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Convergence of fully discrete implicit and semi-implicit approximations of nonlinear parabolic equationsFeb 21 2019The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the $p$-Laplace operator ... More
A Joint Deep Learning Approach for Automated Liver and Tumor SegmentationFeb 21 2019Hepatocellular carcinoma (HCC) is the most common type of primary liver cancer in adults, and the most common cause of death of people suffering from cirrhosis. The segmentation of liver lesions in CT images allows assessment of tumor load, treatment ... More
Two exponential-type integrators for the "good" Boussinesq equationFeb 20 2019We introduce two exponential-type integrators for the "good" Bousinessq equation. They are of orders one and two, respectively, and they require lower regularity of the solution compared to the classical exponential integrators. More precisely, we will ... More
A geometric approach for the addition of nodes to an interpolatory quadrature rule with positive weightsFeb 20 2019A novel mathematical framework is derived for the addition of nodes to interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde-matrix describing the relation between the nodes and the weights and can ... More
FFT-based homogenisation accelerated by low-rank approximationsFeb 20 2019Fast Fourier transform (FFT) based methods has turned out to be an effective computational approach for numerical homogenisation. Particularly, Fourier-Galerkin methods are computational methods for partial differential equations that are discretised ... More
Haar wavelet method for the coupled degenerate reaction-diffusion PDEs and the ODEs having a non-linear sourceFeb 19 2019In this work, we propose the Haar wavelet method for the coupled degenerate reaction-diffusion PDEs and the ODEs having non-linear a source with Neumann boundary, applicable in various fields of the natural sciences, engineering, and economics, for example ... More
Gain function approximation in the Feedback Particle FilterFeb 19 2019This paper is concerned with numerical algorithms for the problem of gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical problem ... More
A level-set multigrid technique for nonlinear diffusion in the numerical simulation of marble degradation under chemical pollutantsFeb 19 2019Having in mind the modelling of marble degradation under chemical pollutants, e.g. the sulfation process, we consider governing nonlinear diffusion equations and their numerical approximation. The space domain of a computation is the pristine marble object ... More
A Sequential Homotopy Method for Mathematical Programming ProblemsFeb 19 2019We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler timestepping ... More
Ordered Line Integral Methods for Solving the Eikonal EquationFeb 18 2019The eikonal equation is used to model high-frequency wave propagation and solve a variety of applied problems in computational science. We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and factored eikonal equation, ... More
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularityFeb 18 2019We present a new filtered low-regularity Fourier integrator for the cubic nonlinear Schr\"odinger equation based on recent time discretization and filtering techniques. For this new scheme, we perform a rigorous error analysis and establish better convergence ... More
Manifold interpolation and model reductionFeb 18 2019One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric structure and thus ... More
Simplex Stochastic Collocation for Piecewise Smooth Functions with KinksFeb 18 2019Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for non-smooth functions with kinks. For example, such kinks can arise in the uncertainty quantification ... More
Boundary integral equation methods for the two dimensional wave equation in time domain revisitedFeb 18 2019This study considers the stability of time domain BIEMs for the wave equation in 2D. We show that the stability of time domain BIEMs is reduced to a nonlinear eigenvalue problem related to frequency domain integral equations. We propose to solve this ... More
Sparse residual tree and forestFeb 18 2019Sparse residual tree (SRT) is an adaptive exploration method for multivariate scattered data approximation. It leads to sparse and stable approximations in areas where the data is sufficient or redundant, and points out the possible local regions where ... More
Stability of Galerkin discretizations of a mixed space-time variational formulation of parabolic evolution equationsFeb 17 2019We analyze Galerkin discretizations of a new well-posed mixed space-time variational formulation of parabolic PDEs. For suitable pairs of finite element trial spaces, the resulting Galerkin operators are shown to be uniformly stable. The method is compared ... More
Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosonsFeb 17 2019Kaniadakis and Quarati (1994) proposed a Fokker-Planck equation with quadratic drift as a PDE model for the dynamics of Bose-Einstein condensation in a homogeneous Bose gas. It is an open question whether this equation has solutions exhibiting condensates ... More
Numerical upscaling of the free boundary dam problem in multiscale high-contrast mediaFeb 17 2019In this paper, we address the numerical homogenization approximation of a free-boundary dam problem posed in a heterogeneous media. More precisely, we propose a generalized multiscale finite element (GMsFEM) method for the heterogeneous dam problem. The ... More
