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Enhancing Compressed Sensing Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More
Adaptive generalized multiscale finite element methods for H(curl)-elliptic problems with heterogeneous coefficientsFeb 08 2018In this paper, we construct an adaptive multiscale method for solving H(curl)-elliptic problems in highly heterogeneous media. Our method is based on the generalized multiscale finite element method. We will first construct a suitable snapshot space, ... More
Uncertainty Quantification for Geometry Deformations of Superconducting Cavities using Eigenvalue TrackingFeb 08 2018The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities are sensitive to small geometry deformations. The occurring variations are motivated by measurements of an available set of resonators ... More
A mixed finite element for weakly-symmetric elasticityFeb 08 2018We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement, $H(\mathrm{div})$-conforming ... More
The nonconforming virtual element method for eigenvalue problemsFeb 08 2018We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the ... More
Finite Element Error Estimates for Optimal Control Problems with Pointwise TrackingFeb 08 2018We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three different approaches ... More
QTT-isogeometric solver in two dimensionsFeb 08 2018The goal of this paper is to develop a numerical algorithm that solves a two-dimensional elliptic partial differential equation in a polygonal domain using tensor methods and ideas from isogeometric analysis. The proposed algorithm is based on the Finite ... More
Arbitrary-order energy-preserving exponential integrators for the cubic Schrödinger equationFeb 08 2018In this paper we derive and analyse new and efficient energy-preserving exponential integrators of arbitrarily high order to solve the cubic Schr\"{o}dinger Cauchy problem on a $d$-dimensional torus. Energy preservation is a key feature of the cubic Schr\"{o}dinger ... More
Rank Revealing Gaussian Elimination by the Maximum Volume ConceptFeb 08 2018A Gaussian elimination algorithm is presented that reveals the numerical rank of a matrix by yielding small entries in the Schur complement. The algorithm uses the maximum volume concept to find a square nonsingular submatrix of maximum dimension. The ... More
Primal-dual stochastic gradient method for convex programs with many functional constraintsFeb 08 2018Stochastic gradient (SG) method has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SG assume that the underlying problem is unconstrained or has an easy-to-project ... More
Fourier Analysis and Evaluation of DG, FD and Compact Difference Methods for Conservation LawsFeb 08 2018Large eddy simulation (LES) has been increasingly used to tackle vortex-dominated turbulent flows. In LES, the quality of the simulation results hinges upon the quality of the numerical discretizations in both space and time. It is in this context we ... More
Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functionsFeb 07 2018Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, ... More
Recovering the full Navier Stokes equations with lattice Boltzmann schemesFeb 07 2018We consider multi relaxation times lattice Boltzmann scheme with two particle distributions for the thermal Navier Stokes equations formulated with conservation of mass and momentum and dissipation of volumic entropy.Linear stability is taken into consideration ... More
Discontinuous Galerkin methods for fractional elliptic problemsFeb 07 2018We provide a mathematical framework for studying different versions of discontinuous Galerkin (DG) approaches for solving 2D Riemann-Liouville fractional elliptic problems on a finite domain. The boundedness and stability analysis of the primal bilinear ... More
Positivity-Preserving Analysis of Numerical Schemes for Ideal MagnetohydrodynamicsFeb 07 2018Numerical schemes provably preserving the positivity of density and pressure are highly desired for MHD, but the rigorous positivity-preserving (PP) analysis remains challenging. The difficulties mainly arise from the intrinsic complexity of the MHD equations ... More
