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An inertial extragradient algorithm for equilibrium and generalized split null point problems Adv. Comput. Math. (IF 1.929) Pub Date : 2022-08-01 Yasir Arfat, Poom Kumam, Muhammad Aqeel Ahmad Khan, Parinya Sa Ngiamsunthorn
This paper provides iterative construction of a common solution associated with a class of equilibrium problems and split convex feasibility problems. In particular, we are interested in the equilibrium problems defined with respect to the pseudomonotone and Lipschitz-type continuous equilibrium problem together with the generalized split null point problems in real Hilbert spaces. We propose an iterative
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Weak approximation of SDEs for tempered distributions and applications Adv. Comput. Math. (IF 1.929) Pub Date : 2022-08-01 Yuga Iguchi, Toshihiro Yamada
The paper shows a new weak approximation for generalized expectation of composition of a Schwartz tempered distribution and a solution to stochastic differential equation. Any order discretization is provided by using stochastic weights which do not depend on the Schwartz distribution. The error bound is obtained through stochastic analysis, which is consistent with the results of numerical experiments
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Nonsmooth data optimal error estimates by energy arguments for subdiffusion equations with memory Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-29 Shantiram Mahata, Rajen Kumar Sinha
This paper considers the semidiscrete Galerkin finite element approximation for time fractional diffusion equations with memory in a bounded convex polygonal domain. We use novel energy arguments in conjunction with repeated applications of time integral operators to study the error analysis. Our error estimates cover both smooth and nonsmooth initial data cases. Since the continuous solution u of
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Finding geodesics joining given points Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-27 Lyle Noakes, Erchuan Zhang
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Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-22 Tingting Hao, Manman Ma, Xuejun Xu
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a key contribution, the steady-state Poisson-Nernst-Planck equations are studied systematically and rigorous analysis for a residual-based a posteriori error estimate
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An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-15 Zhoufeng Wang
In this paper, we develop a adaptive finite volume method with the truncation of the nonlocal boundary operators for the wave scattering by periodic structures. The related truncation parameters are chosen through sharp a posteriori error estimate of the finite volume method. The crucial part of the a posteriori error analysis is to develop a duality argument technique and use a L2-orthogonality property
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Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-12 Ying Liu, Zhen Guan, Yufeng Nie
In this paper, we consider the unconditionally optimal error estimates of the linearized backward Euler scheme with the weak Galerkin finite element method for semilinear parabolic equations. With the error splitting technique and elliptic projection, the optimal error estimates in L2-norm and the discrete H1-norm are derived without any restriction on the time stepsize. Numerical results on both polygonal
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Numerical algorithms for water waves with background flow over obstacles and topography Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-09 David M. Ambrose, Roberto Camassa, Jeremy L. Marzuola, Richard M. McLaughlin, Quentin Robinson, Jon Wilkening
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength
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Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-02 Carlos J. S. Alves, Nuno F. M. Martins, Ana L. Silvestre
This paper deals with the numerical approximation of solutions of Stokes and Brinkman systems using meshless methods. The aim is to solve a problem containing a nonzero body force, starting from the well known decomposition in terms of a particular solution and the solution of a homogeneous force problem. We propose two methods for the numerical construction of a particular solution. One method is
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Design and analysis of the Extended Hybrid High-Order method for the Poisson problem Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-02 Liam Yemm
We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is formulated by enriching the local polynomial spaces with appropriate singular functions. Via a detailed error analysis, the method is shown to converge optimally
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Numerical analysis of a stabilized scheme applied to incompressible elasticity problems with Dirichlet and with mixed boundary conditions Adv. Comput. Math. (IF 1.929) Pub Date : 2022-07-01 Tomás P. Barrios, Edwin M. Behrens, Rommel Bustinza