Numerical solution of the two-phase tumour growth model with moving boundaryFeb 16 2019A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution is proved. The ... More
Taylor expansion based fast Multipole Methods for 3-D Helmholtz equations in Layered MediaFeb 15 2019In this paper, we develop fast multipole methods for 3D Helmholtz kernel in layered media. Two algorithms based on different forms of Taylor expansion of layered media Green's function are developed. A key component of the first algorithm is an efficient ... More
A polynomial spectral method for the spatially homogeneous Boltzmann equationFeb 15 2019We present a spectral Petrov-Galerkin method for the Boltzmann collision operator. We expand the density distribution $f$ to high order orthogonal polynomials multiplied by a Maxwellian. By that choice, we can approximate on the whole momentum domain ... More
Monolithic and splitting based solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transportFeb 15 2019This paper concerns splitting-based iterative procedures for the coupled nonlinear thermo-poroelasticity model problem. The thermo-poroelastic model problem we consider is formulated as a three-field system of PDE's, consisting of an energy balance equation, ... More
Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable heightFeb 15 2019In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical ... More
A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive propertyFeb 15 2019In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation ... More
Shear rate projection schemes for non-Newtonian fluidsFeb 14 2019The operator splitting approach applied to the Navier-Stokes equations, gave rise to various numerical methods for the simulations of the dynamics of fluids. The separate work of Chorin and Temam on this subject gave birth to the so-called projection ... More
Closed-form evaluation of potential integrals in the Boundary Element MethodFeb 14 2019A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on ... More
The Wasserstein Distances Between Pushed-Forward Measures with Applications to Uncertainty QuantificationFeb 14 2019Feb 20 2019In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we would like ... More
The Wasserstein Distances Between Pushed-Forward Measures with Applications to Uncertainty QuantificationFeb 14 2019In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we would like ... More
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation lawsFeb 14 2019In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial ... More
On parareal algorithms for semilinear parabolic Stochastic PDEsFeb 14 2019Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes, and have been designed to achieve a `parallel in real time' implementation. ... More
High-order generalized-$α$ methodsFeb 14 2019The generalized-$\alpha$ method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user. The method is ... More
The Role of Energy Minimization in Algebraic Multigrid InterpolationFeb 13 2019Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development of improved ... More
Fast Multipole Method For 3-D Helmholtz Equation In Layered MediaFeb 13 2019In this paper, a fast multipole method (FMM) is proposed to compute long-range interactions of wave sources embedded in 3-D layered media. The layered media Green's function for the Helmholtz equation, which satisfies the transmission conditions at material ... More
Fractional Operators Applied to Geophysical ElectromagneticsFeb 13 2019A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is presumed attributable ... More
Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structuresFeb 13 2019In this paper we consider scattering resonance computations in optics when the resonators consist of frequency dependent and lossy materials, such as metals at optical frequencies. The proposed computational approach combines a novel $hp$-FEM strategy, ... More
A global algorithm for the computation of traveling dissipative solitonsFeb 13 2019An algorithm is proposed to calculate traveling dissipative solitons for the FitzHugh-Nagumo equations. It is based on the application of the steepest descent method to a certain functional. This approach can be used to find solitons whenever the problem ... More
Numerical anisotropy study of a class of compact schemesFeb 13 2019We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous analysis applied ... More
Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equationFeb 13 2019The nonlocal Allen-Cahn (NAC) equation is a generalization of the classic Allen-Cahn equation by replacing the Laplacian with a parameterized nonlocal diffusion operator, and satisfies the maximum principle as its local counterpart. In this paper, we ... More
A method for generating coherent spatially explicit maps of seasonal palaeoclimates from site-based reconstructionsFeb 13 2019We describe a new method for reconstructing spatially explicit maps of seasonal palaeoclimate variables from site based reconstructions. Using a 3D-Variational technique, the method finds the best linear unbiased estimate of the palaeoclimate given the ... More
Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equationFeb 13 2019In this paper, we provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, which follows from consistency and stability estimates for the numerical error function. ... More
A Dual Hybrid Virtual Element Method for Plane Elasticity ProblemsFeb 13 2019A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically tested on two benchmarks ... More
A minimal stabilization procedure for Isogeometric methods on trimmed geometriesFeb 13 2019Trimming is a common operation in CAD, and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming the geometric description of the patch remains unchanged, but ... More
The Phase Field Method for Geometric Moving Interfaces and Their Numerical ApproximationsFeb 13 2019This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical methods and their ... More
A sparse spectral method on trianglesFeb 13 2019In this paper, we demonstrate that many of the computational tools for univariate orthogonal polynomials have analogues for a family of bivariate orthogonal polynomials on the triangle, including Clenshaw's algorithm and sparse differentiation operators. ... More
Multivariate Fast Iterative Filtering for the decomposition of nonstationary signalsFeb 13 2019Recently several algorithms based on Empirical Mode Decomposition (EMD) have been proposed to decompose two or higher dimensional nonstationary signals which are varying over time, like the Bivariate, Multivariate EMD and Noise-Assisted Multivariate EMD. ... More
Numerical analysis of the multi-fluid equations with applications for convection modellingFeb 13 2019Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterize convection but are still too coarse to fully resolve it. Recently, numerical solutions of multi-fluid equations ... More
Analysis of the Block Coordinate Descent Method for Non-linear Ill-Posed ProblemsFeb 13 2019Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates simultaneously. ... More
An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: Formulation, analysis, algorithm, and simulationFeb 13 2019Finite element methods (FEM) are widely used for bounded heterogeneous media models, and boundary element methods (BEM) are efficient for simulating wave propagation in unbounded homogeneous media. A natural medium for wave propagation comprises a coupled ... More
Defect removal by solvent vapor annealing in thin films of lamellar diblock copolymersFeb 13 2019Solvent vapor annealing (SVA) is known to be a simple, low-cost and highly efficient technique to produce defect-free diblock copolymer (BCP) thin films. Not only can the solvent dilute the BCP segmental interactions, but also it can vary the characteristic ... More
Jointly Low-Rank and Bisparse Recovery: Questions and Partial AnswersFeb 13 2019This preprint is not a finished product. It is presently intended to gather community feedback. We investigate the problem of recovering jointly $r$-rank and $s$-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements ... More
A positivity-preserving finite volume element method for anisotropic diffusion problems on quadrilateral meshesFeb 13 2019In this paper, we propose a nonlinear positivity-preserving finite volume element(FVE) scheme for anisotropic diffusion problems on quadrilateral meshes. Based on an overlapping dual partition, the one-sided flux is approximated by the iso-parametric ... More
Discrete Darboux polynomials and the search for preserved measures and integrals of rational mapsFeb 13 2019In this paper we propose a systematic approach for calculating the preserved measures and integrals of a rational map. The approach is based on the use of cofactors and Darboux polynomials and relies on the use of symbolic algebra tools. Given sufficient ... More
High-order mass-lumped schemes for nonlinear degenerate elliptic equationsFeb 12 2019We present and analyse a numerical framework for the approximation of nonlinear degenerate elliptic equations of the Stefan or porous medium types. This framework is based on piecewise constant approximations for the functions, which we show are essentially ... More
Monte Carlo gPC methods for diffusive kinetic flocking models with uncertaintiesFeb 12 2019In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a Monte Carlo approach ... More
Numerical Anisotropy in Finite DifferencingFeb 12 2019Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the waves propagate ... More
Combined prefactored compact schemes for first- and second-order derivatives: conceptual derivationFeb 12 2019The derivation of combined prefactored compact schemes for first and second order derivatives is described here, relying on the Fourier analysis of the original prefactored compact schemes. By this approach, the order of accuracy of the original schemes ... More
A Generalization of Prefactored Compact Schemes for Advection EquationsFeb 12 2019A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational load associated ... More
A Multilevel Monte Carlo Asymptotic-Preserving Particle Method for Kinetic Equations in the Diffusion LimitFeb 12 2019We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collisions of particles in a position-velocity phase-space. With a diffusive scaling, the kinetic ... More