Coercivity, hypocoercivity, exponential time decay and simulations for discrete Fokker-Planck equationsFeb 06 2018In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence to the equilibrium ... More
A super--convergent hybridisable discontinuous Galerkin method for linear elasticityFeb 06 2018The first super-convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong ... More
Bayesian model calibration with interpolating polynomials based on adaptively weighted Leja nodesFeb 06 2018An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics: using a prior ... More
Compact ADI method for solving two-dimensional Riesz space fractional diffusion equationFeb 06 2018In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice the order of ... More
Upscaling Singular Sources in Weighted Sobolev Spaces by Sub-Grid CorrectionsFeb 06 2018In this paper, we develop a numerical multiscale method to solve elliptic boundary value problems with heterogeneous diffusion coefficients and with singular source terms. When the diffusion coefficient is heterogeneous, this adds to the computational ... More
Frames and numerical approximation II: generalized samplingFeb 06 2018In a previous paper [Adcock & Huybrechs, 2016] we described the numerical properties of function approximation using frames, i.e. complete systems that are generally redundant but provide infinite representations with coefficients of bounded norm. Frames ... More
High accuracy methods for eigenvalues of elliptic operators by nonconforming elementsFeb 06 2018In this paper, three high-accuracy methods for eigenvalues of second order elliptic operators are proposed by using the nonconforming Crouzeix-Raviart(CR for short) element and the nonconforming enriched Crouzeix-Raviart(ECR for short) element. They are ... More
Unified Models for Second-Order TV-Type Regularisation in Imaging - A New Perspective Based on Vector OperatorsFeb 06 2018We introduce a novel regulariser based on natural vector field operations. For suitable choices of the weighting parameters it generalises several well-known first- and second-order TV-type regularisation methods like for example the total variation (TV), ... More
A Posteriori Error Estimates for Non-Stationary Non-Linear Convection-Diffusion EquationsFeb 06 2018Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the standard linear ... More
Optimal consensus control of the Cucker-Smale modelFeb 05 2018We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive first-order necessary ... More
Simulation of multiphase porous media flows with minimizing movement and finite volume schemesFeb 05 2018The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Canc\`es, T. O. Gallou\"et, and L. Monsaingeon, {\it Anal. PDE} 10(8):1845--1876, 2017]. The model can thus be approximated ... More
On Uniform Connectivity of Algebraic Matrix SetsFeb 05 2018In this document we study the uniform local path connectivity of sets of $m$-tuples of pairwise commuting normal matrices with some additional constraints. More specifically, given given $\varepsilon>0$, a fixed metric $\eth$ in ${M_n(\mathbb{C})}^m$ ... More
A parallel-in-time fixed-stress splitting method for Biot's consolidation modelFeb 03 2018In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress splitting method, ... More
The Legendre Spectral-Collocation method for a class of fractional integral equationsFeb 03 2018In this paper, we consider spectral-collocation method base on Legendre-Gauss-Lobatto point. We present a computational method for solving a class of fractional integral equation of the second kind. Then based on Legendre-Gauss-Lobatto point and using, ... More
Parameter and Uncertainty Estimation for Dynamical Systems Using Surrogate Stochastic ProcessesFeb 02 2018Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical ... More
Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamicsFeb 02 2018In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cell density level, the spatial availability of the tumor density $n$ is governed ... More
Optimal interpolation formulas in $W_2^{(m,m-1)}$ spaceFeb 02 2018In the present paper optimal interpolation formulas are constructed in $W_2^{(m,m-1)}(0,1)$ space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.