We analyze a new stabilized dual-mixed method applied to incompressible linear elasticity problems, considering two kinds of data on the boundary of the domain: non homogeneous Dirichlet and mixed boundary conditions. In this approach, we circumvent the standard use of the rotation to impose weakly the symmetry of stress tensor. We prove that the new variational formulation and the corresponding Galerkin
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An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane Adv. Comput. Math. (IF 1.929) Pub Date : 2022-06-29 Abinand Gopal, Per-Gunnar Martinsson
An efficient direct solver for solving the Lippmann–Schwinger integral equation modeling acoustic scattering in the plane is presented. For a problem with N degrees of freedom, the solver constructs an approximate inverse in \(\mathcal {O}(N^{3/2})\) operations and then, given an incident field, can compute the scattered field in \(\mathcal {O}(N \log N)\) operations. The solver is based on a previously
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Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime Adv. Comput. Math. (IF 1.929) Pub Date : 2022-06-21 Teng Zhang, Tingchun Wang
We present rigorous analysis on the error bound and conservation laws of a fourth-order compact finite difference scheme for Zakharov system (ZS) with a dimensionless parameter ε ∈ (0,1], which is inversely proportional to the acoustic speed. In the subsonic limit regime, i.e., 0 < ε ≪ 1, the solutions have highly oscillatory waves and outgoing initial layers due to the perturbation from wave operator
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High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation Adv. Comput. Math. (IF 1.929) Pub Date : 2022-06-21 Xin Li, Luming Zhang
In this paper, we design two classes of high-accuracy conservative numerical algorithms for the nonlinear Klein-Gordon-Schrödinger system in two dimensions. By introducing the energy quadratization technique, we first transform the original system into an equivalent one, where the energy is modified as a quadratic form. The Gauss-type Runge-Kutta method and the Fourier pseudo-spectral method are then
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Linear approximation method for solving split inverse problems and its applications Adv. Comput. Math. (IF 1.929) Pub Date : 2022-06-19 Guash Haile Taddele, Yuan Li, Aviv Gibali, Poom Kumam, Jing Zhao
We study the problem of finding a common element that solves the multiple-sets feasibility and equilibrium problems in real Hilbert spaces. We consider a general setting in which the involved sets are represented as level sets of given convex functions, and propose a constructible linear approximation scheme that involves the subgradient of the associated convex functions. Strong convergence of the
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Accurate computations with matrices related to bases {tieλt} Adv. Comput. Math. (IF 1.929) Pub Date : 2022-06-15 E. Mainar, J. M. Peña, B. Rubio
The total positivity of collocation, Wronskian and Gram matrices corresponding to bases of the form (eλt,teλt,…,tneλt) is analyzed. A bidiagonal decomposition providing the accurate numerical resolution of algebraic linear problems with these matrices is derived. The numerical experimentation confirms the accuracy of the proposed methods.
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Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency? Adv. Comput. Math. (IF 1.929) Pub Date : 2022-06-04 P. Marchand, J. Galkowski, E. A. Spence, A. Spence
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Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-27 Bo Zheng, Jin Qin, Yueqiang Shang
Based on finite element discretization and a fully overlapping domain decomposition, we propose and study some parallel iterative subgrid stabilized algorithms for the simulation of the steady Navier-Stokes equations with high Reynolds numbers, where the quadratic equal-order elements are used for the velocity and pressure approximations, and the subgrid-scale model based on an elliptic projection
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Numerical investigation into the dependence of the Allen–Cahn equation on the free energy Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-27 Yunho Kim, Dongsun Lee
Phase-field modeling is strongly influenced by the shape of a free energy functional. In the theory of thermodynamics, it is a logarithmic type potential that is legitimate for modeling and simulating binary systems. Nevertheless, a tremendous amount of works have been dedicated to phase-field equations driven by 4-th double-well potentials as a polynomial approximation to the logarithmic type, which
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Fast gradient methods for uniformly convex and weakly smooth problems Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-24 Jongho Park
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A multilevel Newton’s method for the Steklov eigenvalue problem Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-13 Meiling Yue, Fei Xu, Manting Xie
This paper proposes a new type of multilevel method for solving the Steklov eigenvalue problem based on Newton’s method. In this iteration method, solving the Steklov eigenvalue problem is replaced by solving a small-scale eigenvalue problem on the coarsest mesh and a sequence of augmented linear problems on refined meshes, derived by Newton step. We prove that this iteration scheme obtains the optimal