About one method for constructing Hermite trigonometric polynomialsFeb 12 2019The method of constructing Hermite trigonometric polynomials, which interpolate the values of a certain periodic function and its derivatives up to (including ) the -th ( ) order in nodes of a uniform grid, is considered. The proposed method is based ... More
Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regimeFeb 12 2019Time dependent Schr\"odinger equations with conservative force field U commonly constitute a major challenge in the numerical approximation, especially when they are analysed in the semiclassical regime. Extremely high oscillations originate from the ... More
On the Robust PCA and Weiszfeld's AlgorithmFeb 12 2019Principal component analysis (PCA) is a powerful standard tool for reducing the dimensionality of data. Unfortunately, it is sensitive to outliers so that various robust PCA variants were proposed in the literature. This paper addresses the robust PCA ... More
Fixing Nonconvergence of Algebraic Iterative Reconstruction with an Unmatched BackprojectorFeb 12 2019Feb 13 2019We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact adjoint or transpose ... More
Fixing Nonconvergence of Algebraic Iterative Reconstruction with an Unmatched BackprojectorFeb 12 2019We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact adjoint or transpose ... More
A convergent linearized Lagrange finite element method for the magneto-hydrodynamic equations in 2D nonsmooth and nonconvex domainsFeb 12 2019A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical solutions that ... More
Topology Optimization under Uncertainty using a Stochastic Gradient-based ApproachFeb 11 2019Topology optimization under uncertainty (TOuU) often defines objectives and constraints by statistical moments of geometric and physical quantities of interest. Most traditional TOuU methods use gradient-based optimization algorithms and rely on accurate ... More
Multi-frequency iterative methods for the inverse medium scattering problems in elasticityFeb 11 2019This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is reduced to an ... More
Boundary integral equation methods for the elastic and thermoelastic waves in three dimensionsFeb 11 2019In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first kind. The innovative ... More
Generating boundary conditions for a Boussinesq systemFeb 11 2019We present a new method for the numerical implementation of generating boundary conditions for a one dimensional Boussinesq system. This method is based on a reformulation of the equations and a resolution of the dispersive boundary layer that is created ... More
Primal-dual gap estimators for a posteriori error analysis of nonsmooth minimization problemsFeb 11 2019The primal-dual gap is a natural upper bound for the energy error and, for uniformly convex minimization problems, also for the error in the energy norm. This feature can be used to construct reliable primal-dual gap error estimators for which the constant ... More
Equivalent Polyadic Decompositions of Matrix Multiplication TensorsFeb 11 2019Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present an algorithm to efficiently decide whether two polyadic decompositions of ... More
On the rotational invariant $L_1$-norm PCAFeb 11 2019Principal component analysis (PCA) is a powerful tool for dimensionality reduction. Unfortunately, it is sensitive to outliers, so that various robust PCA variants were proposed in the literature. Among them the so-called rotational invariant $L_1$-norm ... More
Residual minimization for isogeometric analysis in reduced and mixed formsFeb 11 2019Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, isogeometric analysis with highly-continuous basis functions for trial space ... More
The Smooth Selection Embedding Method with Chebyshev PolynomialsFeb 11 2019We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method which solves boundary value problems in complex domains by recasting them ... More
Acceleration via Symplectic Discretization of High-Resolution Differential EquationsFeb 11 2019We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization schemes: an explicit ... More
On the Scalability of the Schwarz MethodFeb 10 2019In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global domain. Such ... More
Analysis of an approximation to a fractional extension problemFeb 09 2019The purpose of this work is to study an approximation to an abstract Bessel-type problem, which is a generalization of the extension problem associated with fractional powers of the Laplace operator. Motivated by the success of such approaches in the ... More
Fully Adaptive Multilevel Stochastic Collocation Method for Randomized Elliptic PDEsFeb 09 2019In this paper, we propose and analyse a new adaptive multilevel stochastic collocation method for randomized elliptic PDEs. A hierarchical sequence of adaptive mesh refinements for the spatial approximation is combined with adaptive anisotropic sparse ... More
Quasi-optimal and pressure robust discretizations of the Stokes equations by new augmented Lagrangian formulationsFeb 08 2019We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is quasi-optimal and pressure ... More
A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial dataFeb 08 2019We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on time as well ... More
Bernstein Concentration Inequalities for Tensors via Einstein ProductsFeb 08 2019A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established between matrices ... More
