient decent-based optimization methods underpin the parameter training which results in the impressive results now found when testing neural networks. Introducing stochasticity is key to their success in practical problems, and there is some understanding ... More

Linear and Nonlinear Fractional DiffusionJun 10 2019This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity, including boundary ... More

Refinement of Low Rank Approximation of a Matrix at Sub-linear CostJun 10 2019Low rank approximation (LRA}) of a matrix is a hot subject of modern computations. In application to Big Data mining and analysis the input matrices are so immense that one must apply sub-linear cost algorithms, which only access and process a tiny fraction ... More

A fast solver for the narrow capture and narrow escape problems in the sphereJun 10 2019We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian particle in the exterior of a sphere whose surface is reflective, except for ... More

Convergence analysis of a Crank-Nicolson Galerkin method for an inverse source problem for parabolic systems with boundary observationsJun 10 2019This work is devoted to an inverse problem of identifying a source term depending on both spatial and time variables in a parabolic equation from single Cauchy data on a part of the boundary. A Crank-Nicolson Galerkin method is applied to the least squares ... More

CUR Low Rank Approximation of a Matrix at Sub-linear CostJun 10 2019Low rank approximation of a matrix (LRA}) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis with numerous important applications to modern computations. One can operate with LRA of a matrix at sub-linear ... More

Models of dynamic damage and phase-field fracture, and their various time discretisationsJun 10 2019Several variants of models of damage in viscoelastic continua under small strains in the Kelvin-Voigt rheology are presented and analyzed by using the Galerkin method. The particular case, known as a phase-field fracture approximation of cracks, is discussed ... More

Approximation of Invariant Measures for Stochastic Differential Equations with Piecewise Continuous Arguments via Backward Euler MethodJun 10 2019For the stochastic differential equation (SDE) which has piecewise continuous arguments (PCAs), is driven by multiplicative noises and its drift coefficients are dissipative, we show that the solution at integer time is a Markov chain and admits a unique ... More

A note on the continuous-stage Runge-Kutta formulation of Hamiltonian Boundary Value Methods (HBVMs)Jun 10 2019In recent years, the class of energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) has been devised for numerically solving Hamiltonian problems. In this short note, we study their natural formulation as continuous-stage Runge-Kutta ... More

Weighted Quasi Interpolant Spline Approximation of 3D point clouds via local refinementJun 10 2019We present a new surface approximation, the Weighted Quasi Interpolant Spline Approximation (w-QISA), to approximate very large and noisy point clouds. We adopt local implicit representations based on three key ingredients: 1) a local mesh for the piecewise ... More

Coupled Optoelectronic Simulation and Optimization of Thin-Film Photovoltaic Solar CellsJun 10 2019A design tool was formulated for optimizing the efficiency of inorganic, thin-film, photovoltaic solar cells. The solar cell can have multiple semiconductor layers in addition to antireflection coatings, passivation layers, and buffer layers. The solar ... More

A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangleJun 10 2019We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to achieve high efficiency ... More

A Unified Definition and Computation of Laplacian Spectral DistancesJun 10 2019Laplacian spectral kernels and distances (e.g., biharmonic, heat diffusion, wave kernel distances) are easily defined through a filtering of the Laplacian eigenpairs. They play a central role in several applications, such as dimensionality reduction with ... More

Multiscale modeling of fiber reinforced materials via non-matching immersed methodsJun 10 2019Fiber reinforced materials (FRMs) can be modeled as bi-phasic materials, where different constitutive behaviors are associated with different phases. The numerical study of FRMs through a full geometrical resolution of the two phases is often computationally ... More

Laplacian Spectral Basis FunctionsJun 10 2019Representing a signal as a linear combination of a set of basis functions is central in a wide range of applications, such as approximation, de-noising, compression, shape correspondence and comparison. In this context, our paper addresses the main aspects ... More

Randomization and reweighted $\ell_1$-minimization for A-optimal design of linear inverse problemsJun 10 2019We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the posterior covariance ... More

Randomized Approximation of Linear Least Squares Regression at Sub-linear CostJun 10 2019We prove that with a high probability nearly optimal solution of the highly important problem of Linear Least Squares Regression can be computed at sub-linear cost for a random input. Our extensive tests are in good accordance with this result.