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H2Opus: a distributed-memory multi-GPU software package for non-local operators Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-10 Stefano Zampini, Wajih Boukaram, George Turkiyyah, Omar Knio, David Keyes
Hierarchical \({\mathscr{H}}^{2}\)-matrices are asymptotically optimal representations for the discretizations of non-local operators such as those arising in integral equations or from kernel functions. Their O(N) complexity in both memory and operator application makes them particularly suited for large-scale problems. As a result, there is a need for software that provides support for distributed
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A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-10 Yang Li, Minfu Feng, Yan Luo
For the Oseen problem, we present a new stabilized virtual element method on polygonal meshes that allows us to employ “equal-order” virtual element pairs to approximate both velocity and pressure. By introducing the local projection type stabilization terms to the virtual element method, the method can not only circumvent the discrete Babuška-Brezzi condition, but also maintain the favorable stability
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One-step optimization method for equilibrium problems Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-10 Dang Van Hieu, Le Dung Muu, Pham Kim Quy
The paper introduces an one-step optimization method for solving a monotone equilibrium problem including a Lipschitz-type condition in a Hilbert space. The method uses variable stepsizes and is constructed by the proximal-like mapping associated with the cost bifunction and incorporated with regularization terms. Comparing with the extragradient-like methods, our new method has an elegant and simple
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Inexact GMRES iterations and relaxation strategies with fast-multipole boundary element method Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-10 Tingyu Wang, Simon K. Layton, Lorena A. Barba
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Optimal control for a coupled spin-polarized current and magnetization system Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-06 Xin An, Ananta K. Majee, Andreas Prohl, Thanh Tran
This paper is devoted to an optimal control problem of a coupled spin drift-diffusion Landau–Lifshitz–Gilbert system describing the interplay of magnetization and spin accumulation in magnetic-nonmagnetic multilayer structures, where the control is given by the electric current density. A variational approach is used to prove the existence of an optimal control. The first-order necessary optimality
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A new linearized fourth-order conservative compact difference scheme for the SRLW equations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-03 Yuyu He, Xiaofeng Wang, Ruihua Zhong
In this paper, a novel three-point fourth-order compact operator is considered to construct new linearized conservative compact finite difference scheme for the symmetric regularized long wave (SRLW) equations based on the reduction order method with three-level linearized technique. The discrete conservative laws, boundedness and unique solvability are studied. The convergence order \(\mathcal {O}(\tau
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Numerical analysis of a chemotaxis model for tumor invasion Adv. Comput. Math. (IF 1.929) Pub Date : 2022-05-03 Jhean E. Pérez-López, Diego A. Rueda-Gómez, Élder J. Villamizar-Roa
This paper is devoted to the study of a time-discrete scheme and its corresponding fully discretization approximating a d-dimensional chemotaxis model describing tumor invasion, d ≤ 3. This model describes the chemotactic attraction experienced by the tumor cells and induced by a so-called active extracellular matrix, which is a chemical signal produced by a biological reaction between the extracellular
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Randomized continuous frames in time-frequency analysis Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-27 Ron Levie, Haim Avron
Recently, a Monte Carlo approach was proposed for processing highly redundant continuous frames. In this paper, we present and analyze applications of this new theory. The computational complexity of the Monte Carlo method relies on the continuous frame being so-called linear volume discretizable (LVD). The LVD property means that the number of samples in the coefficient space required by the Monte
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Development and analysis of two new finite element schemes for a time-domain carpet cloak model Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-21 Jichun Li, Chi-Wang Shu, Wei Yang
In this paper, we are concerned about a time-domain carpet cloak model, which was originally derived in our previous work Li et al. (SIAM J. Appl. Math., 74(4), pp. 1136–1151, 2014). Some finite element schemes have been developed for this model and used to simulate the cloaking phenomenon in Li et al. (SIAM J. Appl. Math., 74(4), pp. 1136–1151, 2014) and Li et al. (Methods Appl. Math., 19(2), pp.
