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The saturation assumption yields optimal convergence of two-level adaptive BEMJul 15 2019We consider the convergence of adaptive BEM for weakly-singular and hypersingular integral equations associated with the Laplacian and the Helmholtz operator in 2D and 3D. The local mesh-refinement is driven by some two-level error estimator. We show ... More
Out-of-core singular value decompositionJul 15 2019Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However, many common ... More
Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) ProblemsJul 15 2019Optimal control problems including partial differential equation (PDE) as well as integer constraints combine the combinatorial difficulties of integer programming and large-scale systems resulting from discretizing the PDE. A common solution strategy ... More
Stochastic Galerkin finite volume shallow flow model: well-balanced treatment over uncertain topographyJul 15 2019Stochastic Galerkin methods can quantify uncertainty at a fraction of the computational expense of conventional Monte Carlo techniques, but such methods have rarely been studied for modelling shallow water flows. Existing stochastic shallow flow models ... More
Multilevel Particle Filters for the Non-Linear Filtering Problem in Continuous TimeJul 15 2019In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we resort to a ... More
Gradient Flow Based Discretized Kohn-Sham Density Functional TheoryJul 15 2019In this paper, we propose and analyze a gradient flow based Kohn-Sham density functional theory. First, we prove that the critical point of the gradient flow based model can be a local minimizer of the Kohn-Sham total energy. Then we apply a midpoint ... More
Numerical study of vanishing and spreading dynamics of chemotaxis systems with logistic source and a free boundaryJul 15 2019The current paper is to investigate the numerical approximation of logistic type chemotaxis models in one space dimension with a free boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject to the influence ... More
Tensor train-Karhunen-Loève expansion for continuous-indexed random fields using higher-order cumulant functionsJul 15 2019The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional geometrical domain in the tensor train format; secondly, to develop a new algorithm framework for ... More
Wave solutions of Gilson-Pickering equationJul 14 2019In this work, we apply the (1/G')-expansion method to produce the novel soliton solution of the Gilson-Pickering equation. This method is fundamental on homogeneous balance procedure that gives the order of the estimating polynomial-type solution. Also ... More
Avoiding Membrane Locking with Regge InterpolationJul 14 2019In this paper a novel method to overcome membrane locking of thin shells is presented. An interpolation operator into the so-called Regge finite element space is inserted in the membrane energy term to weaken the implicitly given kernel constraints. Due ... More
A fast direct solver for two dimensional quasi-periodic multilayered medium scattering problemsJul 14 2019This manuscript presents a fast direct solution technique for solving two dimensional wave scattering problems from quasi-periodic multilayered structures. The fast solver is built from the linear system that results from the discretization of a boundary ... More
Wong-Zakai approximations with convergence rate for stochastic partial differential equationsJul 14 2019The goal of this paper is to prove a convergence rate for Wong-Zakai approximations of semilinear stochastic partial differential equations driven by a finite dimensional Brownian motion. Several examples, including the HJMM equation from mathematical ... More
A GPU implementation of the Discontinuous Galerkin method for simulation of diffusion in brain tissueJul 14 2019In this work we develop a methodology to approximate the covariance matrix associated to the simulation of water diffusion inside the brain tissue. The computation is based on an implementation of the Discontinuous Galerkin method of the diffusion equation, ... More
A semi-Lagrangian discontinuous Galerkin (DG) -- local DG method for solving convection-diffusion-reaction equationsJul 13 2019In this paper, we propose an efficient high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for solving linear convection-diffusion-reaction equations. The method generalizes our previous work on developing the SLDG method for transport ... More
On the convergence rate of some nonlocal energiesJul 13 2019We study the rate of convergence of some nonlocal functionals recently considered by Bourgain, Brezis and Mironescu. In particular we establish the $\Gamma$-convergence of the corresponding rate functionals, suitably rescaled, to a limit functional of ... More
ND-Wavelets Derived from Anti-symmetric Systems of Isolated Particles using the Determinant of SlaterJul 13 2019Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states is used to generate ... More