Proposal to Use the Fractional Derivative of Radial Functions in Interpolation ProblemsJun 10 2019In this document we present the construction of a radial functions that have the objective of emulating the behavior of the radial basis function thin plate spline (TPS), which we will name as function TPS, we propose a way to partially and totally apply ... More

a sequential least squares method for elliptic equations in non-divergence formJun 10 2019We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation to the gradient ... More

Fast Cadzow's Algorithm and a Gradient VariantJun 09 2019Jun 11 2019The Cadzow's algorithm is a signal denoising and recovery method which was designed for signals corresponding to low rank Hankel matrices. In this paper we first introduce a Fast Cadzow's algorithm which is developed by incorporating a novel subspace ... More

On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical RegimeJun 09 2019By using the pseudo-metric introduced in [F. Golse, T. Paul: Archive for Rational Mech. Anal. 223 (2017) 57-94], which is an analogue of the Wasserstein distance of exponent $2$ between a quantum density operator and a classical (phase-space) density, ... More

Nektar++: enhancing the capability and application of high-fidelity spectral/$hp$ element methodsJun 08 2019Nektar++ is an open-source framework that provides a flexible, performant and scalable platform for the development of solvers for partial differential equations using the high-order spectral/$hp$ element method. In particular, Nektar++ aims to overcome ... More

The superiority of stochastic symplectic methods for a linear stochastic oscillator via large deviations principlesJun 08 2019It is well known that symplectic methods have been rigorously shown to be superior to non-symplectic ones especially in long-time computation, when applied to deterministic Hamiltonian systems. In this paper, we focus on the superiority of stochastic ... More

Modified symmetry technique for mitigation of flow leak near corners for compressible inviscid fluid flowJun 08 2019Using the standard symmetry technique for applying boundary conditions for free slip and flat walls with corners will lead to flow leak through the wall near corners (violation of no penetration condition) and a corresponding error in prediction of pressure. ... More

Convergence in Density of Splitting AVF Scheme for Stochastic Langevin EquationJun 08 2019In this article, we study the density function of the numerical solution of the splitting averaged vector field (AVF) scheme for the stochastic Langevin equation. To deal with the non-globally monotone coefficient in the considered equation, we first ... More

Study of Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations in Data ScienceJun 08 2019In this work, a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV) decomposition along with a CoR-UTV variant aided by the power method technique is proposed. CoR-UTV computes an approximation to a low-rank ... More

Convergence analysis of approximation formulas for analytic functions via duality for potential energy minimizationJun 07 2019We investigate the approximation formulas that were proposed by Tanaka & Sugihara (2018), in weighted Hardy spaces, which are analytic function spaces with certain asymptotic decay. Under the criterion of minimum worst error of $n$-point approximation ... More

Numerical algorithm for the space-time fractional Fokker-Planck system with two internal statesJun 07 2019The fractional Fokker-Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., $\mathbf{13}$, 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power ... More

Pressure-robustness in quasi-optimal a priori estimates for the Stokes problemJun 07 2019Recent analysis of the divergence constraint in the incompressible Stokes/Navier--Stokes problem has stressed the importance of equivalence classes of forces and how it plays a fundamental role for an accurate space discretization. Two forces in the momentum ... More

Stochastic learning control of inhomogeneous quantum ensemblesJun 07 2019In quantum control, the robustness with respect to uncertainties in the system's parameters or driving field characteristics is of paramount importance and has been studied theoretically, numerically and experiementally. We test in this paper stochastic ... More

On The Weak Consistency of Finite Volumes Schemes for Conservation Laws on General MeshesJun 07 2019The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, analogues of the Lax-Wendroff theorem for) finite volume schemes for balance laws in the multi-dimensional case and under minimal regularity assumptions ... More

A Finite Volume Scheme for Savage-Hutter Equations on Unstructured GridsJun 07 2019A Godunov-type finite volume scheme on unstructured triangular grids is proposed to numerically solve the Savage-Hutter equations in curvilinear coordinate. We show the direct observation that the model is a not Galilean invariant system. At the cell ... More

Finite Element Methods for the Laplace-Beltrami OperatorJun 06 2019Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to the Laplace-Beltrami problem posed on an $n$-dimensional surface $\gamma$ ... More

New stability estimates for an unfitted finite element method for two-phase Stokes problemJun 06 2019The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori estimates for ... More

Synthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal controlJun 06 2019This paper studies the problem of constructing control Lyapunov functions (CLFs) and feedback stabilization strategies for deterministic nonlinear control systems described by ordinary differential equations. Many numerical methods for solving the Hamilton-Jacobi-Bellman ... More

An efficient data-driven solver for Fokker-Planck equations: algorithm and analysisJun 06 2019Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional Fokker-Planck ... More

Statistical solutions of hyperbolic systems of conservation laws: numerical approximationJun 06 2019Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system of conservation ... More

A neural network based policy iteration algorithm with global $H^2$-superlinear convergence for stochastic games on domainsJun 05 2019In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration ... More

Worst-case optimal approximation with increasingly flat Gaussian kernelsJun 05 2019We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces (RKHSs) induced by increasingly flat Gaussian kernels. This provides a new perspective and some generalisations to the problem of interpolation ... More

On stabilized P1 finite element approximation fortime harmonic Maxwell's equationsJun 05 2019One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear finite element ... More

Direct structural analysis of domains defined by point cloudsJun 05 2019This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a high-order immersed boundary technique that computes on a regular background ... More

Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticityJun 05 2019In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate. The proof relies on a monotonicity result combined with the techniques of ... More

A surrogate model for computational homogenization of elastostatics at finite strain using the HDMR-based neural network approximatorJun 05 2019We propose a surrogate model for two-scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macro-energy density. This energy ... More

On the accuracy of stiff-accurate diagonal implicit Runge-Kutta methods for finite volume based Navier-Stokes equationsJun 05 2019The paper aims at developing low-storage implicit Runge-Kutta methods which are easy to implement and achieve higher-order of convergence for both the velocity and pressure in the finite volume formulation of the incompressible Navier-Stokes equations ... More

Explicit $θ$-Schemes for Solving Anticipated Backward Stochastic Differential EquationsJun 05 2019Jun 10 2019In this paper, a class of stable explicit $\theta$-schemes are proposed for solving anticipated backward stochastic differential equations (anticipated BSDEs) which generator not only contains the present values of the solutions but also the future. We ... More

Explicit $θ$-Schemes for Solving Anticipated Backward Stochastic Differential EquationsJun 05 2019In this paper, a class of stable explicit $\theta$-schemes are proposed for solving anticipated backward stochastic differential equations (anticipated BSDEs) which generator not only contains the present values of the solutions but also the future. We ... More

RIP-based performance guarantee for low-tubal-rank tensor recoveryJun 05 2019The essential task of multi-dimensional data analysis focuses on the tensor decomposition and the corresponding notion of rank. In this paper, by introducing the notion of tensor singular value decomposition (t-SVD), we establish a regularized tensor ... More

$hp$-Version discontinuous Galerkin methods on essentially arbitrarily-shaped elementsJun 04 2019We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In particular, our ... More

Stochastic Gradients for Large-Scale Tensor DecompositionJun 04 2019Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently ... More

A parameter uniform essentially first order convergent numerical method for a parabolic singularly perturbed differential equation of reaction-diffusion type with initial and Robin boundary conditionsJun 04 2019In this paper, a class of linear parabolic singularly perturbed second order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered. The solution u of this equation is smooth, whereas the first derivative ... More

Extrapolation Methods for fixed-point Multilinear PageRank computationsJun 04 2019Nonnegative tensors arise very naturally in many applications that involve large and complex data flows. Due to the relatively small requirement in terms of memory storage and number of operations per step, the (shifted) higher-order power method is one ... More

On Optimal Algebraic Multigrid MethodsJun 04 2019In this note we present an alternative way to obtain optimal interpolation operators for two-grid methods applied to Hermitian positive definite linear systems. Falgout and Vassilevski in [SIAM J. Numer. Anal, 42 (2004), pp. 1669-1693] and Zikatanov [Numer. ... More

Kernel-based collocation methods for heat transport on evolving surfacesJun 04 2019We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on intrinsic kernel-based meshless collocation methods. The algorithms can ... More

Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensorsJun 04 2019A numerical integrator is presented that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-dependent matrices that are either given explicitly or are the unknown solution to a matrix differential equation. ... More

Algebraic representation of dual scalar products and stabilization of saddle point problemsJun 04 2019We provide a systematic way to design computable bilinear forms which, on the class of subspaces $W^* \subseteq \V'$ that can be obtained by duality from a given finite dimensional subspace $W$ of an Hilbert space $\V$, are spectrally equivalent to the ... More