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Stokes equations under Tresca friction boundary condition: a truncated approach Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-21 Jules K. Djoko, Jonas Koko, Sognia Konlack
A priori error analysis of the finite element approximation of Stokes equations under slip boundary condition of friction type has been centered on the interpolation error on the slip zone. In this work, we propose a novel approach based on the approximation of the tangential component of traction force by a truncated (cutoff) function. More precisely, we carry out (i) a complete analysis of the truncated
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Stabilization of spline bases by extension Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-21 Ba-Duong Chu, Florian Martin, Ulrich Reif
We present a method to stabilize bases with local supports by means of extension. It generalizes the known approach for tensor product B-splines to a much broader class of functions, which includes hierarchical and weighted variants of polynomial, trigonometric, and exponential splines, but also box splines, T-splines, and other function spaces of interest with a local basis. Extension removes elements
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A fast solver for elastic scattering from axisymmetric objects by boundary integral equations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-18 J. Lai, H. Dong
Fast and high-order accurate algorithms for three-dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a novel boundary integral formulation for the three-dimensional elastic scattering based on the Helmholtz decomposition of elastic fields, which converts the Navier
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Implicit finite volume method with a posteriori limiting for transport networks Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-18 Matthias Eimer, Raul Borsche, Norbert Siedow
Simulating the flow of water in district heating networks requires numerical methods which are independent of the CFL condition. We develop a high order scheme for networks of advection equations allowing large time steps. With the MOOD technique, unphysical oscillations of nonsmooth solutions are avoided. In numerical tests, the applicability to real networks is shown.
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Tensor rank bounds for point singularities in ℝ3 Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-14 C. Marcati, M. Rakhuba, Ch. Schwab
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The essence of invertible frame multipliers in scalability Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-14 Hossein Javanshiri, Mohammad Abolghasemi, Ali Akbar Arefijamaal
The purpose of this paper is twofold. The first is to give some new structural results for the invertibility of Bessel multipliers. Secondly, as applications of these results, we provide some conditions regarding the scaling sequence c = {cn}n which can be used in the role of the scalability of a given frame, a notion which has found more and more applications in the last decade. More precisely, we
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A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-06 Jun Liu,Xiang-Sheng Wang,Shu-Lin Wu,Tao Zhou
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A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-06 Rob Stevenson,Raymond van Venetië,Jan Westerdiep
AbstractIn this work, an r-linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the space-time cylinder, the family of trial spaces that we consider are given as the spans of wavelets-in-time and (locally refined) finite element spaces-in-space. Numerical results illustrate our
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Linear/Ridge expansions: enhancing linear approximations by ridge functions Adv. Comput. Math. (IF 1.929) Pub Date : 2022-04-04 Constantin Greif, Philipp Junk, Karsten Urban
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions—a Linear/Ridge expansion. For an explicitly or implicitly given objective function, we reformulate finding a best Linear/Ridge expansion in terms of an optimization problem. We introduce a particle grid algorithm for its solution. Several numerical results underline the flexibility, robustness
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On basis constructions in finite element exterior calculus Adv. Comput. Math. (IF 1.929) Pub Date : 2022-03-23 Martin W. Licht
We give a systematic self-contained exposition of how to construct geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the families of finite element spaces, which is of interest for implementations. Moreover, we give details for the construction of isomorphisms and duality pairings between
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A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction Adv. Comput. Math. (IF 1.929) Pub Date : 2022-03-16 Xijun Ma, Chungen Shen, Li Wang, Lei-Hong Zhang, Ren-Cang Li