On commuting $p$-version projection-based interpolation on tetrahedraFeb 01 2018On the reference tetrahedron $\widehat K$, we define three projection-based interpolation operators on $H^2(\widehat K)$, ${\mathbf H}^1(\widehat K,\operatorname{\mathbf{curl}})$, and ${\mathbf H}^1(\widehat K,\operatorname{div})$. These operators are ... More
Compressed Anomaly Detection with Multiple Mixed ObservationsJan 31 2018We consider a collection of independent random variables that are identically distributed, except for a small subset which follows a different, anomalous distribution. We study the problem of detecting which random variables in the collection are governed ... More
Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditionsJan 30 2018We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the spatial discretization ... More
An iterative support shrinking algorithm for $\ell_{p}$-$\ell_{q}$ minimizationJan 30 2018We present an iterative support shrinking algorithm for $\ell_{p}$-$\ell_{q}$ minimization~($0 <p < 1 \leq q < \infty $). This algorithm guarantees the nonexpensiveness of the signal support set and can be easily implemented after being proximally linearized. ... More
A time-optimal algorithm for solving (block-)tridiagonal linear systems of dimension N on a distributed computer of N nodesJan 30 2018Jan 31 2018We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension $N$ on a distributed computing network of $N$ nodes that is connected in a binary communication tree. Our research ... More
Time domain boundary elements for dynamic contact problemsJan 29 2018This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point formulation using ... More
What Is the Fractional Laplacian?Jan 29 2018The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature ... More
Boundary elements with mesh refinements for the wave equationJan 29 2018The solution of the wave equation in a polyhedral domain in $\mathbb{R}^3$ admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation as equivalent ... More
A BDF2-Approach for the Non-linear Fokker-Planck EquationJan 29 2018We prove convergence of a variational formulation of the BDF2 method applied to the non-linear Fokker-Planck equation. Our approach is inspired by the JKO-method and exploits the differential structure of the underlying $L^2$-Wasserstein space. The technique ... More
Strong error analysis for stochastic gradient descent optimization algorithmsJan 29 2018Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analysis for SGD optimization algorithms. In particular, we prove for every ... More
Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequenciesJan 27 2018We develop a non-overlapping domain decomposition method (DDM) for the solution of quasi-periodic scalar transmission problems in layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout ... More
Algebraic Hybridization and Static Condensation with Application to Scalable H(div) PreconditioningJan 26 2018We propose an unified algebraic approach for static condensation and hybridization, two popular techniques in finite element discretizations. The algebraic approach is supported by the construction of scalable solvers for problems involving H(div)-spaces ... More
Toward free-surface flow simulations with correct energy evolution: an isogeometric level-set approach with monolithic time-integrationJan 26 2018This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. Correct energy behavior means here that the energy evolution of the discretized and continuous two-fluid equations matches. We adopt ... More
Automatic rational approximation and linearization of nonlinear eigenvalue problemsJan 25 2018Feb 02 2018We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, S\`{e}te, and Trefethen to approximate the nonlinear eigenvalue problem by a rational eigenvalue problem and is ... More
A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equationsJan 25 2018In this paper the numerical solution of non-autonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully discrete numerical approximation that combines a standard Galerkin finite element ... More
Stable 3D FDTD Method for arbitrary Fully Electric and Magnetic Anisotropic Maxwell EquationsJan 25 2018We have developed a new fully anisotropic 3D FDTD Maxwell solver for arbitrary electrically and magnetically anisotropic media for piecewise constant electric and magnetic materials that are co-located over the primary computational cells. Two numerical ... More
Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitionsJan 25 2018Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting ... More
Quasi-Toeplitz matrix arithmetic: a MATLAB toolboxJan 24 2018A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind $A=T(a)+E$ where $T(a)=(a_{j-i})_{i,j\in\mathbb Z^+}$, $E=(e_{i,j})_{i,j\in\mathbb Z^+}$ is compact and the norms $\lVert a\rVert_{\mathcal W} = \sum_{i\in\mathbb Z}|a_i|$ and $\lVert ... More
Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic TomographyJan 22 2018Feb 08 2018The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as accurate ... More
A general approach to approximation theory of operator semigroupsJan 21 2018We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields optimal convergence ... More
A finite element method for the surface Stokes problemJan 19 2018We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and serve as a model problem in the dynamics of material interfaces. In this ... More
Invitation to Real Complexity Theory: Algorithmic Foundations to Reliable Numerics with Bit-CostsJan 19 2018While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and efficiency is demonstrated ... More
Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise Model for X-Ray CTJan 19 2018Statistical image reconstruction (SIR) methods for X-ray CT produce high-quality and accurate images, while greatly reducing patient exposure to radiation. When further reducing X-ray dose to an ultra-low level by lowering the tube current, photon starvation ... More
A Kotel'nikov Representation for WaveletsJan 17 2018This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an analysis with ... More
Efficient Computation of the 8-point DCT via Summation by PartsJan 17 2018This paper introduces a new fast algorithm for the 8-point discrete cosine transform (DCT) based on the summation-by-parts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed into sparse ... More
Parallel Block-Preconditioned Monolithic Solvers for Fluid-Structure-Interaction ProblemsJan 17 2018In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian-Eulerian framework ... More
Computation of the State Bias and Initial States for Stochastic State Space Systems in the General 2-D Roesser Model FormJan 14 2018Recently \cite{Ramos2017a} presented a subspace system identification algorithm for 2-D purely stochastic state space models in the general Roesser form. However, since the exact problem requires an oblique projection of $Y_f^h$ projected onto $W_p^h$ ... More
On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scalesJan 13 2018The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is \emph{strong homogeneity} meaning that ... More
Convexification of a 3-D coefficient inverse scattering problemJan 13 2018A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a single direction ... More
Determining Projection Constants of Univariate Polynomial SpacesJan 12 2018The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a linear program, ... More
Higher-order models for glioma invasion: from a two-scale description to effective equations for mass density and momentumJan 09 2018Starting from a two-scale description involving receptor binding dynamics and a kinetic transport equation for the evolution of the cell density function under velocity reorientations, we deduce macroscopic models for glioma invasion featuring partial ... More
Kinetic layers and coupling conditions for nonlinear scalar equations on networksJan 01 2018We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derived from the kinetic coupling conditions via an asymptotic analysis near ... More
An Efficient, Second Order Accurate, Universal Generalized Riemann Problem Solver Based on the HLLI Riemann SolverJan 01 2018The Riemann problem, and the associated generalized Riemann problem, are increasingly seen as the important building blocks for modern higher order Godunov-type schemes. In the past, building a generalized Riemann problem solver was seen as an intricately ... More
Case study: Approximations of the Bessel FunctionDec 31 2017The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
Coupling of Magneto-Thermal and Mechanical Superconducting Magnet Models by Means of Mesh-Based InterpolationDec 29 2017In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the ... More
Variational order for forced Lagrangian systemsDec 26 2017We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley [2013], Galley, ... More
Novel Method for Background Phase Removal on MRI Proton Resonance Frequency MeasurementsDec 22 2017MR images have a magnitude and a phase, but in almost all clinical applications only the magnitude images are used, because the phase images have a smooth but strong background signal that masks useful information. The phase contains information such ... More
Limited Angle Electrical Impedance Tomography with Power Density DataDec 21 2017This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed ... More
Well balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gasdynamics with gravityDec 21 2017In this work we present a novel second order accurate well balanced Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gasdynamics with gravity in cylindrical coordinates. The ... More
Quadrilateral grid generation supported on complex internal boundaries using spectral methodsDec 19 2017This work concerns with the following problem. Given a two-dimensional domain whose boundary is a closed polygonal line with internal boundaries defined also by polygonal lines, it is required to generate a grid consisting only of quadrilaterals with ... More
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equationsDec 18 2017We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging transformation, the ... More
Derivation of higher-order terms in FFT-based numerical homogenizationDec 14 2017In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier transform on homogenized microstructures to accelerate otherwise time-consuming ... More
A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equationDec 12 2017In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad-Shafranov equation, the solution of which determines the poloidal component of the magnetic ... More
Estimates for the Green's function of the discrete bilaplacian in dimensions 2 and 3Dec 07 2017We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes in two and three dimensions which are optimal except possibly near the corners of the square and the edges and corners of the cube. The main idea is to transfer ... More
Convergence of Multilevel Stationary Gaussian ConvolutionNov 29 2017In this paper we give a short note showing convergence rates for multilevel periodic approximation of smooth functions by multilevel Gaussian convolution. We will use the Gaussian scaling in the convolution at the finest level as a proxy for degrees of ... More