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: I -- The Ergodic CaseJul 13 2019We propose two algorithms for the solution of the optimal control of ergodic McKean-Vlasov dynamics. Both algorithms are based on the approximation of the theoretical solutions by neural networks, the latter being characterized by their architecture and ... More
Entropy-stable discontinuous Galerkin approximation with summation-by-parts for the incompressible Navier-Stokes equations with variable density and artificial compressibilityJul 12 2019We present a provably stable discontinuous Galerkin spectral element method for the incompressible Navier-Stokes equations with artificial compressibility and variable density. Stability proofs, which include boundary conditions, that follow a continuous ... More
Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEsJul 12 2019We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical decomposition of the ... More
Fast, higher-order direct/iterative hybrid solver for scattering by Inhomogeneous media -- with application to high-frequency and discontinuous refractivity problemsJul 12 2019This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities. The method ... More
Convergent discretisation schemes for transition path theory for diffusion processesJul 12 2019In the analysis of metastable diffusion processes, Transition Path Theory (TPT) provides a way to quantify the probability of observing a given transition between two disjoint metastable subsets of state space. However, many TPT-based methods for diffusion ... More
Structured inversion of the Bernstein mass matrixJul 12 2019Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to interesting linear ... More
$L^2$-Error estimates for H(div)-conforming schemes applied to a linearised model of inviscid incompressible flowJul 12 2019In this note an error estimate in the $L^2$-norm of order $O(h^{k+\frac12})$ is proven for a finite element method for a linearised model of inviscid incompressible flow. We also prove error estimates of the same order for the pressure error in the $L^2$-norm. ... More
Regularized HessELM and Inclined Entropy Measurement for Congestive Heart Failure PredictionJul 12 2019Our study concerns with automated predicting of congestive heart failure (CHF) through the analysis of electrocardiography (ECG) signals. A novel machine learning approach, regularized hessenberg decomposition based extreme learning machine (R-HessELM), ... More
Adaptive Regularization Parameter Choice Rules for Large-Scale ProblemsJul 12 2019This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and projection onto ... More
Analytic functions in shift-invariant spaces and analytic limits of level dependent subdivisionJul 12 2019The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable function vectors and related multi-wavelets is well studied. In this paper, ... More
A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equationsJul 12 2019In this paper, we propose to improve the stabilized POD-ROM introduced by S. Rubino in [37] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we introduce a stabilizing post-processing ... More
Eigenvalues of the non-backtracking operator detached from the bulkJul 12 2019We describe the non-backtracking spectrum of a stochastic block model with connection probabilities $p_{\mathrm{in}}, p_{\mathrm{out}} = \omega(\log n)/n$. In this regime we answer a question posed in Dall'Amico and al. (2019) regarding the existence ... More
A higher order perturbation approach for electromagnetic scattering problems on random domainsJul 11 2019We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain boundary variations ... More
An $L^2_T$-error bound for time-limited balanced truncationJul 11 2019Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced truncation, a method ... More
Simulation of 3D elasto-acoustic wave propagation based on a Discontinuous Galerkin Spectral Element methodJul 11 2019In this paper we present a numerical discretization of the coupled elasto-acoustic wave propagation problem based on a Discontinuous Galerkin Spectral Element (DGSE) approach in a three-dimensional setting. The unknowns of the coupled problem are the ... More
Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing anglesJul 11 2019Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3-D structure of a molecule from several noisy 2-D projections images taken at unknown viewing angles. Most reconstruction algorithms ... More
Arbitrarily High-order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow ModelsJul 11 2019We present a systematical approach to developing arbitrarily high order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that satisfy energy dissipation laws. Utilizing the energy quadratization (EQ) ... More
Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learningJul 11 2019Recently, the deep learning method has been used for solving forward backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). It has good accuracy and performance for high-dimensional problems. In this paper, ... More