As an extension of the traditional principal component analysis, the multi-view canonical correlation analysis (MCCA) aims at reducing m high dimensional random variables \(\boldsymbol {s}_{i}\in \mathbb {R}^{n_{i}}~(i=1,2,\ldots ,m)\) by proper projection matrices \(X_{i}\in \mathbb {R}^{n_{i}\times \ell }\) so that the m reduced ones \(\boldsymbol {y}_{i}=X_{i}^{\mathrm {T}}\boldsymbol {s}_{i}\in
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An adaptive kernel-split quadrature method for parameter-dependent layer potentials Adv. Comput. Math. (IF 1.929) Pub Date : 2022-03-09 Fredrik Fryklund, Ludvig af Klinteberg, Anna-Karin Tornberg
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer potentials belonging to the modified Helmholtz, modified biharmonic, and modified Stokes equations. These equations depend on a parameter, denoted α, and kernel-split quadrature
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Convergence analysis of oversampled collocation boundary element methods in 2D Adv. Comput. Math. (IF 1.929) Pub Date : 2022-02-28 Georg Maierhofer, Daan Huybrechs
Collocation boundary element methods for integral equations are easier to implement than Galerkin methods because the elements of the discretisation matrix are given by lower-dimensional integrals. For that same reason, the matrix assembly also requires fewer computations. However, collocation methods typically yield slower convergence rates and less robustness, compared to Galerkin methods. We explore
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Wavelet adaptive proper orthogonal decomposition for large-scale flow data Adv. Comput. Math. (IF 1.929) Pub Date : 2022-02-17 Philipp Krah, Thomas Engels, Kai Schneider, Julius Reiss
The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by three-dimensional direct numerical simulations, is limited owing to its computational complexity. Here, we propose a wavelet-based adaptive version of the POD (the
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Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber Adv. Comput. Math. (IF 1.929) Pub Date : 2022-02-15 Laura Bagur, Stéphanie Chaillat, Patrick Ciarlet
It is well known in the literature that standard hierarchical matrix (\({\mathscr{H}}\)-matrix)-based methods, although very efficient for asymptotically smooth kernels, are not optimal for oscillatory kernels. In a previous paper, we have shown that the method should nevertheless be used in the mechanical engineering community due to its still important data compression rate and its straightforward
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Complex-scaled infinite elements for resonance problems in heterogeneous open systems Adv. Comput. Math. (IF 1.929) Pub Date : 2022-02-09 Lothar Nannen, Markus Wess
The technique of complex scaling for time harmonic wave-type equations relies on a complex coordinate stretching to generate exponentially decaying solutions. In this work, we use a Galerkin method with ansatz functions with infinite support to discretize complex-scaled scalar Helmholtz-type resonance problems with inhomogeneous exterior domains. We show super-algebraic convergence of the method with
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A structure-preserving algorithm for surface water flows with transport processes Adv. Comput. Math. (IF 1.929) Pub Date : 2022-01-22 Karjoun, Hasan, Beljadid, Abdelaziz, LeFloch, Philippe G.
We consider a system of coupled equations modeling a shallow water flow with solute transport and introduce an artificial dissipation in order to improve the dissipation properties of the original cell-vertex central-upwind numerical scheme applied to these equations. Namely, a formulation is proposed which involves an artificial dissipation parameter and guarantees a consistency property between the
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Persistence Curves: A canonical framework for summarizing persistence diagrams Adv. Comput. Math. (IF 1.929) Pub Date : 2022-01-18 Chung, Yu-Min, Lawson, Austin
Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to be challenging as the space lacks an inner product. For that reason, transforming these diagrams in a way that is compatible with machine learning is an important
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A generalisation of de la Vallée-Poussin procedure to multivariate approximations Adv. Comput. Math. (IF 1.929) Pub Date : 2022-01-07 Sukhorukova, Nadezda, Ugon, Julien
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs). There are a number of approximation methods for polynomial and polynomial spline approximation. Some of them are based on the classical de la Vallée-Poussin procedure
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Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes Adv. Comput. Math. (IF 1.929) Pub Date : 2022-01-04 Gemignani, Luca, Romani, Lucia, Viscardi, Alberto
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of certain associated polynomial equations. The proposed approach also makes it possible to identify conditions for the existence of the sought schemes.
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The role of mesh quality and mesh quality indicators in the virtual element method Adv. Comput. Math. (IF 1.929) Pub Date : 2021-12-27 Sorgente, T., Biasotti, S., Manzini, G., Spagnuolo, M.