On $\ell^1$-regularization under continuity of the forward operator in weaker topologiesNov 23 2017Our focus is on the stable approximate solution of linear operator equations based on noisy data by using $\ell^1$-regularization as a sparsity-enforcing version of Tikhonov regularization. We summarize recent results on situations where the sparsity ... More
Scaled Boundary Parametrizations in Isogeometric AnalysisNov 15 2017Nov 21 2017This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational domain is available. ... More
A Variational Formulation of the BDF2 Method for Metric Gradient FlowsNov 08 2017Dec 22 2017We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no smoothness --- ... More
Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement VectorsNov 07 2017Jan 03 2018While single measurement vector (SMV) models have been widely studied in signal processing, there is a surging interest in addressing the multiple measurement vectors (MMV) problem. In the MMV setting, more than one measurement vector is available and ... More
A mixed EIM-SVD tensor decomposition for bivariate functionsNov 06 2017In this paper we present a mixed EIM-SVD tensor decomposition for bivariate functions. This method is composed, as its name suggests, of two main steps. The first one, provides an approximate representation of a function $f$ in separate form by the use ... More
Stochastic Greedy Algorithms For Multiple Measurement VectorsNov 05 2017Sparse representation of a single measurement vector (SMV) has been explored in a variety of compressive sensing applications. Recently, SMV models have been extended to solve multiple measurement vectors (MMV) problems, where the underlying signal is ... More
Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse ProblemsOct 28 2017Jan 19 2018We consider a problem of quantitative static elastography, the estimation of the Lam\'e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber ... More
PDE-Net: Learning PDEs from DataOct 26 2017Jan 01 2018In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the ... More
Multilevel ensemble Kalman filtering for spatio-temporal processesOct 19 2017This work concerns state-space models, in which the state-space is an infinite-dimensional spatial field, and the evolution is in continuous time, hence requiring approximation in space and time. The multilevel Monte Carlo (MLMC) sampling strategy is ... More
A nonlinear discrete-velocity relaxation model for traffic flowOct 17 2017We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit for all ranges of traffic data. Moreover, the model has an ... More
A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equationsOct 10 2017Uncertainty Quantification through stochastic spectral methods is rising in popularity. We derive a modification of the classical stochastic Galerkin method, that ensures the hyperbolicity of the underlying hyperbolic system of partial differential equations. ... More
Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gainOct 10 2017In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. ... More
A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilationSep 26 2017The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting ... More
Second-order mixed-moment model with differentiable ansatz function in slab geometrySep 23 2017We study differentiable mixed-moment models (full zeroth and first moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum ... More
A stencil scaling approach for accelerating matrix-free finite element implementationsSep 20 2017We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces a new operator ... More
On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilationSep 19 2017This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent ... More
Variational Gaussian Approximation for Poisson DataSep 18 2017The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution ... More
A Hybrid High-Order method for highly oscillatory elliptic problemsSep 14 2017Feb 15 2018We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh; those attached ... More
Stable evaluation of Gaussian radial basis functions using Hermite polynomialsSep 07 2017Gaussian radial basis functions can be an accurate basis for multivariate interpolation. In practise, high accuracies are often achieved in the flat limit where the interpolation matrix becomes increasingly ill-conditioned. Stable evaluation algorithms ... More
On ill-posedness concepts, stable solvability and saturationSep 04 2017We consider different concepts of well-posedness and ill-posedness and their relations for solving nonlinear and linear operator equations in Hilbert spaces. First, the concepts of Hadamard and Nashed are recalled which are appropriate for linear operator ... More
Kinetic layers and coupling conditions for macroscopic equations on networks I: the wave equationAug 25 2017We consider kinetic and associated macroscopic equations on networks. The general approach will be explained in this paper for a linear kinetic BGK model and the corresponding limit for small Knudsen number, which is the wave equation. Coupling conditions ... More
A Stabilized Normal Form Algorithm for Generic Systems of Polynomial EquationsAug 25 2017We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring $\mathbb{C}[x]/I$ associated to a zero-dimensional ideal $I$ generated by $n$ $\mathbb{C}$-polynomials in $n$ variables. We assume that the polynomials ... More
Automated adjoints of coupled PDE-ODE systemsAug 25 2017Mathematical models that couple partial differential equations (PDEs) and spatially distributed ordinary differential equations (ODEs) arise in biology, medicine, chemistry and many other fields. In this paper we discuss an extension to the FEniCS finite ... More