On Expansions and Nodes for Sparse Grid Collocation of Lognormal Elliptic PDEsJun 04 2019This work is a follow-up on a previous contribution (`Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)' SIAM Journal of Numerical Analysis 2018), and contains further insights ... More

Two families of novel second-order fractional numerical formulas and their applications to fractional differential equationsJun 04 2019Jun 05 2019In this article, we introduce two families of novel fractional $\theta$-methods by constructing some new generating functions to discretize the Riemann-Liouville fractional calculus operator $\mathit{I}^{\alpha}$ with a second order convergence rate. ... More

Two families of novel second-order fractional numerical formulas and their applications to fractional differential equationsJun 04 2019In this article, we introduce two families of novel fractional $\theta$-methods by constructing some new generating functions to discretize the Riemann-Liouville fractional calculus operator $\mathit{I}^{\alpha}$ with a second order convergence rate. ... More

Surface Fluctuating Hydrodynamics Methods for the Drift-Diffusion Dynamics of Particles and Microstructures within Curved Fluid InterfacesJun 04 2019We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial hydrodynamic coupling, ... More

A Stabilized Hybrid Mixed Finite Element Method for PoroelasticityJun 03 2019In this work, we consider a hybrid mixed finite element method for Biot's model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy's velocity system of Biot's model presented in \cite{C. Niu} is not uniformly stable with respect to ... More

A Posteriori Error Estimates with Boundary Correction for a Cut Finite Element MethodJun 03 2019In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary and the analysis takes into account the geometry and data approximation ... More

Exploiting nested task-parallelism in the $\mathcal{H}-LU$ factorizationJun 03 2019We address the parallelization of the LU factorization of hierarchical matrices ($\mathcal{H}$-matrices) arising from boundary element methods. Our approach exploits task-parallelism via the OmpSs programming model and runtime, which discovers the data-flow ... More

An ergodic theorem for weighted ensembleJun 03 2019We study long-time averaging for weighted ensemble, a particle method in which the resampling is based on stratification, or binning of state space. By analyzing the scaling of the variance, we prove an ergodic theorem for weighted ensemble time averages. ... More

Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problemsJun 03 2019We propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and the flow can simply ... More

An adaptive multiresolution discontinuous Galerkin method with artificial viscosity for scalar hyperbolic conservation laws in multidimensionsJun 03 2019Jun 04 2019In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for scalar hyperbolic conservation laws in multidimensions. Compared with previous work for linear hyperbolic equations \cite{guo2016transport, guo2017adaptive}, ... More

PBDW method for state estimation: error analysis for noisy data and nonlinear formulationJun 03 2019We present an error analysis and further numerical investigations of the Parameterized-Background Data-Weak (PBDW) formulation to variational Data Assimilation (state estimation), proposed in [Y Maday, AT Patera, JD Penn, M Yano, Int J Numer Meth Eng, ... More

A high-order discretization of nonlinear poroelasticityJun 03 2019In this work we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. ... More

Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction AlgorithmJun 03 2019We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only coefficients. ... More

Numerical investigations into a model of partially incompressible two-phase flow in pipesJun 03 2019We consider a model for flow of liquid and gas in a pipe. We assume that the gas is ideal and that the liquid is incompressible. Under this assumption the resulting equations, expressing conservation of mass and momentum, splits into two subsystems such ... More

Modelling pattern formation through differential repulsionJun 03 2019Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a macroscopic one and ... More

Fast variable density 3-D node generationJun 03 2019Mesh-free solvers for partial differential equations perform best on scattered quasi-uniform nodes. Computational efficiency can be improved by using nodes with greater spacing in regions of less activity. We present an advancing front type method to ... More

On a class of parameterized solutions to interval parametric linear systemsJun 03 2019Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown that an application, ... More

An adaptive finite element method for the sparse optimal control of fractional diffusionJun 03 2019We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the Dirichlet-to-Neumann ... More

On The Radon--Nikodym Spectral Approach With Optimal ClusteringJun 02 2019Jun 06 2019Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\langle f(\mathbf{x})\psi^2 \rangle / \langle\psi^2\rangle$, where the $\psi(\mathbf{x})$ is a linear function on input attributes, all ... More