Splitting methods for Fourier spectral discretizations of the strongly magnetized Vlasov-Poisson and the Vlasov-Maxwell systemJul 11 2019Fourier spectral discretizations belong to the most straightforward methods for solving the unmagnetized Vlasov--Poisson system in low dimensions. In this article, this highly accurate approach is extended two the four-dimensional magnetized Vlasov--Poisson ... More
Improved PDE Models for Image Restoration through BackpropagationJul 11 2019In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration problem is modelled ... More
Global Stabilization of 2D Forced Viscous Burgers' Equation Around Nonconstant Steady State Solution by Nonlinear Neumann Boundary Feedback Control:Theory and Finite Element AnalysisJul 11 2019Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers' equation around a ... More
Capillary Rise -- A Computational Benchmark for Wetting ProcessesJul 11 2019Four different numerical approaches are compared for the rise of liquid between two parallel plates. These are an Arbitrary Lagrangian-Eulerian method (OpenFOAM solver interTrackFoam), a geometric volume of fluid code (FS3D), an algebraic volume of fluid ... More
Efficient Uncertainty Modeling for System Design via Mixed Integer ProgrammingJul 10 2019The post-Moore era casts a shadow of uncertainty on many aspects of computer system design. Managing that uncertainty requires new algorithmic tools to make quantitative assessments. While prior uncertainty quantification methods, such as generalized ... More
Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methodsJul 10 2019We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element spectral methods by Wissink et al. (B.W. Wissink, G.B. Jacobs, J.K. Ryan, W.S. Don, and E.T.A. van der Weide. ... More
Tensor-Free Proximal Methods for Lifted Bilinear/Quadratic Inverse Problems with Applications to Phase RetrievalJul 10 2019We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying first-order proximal algorithms, these problems could be solved numerically ... More
Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying directionJul 10 2019In this paper, we consider the three dimensional Vlasov equation with an inhomogeneous, varying direction, strong magnetic field. Whenever the magnetic field has constant intensity, the oscillations generated by the stiff term are periodic. The homogenized ... More
Higher-order ergodicity coefficientsJul 10 2019Ergodicity coefficients for stochastic matrices provide valuable upper bounds for the magnitude of subdominant eigenvalues, allow to bound the convergence rate of methods for computing the stationary distribution and can be used to estimate the sensitivity ... More
A positivity preserving iterative method for finding the ground states of saturable nonlinear Schrödinger equationsJul 10 2019In this paper, we propose an iterative method to compute the positive ground states of saturable nonlinear Schr\"odinger equations. A discretization of the saturable nonlinear Schr\"odinger equation leads to a nonlinear algebraic eigenvalue problem (NAEP). ... More
A multilevel Monte Carlo method for asymptotic-preserving particle schemesJul 10 2019Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in the diffusive limit, in which the collision rate tends to infinity. Classical particle-based ... More
An inverse acoustic-elastic interaction problem with phased or phaseless far-field dataJul 10 2019Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the location and ... More
Analysis and Simulation of a Coupled Diffusion based Image Denoising ModelJul 10 2019In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which performs efficient ... More
Improved Structural Methods for Nonlinear Differential-Algebraic Equations via Combinatorial RelaxationJul 10 2019Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. In numerical analysis of DAEs, consistent initialization and index reduction are important preprocessing prior to numerical integration. Existing DAE solvers commonly ... More
The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learningJul 10 2019Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic type. We study ... More
A family of multi-parameterized proximal point algorithmsJul 10 2019In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate from the prospective ... More
Improving Solve Time of aggregation-based adaptive AMGJul 09 2019This paper proposes improving the solve time of a bootstrap AMG designed previously by the authors. This is achieved by incorporating the information, set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by ... More
Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methodsJul 09 2019In this paper the discrete eigenvalues of elliptic second order differential operators in $L^2(\mathbb{R}^n)$, $n \in \mathbb{N}$, with singular $\delta$- and $\delta'$-interactions are studied. We show the self-adjointness of these operators and derive ... More