Since its introduction, the virtual element method (VEM) was shown to be able to deal with a large variety of polygons, while achieving good convergence rates. The regularity assumptions proposed in the VEM literature to guarantee the convergence on a theoretical basis are therefore quite general. They have been deduced in analogy to the similar conditions developed in the finite element method (FEM)
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Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization Adv. Comput. Math. (IF 1.929) Pub Date : 2021-12-23 Borges, Carlos, Rachh, Manas
In this paper, we consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at a collection of receivers outside the object. The data is assumed to be generated by plane waves impinging on the unknown obstacle from multiple directions and at multiple frequencies. This inverse problem can be reformulated as an optimization problem: that
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Computing the reciprocal of a ϕ-function by rational approximation Adv. Comput. Math. (IF 1.929) Pub Date : 2021-12-22 Boito, Paola, Eidelman, Yuli, Gemignani, Luca
In this paper, we introduce a family of rational approximations of the reciprocal of a ϕ-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The derivation and properties of this family of approximations applied to scalar and matrix arguments are presented. Moreover, we show that the matrix functions computed
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A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes Adv. Comput. Math. (IF 1.929) Pub Date : 2021-12-10 Guillén-González, F., Rodríguez-Bellido, M. A., Rueda-Gómez, D. A.
We consider the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical concentration, satisfying $$ \left\{ \begin{array}{l} \partial_t u - {\Delta} u - \nabla\cdot (u\nabla v)=0 \ \ \text{ in}\ {\Omega},\ t>0,\\ \partial_t v - {\Delta} v + v = u^p \ \ { in}\ {\Omega},\ t>0, \end{array} \right. $$(1) with p ∈ (1, 2), \({\Omega }\subseteq \mathbb {R}^{d}\)
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Riemannian optimization for phase retrieval from masked Fourier measurements Adv. Comput. Math. (IF 1.929) Pub Date : 2021-12-10 Li, Huiping, Li, Song
In this paper, we consider the noisy phase retrieval problem under the measurements of Fourier transforms with complex random masks. Here two kinds of Riemannian optimization algorithms, namely, Riemannian gradient descent algorithm (RGrad) and Riemannian conjugate gradient descent algorithm (RCG), are presented to solve such problem from these special but widely used measurements in practical applications
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A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size Adv. Comput. Math. (IF 1.929) Pub Date : 2021-12-07 Gross, Craig, Iwen, Mark A., Kämmerer, Lutz, Volkmer, Toni
In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The algorithm works by converting a potentially large reconstructing single rank-1 lattice for some d-dimensional frequency set I ⊂{0,…,N − 1}d into a collection of much smaller rank-1 lattices which allow for accurate and efficient
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The hot spots conjecture can be false: some numerical examples Adv. Comput. Math. (IF 1.929) Pub Date : 2021-12-04 Kleefeld, Andreas
The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization
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High-resolution signal recovery via generalized sampling and functional principal component analysis Adv. Comput. Math. (IF 1.929) Pub Date : 2021-11-23 Gataric, Milana
In this paper, we introduce a computational framework for recovering a high-resolution approximation of an unknown function from its low-resolution indirect measurements as well as high-resolution training observations by merging the frameworks of generalized sampling and functional principal component analysis. In particular, we increase the signal resolution via a data-driven approach, which models
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A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes Adv. Comput. Math. (IF 1.929) Pub Date : 2021-11-15 Wang, Gang, Wang, Feng, He, Yinnian
In this paper, we present a divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes. The velocity and the pressure are discretized by the H(div) virtual element and discontinuous piecewise polynomials, respectively. An additional polynomial space that lives on the element edges is introduced to approximate the tangential trace of the velocity. The velocity at
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A family of C1 quadrilateral finite elements Adv. Comput. Math. (IF 1.929) Pub Date : 2021-11-03 Kapl, Mario, Sangalli, Giancarlo, Takacs, Thomas
We present a novel family of C1 quadrilateral finite elements, which define global C1 spaces over a general quadrilateral mesh with vertices of arbitrary valency. The elements extend the construction by Brenner and Sung (J. Sci. Comput. 22(1-3), 83-118, 2005), which is based on polynomial elements of tensor-product degree p ≥ 6, to all degrees p ≥ 3. The proposed C1 quadrilateral is based upon the