A numerical model based on the curvilinear coordinate system for the MAC method simplifiedFeb 08 2019In this paper we developed a numerical methodology to study some incompressible fluid flows without free surface, using the curvilinear coordinate system and whose edge geometry is constructed via parametrized spline. First, we discussed the representation ... More
High-order energy-conserving methods Line Integral Methods for charged particle dynamicsFeb 08 2019In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line Integral Methods (LIMs), previously used for defining Hamiltonian Boundary ... More
High-order energy-conserving Line Integral Methods for charged particle dynamicsFeb 08 2019Feb 11 2019In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line Integral Methods (LIMs), previously used for defining Hamiltonian Boundary ... More
Implementation and Evaluation of Breaking Detection Criteria for a Hybrid Boussinesq ModelFeb 08 2019The aim of the present work is to develop a model able to represent the propagation and transformation of waves in nearshore areas. The focus is on the phenomena of wave breaking, shoaling and run-up. These different phenomena are represented through ... More
Adaptive Step Size Control for Polynomial Homotopy Continuation MethodsFeb 08 2019In this paper we develop an adaptive step size control for the numerical tracking of implicitly defined paths in the context of polynomial homotopy continuation methods. We focus on the case where the paths are tracked using a predictor-corrector scheme ... More
Lattices from tight frames and vertex transitive graphsFeb 07 2019We show that real tight frames that generate lattices must be rational. In the case of irreducible group frames, we show that the corresponding lattice is always strongly eutactic. We use this observation to describe a construction of strongly eutactic ... More
Error localization of best L1 polynomial approximantsFeb 07 2019An important observation in compressed sensing is that the $\ell_0$ minimizer of an underdetermined linear system is equal to the $\ell_1$ minimizer when there exists a sparse solution vector. Here, we develop a continuous analogue of this observation ... More
Coupling Staggered-Grid and MPFA Finite Volume Methods for Free Flow/Porous-Medium Flow ProblemsFeb 07 2019A discretization is proposed for models coupling free flow with anisotropic porous medium flow. Our approach employs a staggered grid finite volume method for the Navier-Stokes equations in the free flow subdomain and a MPFA finite volume method to solve ... More
An Immersed Boundary Hierarchical B-spline method for flexoelectricityFeb 07 2019This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order nature of ... More
Support and Approximation Properties of Hermite SplinesFeb 07 2019In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstrate that Hermite splines are maximally localized in the sense that their ... More
Support and Approximation Properties of Hermite SplinesFeb 07 2019Feb 08 2019In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstrate that Hermite splines are maximally localized in the sense that their ... More
Dual-Reference Design for Holographic Coherent Diffraction ImagingFeb 07 2019A new reference design is introduced for Holographic Coherent Diffraction Imaging. This consists of two reference portions - being "block" and "pinhole" shaped regions - adjacent to the imaging specimen. Expected error analysis on data following a Poisson ... More
A sharp interface method for an immersed viscoelastic solidFeb 06 2019The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous stress at the ... More
On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped networkFeb 06 2019In this paper we validate the implementation of the numerical scheme proposed in [3]. The validation is made by comparison with an explicit solution here obtained, and the solutions of Riemann problems for several networks. We then perform some simulations ... More
A low-order nonconforming method for linear elasticity on general meshesFeb 06 2019In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method, that requires ... More
A modification of the Jacobi-Davidson methodFeb 06 2019Each iteration in Jacobi-Davidson method for solving large sparse eigenvalue problems involves two phases, called subspace expansion and eigen pair extraction. The subspace expansion phase involves solving a correction equation. We propose a modification ... More
On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matricesFeb 06 2019The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show that such a ... More
A Physics-Based Estimation of Mean Curvature Normal Vector for Triangulated SurfacesFeb 06 2019In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based ... More
Boundary integral equations for isotropic linear elasticityFeb 06 2019This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam\'e coefficients in the form of a bounded domain of arbitrary shape surrounded by a background ... More
GMRES with Singular Vector ApproximationsFeb 06 2019This paper has proposed the GMRES that augments Krylov subspaces with a set of approximate right singular vectors. The proposed method suppresses the error norms of a linear system of equations. Numerical experiments comparing the proposed method with ... More