Arbitrarily High-order Unconditionally Energy Stable Schemes for Gradient Flow Models Using the Scalar Auxiliary Variable ApproachJul 09 2019In this paper, we propose a novel family of high-order numerical schemes for the gradient flow models based on the scalar auxiliary variable (SAV) approach, which is named the high-order scalar auxiliary variable (HSAV) method. The newly proposed schemes ... More
A divide-and-conquer algorithm for binary matrix completionJul 09 2019We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the form of binary ... More
Error analysis of an asymptotic preserving dynamical low-rank integrator for the multi-scale radiative transfer equationJul 09 2019Dynamical low-rank algorithm are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensional manifold and writing the solution directly in terms of the ... More
Unified Optimal Analysis of the (Stochastic) Gradient MethodJul 09 2019In this note we give a simple proof for the convergence of stochastic gradient (SGD) methods on $\mu$-strongly convex functions under a (milder than standard) $L$-smoothness assumption. We show that SGD converges after $T$ iterations as $O\left( L \|x_0-x^\star\|^2 ... More
A method for computing the Perron-Frobenius root for primitive matricesJul 09 2019For a nonnegative matrix, the eigenvalue with the maximum magnitude or Perron-Frobenius root exists and is unique if the matrix is primitive. It is shown that for a primitive matrix $A$, there exists a positive rank one matrix $X$ allowing to have the ... More
Shock Capturing by Bernstein Polynomials for Scalar Conservation LawsJul 09 2019A main disadvantage of many high-order methods for hyperbolic conservation laws lies in the famous Gibbs-Wilbraham phenomenon, once discontinuities appear in the solution. Due to the Gibbs-Wilbraham phenomenon, the numerical approximation will be polluted ... More
Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the arteryJul 09 2019The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolics, one elliptic and one ordinary differential equations that are coupled ... More
PDE/PDF-informed adaptive sampling for efficient non-intrusive surrogate modellingJul 09 2019A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure is based on ... More
On alternative quantization for doubly weighted approximation and integration over unbounded domainsJul 09 2019It is known that for a $\rho$-weighted $L_q$-approximation of single variable functions $f$ with the $r$th derivatives in a $\psi$-weighted $L_p$ space, the minimal error of approximations that use $n$ samples of $f$ is proportional to $\|\omega^{1/\alpha}\|_{L_1}^\alpha\|f^{(r)}\psi\|_{L_p}n^{-r+(1/p-1/q)_+},$ ... More
Eigenfunction Behavior and Adaptive Finite Element Approximations of Nonlinear Eigenvalue Problems in Quantum PhysicsJul 09 2019In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that the eigenfunction cannot be a polynomial on any open set, which may be reviewed as a refinement of the classic unique continuation ... More
Bayesian approach for inverse obstacle scattering with Poisson dataJul 09 2019We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form. The prior for ... More
Variational Bayes' method for functions with applications to some inverse problemsJul 08 2019Bayesian approach as a useful tool for quantifying uncertainties has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach is how to extract information from ... More
Variational Bayes' method for functions with applications to some inverse problemsJul 08 2019Jul 13 2019Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how to extract ... More
A fast simple algorithm for computing the potential of charges on a lineJul 08 2019We present a fast method for evaluating expressions of the form $$ u_j = \sum_{i = 1,i \not = j}^n \frac{\alpha_i}{x_i - x_j}, \quad \text{for} \quad j = 1,\ldots,n, $$ where $\alpha_i$ are real numbers, and $x_i$ are points in a compact interval of $\mathbb{R}$. ... More
On numerical stabilization in modeling double-diffusive viscous fingeringJul 08 2019A firm understanding and control of viscous fingering (VF) and miscible displacement will be vital to a wide range of industrial, environmental, and pharmaceutical applications, such as geological carbon-dioxide sequestration, enhanced oil recovery, and ... More
Quasi-optimal adaptive mixed finite element methods for controlling natural norm errorsJul 08 2019For a generalized Hodge--Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method controlling the error in the natural mixed variational norm. In particular, we obtain new quasi-optimal adaptive mixed methods ... More
Solving p-adic polynomial systems via iterative eigenvector algorithmsJul 08 2019In this article, we describe an implementation of a polynomial system solver to compute the approximate solutions of a 0-dimensional polynomial system with finite precision p-adic arithmetic. We also describe an improvement to an algorithm of Caruso, ... More
The Haar System in Triebel-Lizorkin Spaces: Endpoint ResultsJul 08 2019We determine for which parameters natural enumerations of the Haar system in $\mathbb{R}^d$ form a Schauder basis or basic sequence on Triebel-Lizorkin spaces. The new results concern the endpoint cases.
Multirate PWM balance method for the efficient field-circuit coupled simulation of power convertersJul 08 2019The field-circuit coupled simulation of switch-mode power converters with conventional time discretization is computationally expensive since very small time steps are needed to appropriately account for steep transients occurring inside the converter, ... More
A generic finite element framework on parallel tree-based adaptive meshesJul 08 2019We present highly scalable parallel distributed-memory algorithms and associated data structures for a generic finite element framework that supports $h$-adaptivity on computational domains represented as multiple connected adaptive trees, thus providing ... More
Multiscale High-Dimensional Sparse Fourier Algorithms for Noisy DataJul 08 2019We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016), an efficient sparse Fourier algorithm with $\Theta(ds \log s)$ average-case ... More
Admissible and attainable convergence behavior of block Arnoldi and GMRESJul 08 2019It is well-established that any non-increasing convergence curve is possible for GMRES and a family of pairs $(A,b)$ can be constructed for which GMRES exhibits a given convergence curve with $A$ having arbitrary spectrum. No analog of this result has ... More
A convergent FV-FEM scheme for the stationary compressible Navier-Stokes equationsJul 08 2019In this paper, we propose a discretization of the multi-dimensional stationary compressible Navier-Stokes equations combining finite element and finite volume techniques. As the mesh size tends to 0, the numerical solutions are shown to converge (up to ... More
Mean field models for large data-clustering problemsJul 08 2019We consider mean-field models for data--clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes information on the position as well as on additional features of the particles ... More
Solution Landscapes in the Landau-de Gennes Theory on RectanglesJul 08 2019We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau-de Gennes framework. We have one essential model variable---$\tilde{\epsilon}$ which is a geometry-dependent and material-dependent variable. We analytically study ... More
Deep splitting method for parabolic PDEsJul 08 2019In this paper we introduce a numerical method for parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the ... More
On Approximating Discontinuous Solutions of PDEs by Adaptive Finite ElementsJul 08 2019For singularly perturbed problems with a small diffusion, when the transient layer is very sharp and the computational mesh is relatively coarse, the solution can be viewed as discontinuous. For both linear and nonlinear hyperbolic partial differential ... More
Sparse Hierarchical Preconditioners Using Piecewise Smooth Approximations of EigenvectorsJul 08 2019When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a small number of iterations, however, they have to be coupled with an efficient ... More
A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysisJul 07 2019For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is proposed. The structure of the SDE is inspired by stochastic Partial Differential ... More
Entropy stable numerical approximations for the isothermal and polytropic Euler equationsJul 07 2019In this work we analyze the entropic properties of the Euler equations when the system is closed with the assumption of a polytropic gas. In this case, the pressure solely depends upon the density of the fluid and the energy equation is not necessary ... More
Truncation error estimates of approximate operators in a generalized particle methodJul 07 2019To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method that typically ... More
The gradient flow structures of thermo-poro-visco-elastic processes in porous mediaJul 06 2019In this paper, the inherent gradient flow structures of thermo-poro-visco-elastic processes in porous media are examined for the first time. In the first part, a modelling framework is introduced aiming for describing such processes as generalized gradient ... More
On the Convergence of Stochastic Gradient Descent for Nonlinear Ill-Posed ProblemsJul 06 2019In this work, we analyze the regularizing property of the stochastic gradient descent for the efficient numerical solution of a class of nonlinear ill-posed inverse problems in Hilbert spaces. At each step of the iteration, the method randomly chooses ... More
A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous mediaJul 05 2019In petroleum reservoir simulation, the standard preconditioner, the Constrained Pressure Residual (CPR) method, is a two-stage process which involves solving a restricted pressure system. Initially designed for isothermal models, this approach is often ... More
Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniquesJul 05 2019In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are formulated ... More
Generalization of the Neville-Aitken Interpolation Algorithm on Grassmann Manifolds : Applications to Reduced Order ModelJul 05 2019The interpolation on Grassmann manifolds in the framework of parametric evolution partial differential equations is presented. Interpolation points on the Grassmann manifold are the subspaces spanned by the POD bases of the available solutions corresponding ... More
Exponential integrators for semi-linear parabolic problems with linear constraintsJul 05 2019This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained systems with ... More
Stochastic modified equations for symplectic methods applied to rough Hamiltonian systems based on the Wong--Zakai approximationJul 05 2019We investigate the stochastic modified equation which plays an important role in the stochastic backward error analysis for explaining the mathematical mechanism of a numerical method. The contribution of this paper is threefold. First, we construct a ... More
A note on optimal $H^1$-error estimates for Crank-Nicolson approximations to the nonlinear Schrödinger equationJul 05 2019In this paper we consider a mass- and energy--conserving Crank-Nicolson time discretization for a general class of nonlinear Schr\"odinger equations. This scheme, which enjoys popularity in the physics community due to its conservation properties, was ... More
On stable invertibility and global Newton convergence for convex monotonic functionsJul 05 2019We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for finite dimensional inverse problems with a continuously differentiable, componentwise convex and monotonic forward function. Our criterion ... More
Exploration of a Cosine Expansion Lattice SchemeJul 05 2019In this article, we combine a lattice sequence from Quasi-Monte Carlo rules with the philosophy of the Fourier-cosine method to design an approximation scheme for expectation computation. We study the error of this scheme and compare this scheme with ... More
Rational Krylov and ADI iteration for infinite size quasi-Toeplitz matrix equationsJul 05 2019We consider a class of linear matrix equations involving semi-infinite matrices which have a quasi-Toeplitz structure. These equations arise in different settings, mostly connected with PDEs or the study of Markov chains such as random walks on bidimensional ... More
A-priori error analysis of local incremental minimization schemes for rate-independent evolutionsJul 05 2019This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-independent systems with non-convex energies. We first show by means of ... More
A fast method for variable-order space-fractional diffusion equationsJul 05 2019Jul 08 2019We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the resulting stiffness ... More
A fast method for variable-order space-fractional diffusion equationsJul 05 2019We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the resulting stiffness ... More
A stable discontinuous Galerkin method for linear elastodynamics in geometrically complex media using physics based numerical fluxesJul 05 2019High order accurate and explicit time-stable solvers are well suited for hyperbolic wave propagation problems. For the complexities of real geometries, internal interfaces, nonlinear boundary and interface conditions, discontinuities and sharp wave fronts ... More
A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysisJul 04 2019Random microstructures of heterogeneous materials play a crucial role in the material macroscopic behavior and in predictions of its effective properties. A common approach to modeling random multiphase materials is to develop so-called surrogate models ... More
An $hr$-Adaptive Method for the Cubic Nonlinear Schrödinger EquationJul 04 2019The nonlinear Schr\"{o}dinger equation (NLSE) is one of the most important equations in quantum mechanics, and appears in a wide range of applications including optical fibre communications, plasma physics and biomolecule dynamics. It is a notoriously ... More