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A block-randomized stochastic method with importance sampling for CP tensor decomposition Adv. Comput. Math. (IF 1.7) Pub Date : 2024-03-25 Yajie Yu, Hanyu Li
One popular way to compute the CANDECOMP/PARAFAC (CP) decomposition of a tensor is to transform the problem into a sequence of overdetermined least squares subproblems with Khatri-Rao product (KRP) structure involving factor matrices. In this work, based on choosing the factor matrix randomly, we propose a mini-batch stochastic gradient descent method with importance sampling for those special least
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Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-03-22 Xiao Ye, Xiangcheng Zheng, Jun Liu, Yue Liu
Optimal quadratic spline collocation (QSC) method has been widely used in various problems due to its high-order accuracy, while the corresponding numerical analysis is rarely investigated since, e.g., the perturbation terms result in the asymmetry of optimal QSC discretization. We present numerical analysis for the optimal QSC method in two space dimensions via discretizing a nonlinear time-fractional
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A probabilistic reduced basis method for parameter-dependent problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-03-13 Marie Billaud-Friess, Arthur Macherey, Anthony Nouy, Clémentine Prieur
Probabilistic variants of model order reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we propose a probabilistic reduced basis method (RBM) for the approximation of a family of parameter-dependent functions. It relies on a probabilistic greedy algorithm with an error indicator that can be written as an expectation
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Structured interpolation for multivariate transfer functions of quadratic-bilinear systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-03-12 Peter Benner, Serkan Gugercin, Steffen W. R. Werner
High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting large-scale nonlinear systems. The high dimensionality of the dynamics causes computational bottlenecks, especially when these large-scale systems need to be simulated
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New low-order mixed finite element methods for linear elasticity Adv. Comput. Math. (IF 1.7) Pub Date : 2024-03-06 Xuehai Huang, Chao Zhang, Yaqian Zhou, Yangxing Zhu
New low-order \({H}({{\text {div}}})\)-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the \({(d+1)}\)-order normal-normal face bubble space. The reduced counterpart has only \({d(d+1)}^{{2}}\) degrees of freedom. Basis functions are explicitly given in terms of
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Conditioning and spectral properties of isogeometric collocation matrices for acoustic wave problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-03-04 Elena Zampieri, Luca F. Pavarino
The conditioning and spectral properties of the mass and stiffness matrices for acoustic wave problems are here investigated when isogeometric analysis (IGA) collocation methods in space and Newmark methods in time are employed. Theoretical estimates and extensive numerical results are reported for the eigenvalues and condition numbers of the acoustic mass and stiffness matrices in the reference square
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Discrete Helmholtz Decompositions of Piecewise Constant and Piecewise Affine Vector and Tensor Fields Found. Comput. Math. (IF 3.0) Pub Date : 2024-03-01
Abstract Discrete Helmholtz decompositions dissect piecewise polynomial vector fields on simplicial meshes into piecewise gradients and rotations of finite element functions. This paper concisely reviews established results from the literature which all restrict to the lowest-order case of piecewise constants. Its main contribution consists of the generalization of these decompositions to 3D and of
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A space–time DG method for the Schrödinger equation with variable potential Adv. Comput. Math. (IF 1.7) Pub Date : 2024-03-01 Sergio Gómez, Andrea Moiola
We present a space–time ultra-weak discontinuous Galerkin discretization of the linear Schrödinger equation with variable potential. The proposed method is well-posed and quasi-optimal in mesh-dependent norms for very general discrete spaces. Optimal h-convergence error estimates are derived for the method when test and trial spaces are chosen either as piecewise polynomials or as a novel quasi-Trefftz
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Polynomial Factorization Over Henselian Fields Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-21 Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart, Adrien Poteaux, Joaquim Roé, Martin Weimann
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Discrete Pseudo-differential Operators and Applications to Numerical Schemes Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-15 Erwan Faou, Benoît Grébert
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On the Existence of Monge Maps for the Gromov–Wasserstein Problem Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-15 Théo Dumont, Théo Lacombe, François-Xavier Vialard
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Stable Spectral Methods for Time-Dependent Problems and the Preservation of Structure Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-15 Arieh Iserles
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Strong Norm Error Bounds for Quasilinear Wave Equations Under Weak CFL-Type Conditions Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-13 Benjamin Dörich
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Limitations of neural network training due to numerical instability of backpropagation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-02-11 Clemens Karner, Vladimir Kazeev, Philipp Christian Petersen
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Low-Dimensional Invariant Embeddings for Universal Geometric Learning Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-08 Nadav Dym, Steven J. Gortler
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Analysis of a Modified Regularity-Preserving Euler Scheme for Parabolic Semilinear SPDEs: Total Variation Error Bounds for the Numerical Approximation of the Invariant Distribution Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-08 Charles-Edouard Bréhier
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Phaseless Sampling on Square-Root Lattices Found. Comput. Math. (IF 3.0) Pub Date : 2024-02-08 Philipp Grohs, Lukas Liehr
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Book Reviews SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Anita T. Layton
SIAM Review, Volume 66, Issue 1, Page 193-201, February 2024. If you are keen to understand the world around us by developing mathematical or data-driven models, or if you are interested in the methodologies that can be used to analyze those models, this collection of reviews may help you identify a useful book or two. Our featured review was written by Tim Hoheisel, on the book Convex Optimization:
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NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George E. Karniadakis
SIAM Review, Volume 66, Issue 1, Page 161-190, February 2024. Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision and natural language processing, and by the need for reliable tools in risk-sensitive applications. Recently, various machine learning
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Resonantly Forced ODEs and Repeated Roots SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Allan R. Willms
SIAM Review, Volume 66, Issue 1, Page 149-160, February 2024. In a recent article in this journal, Gouveia and Stone [``Generating Resonant and Repeated Root Solutions to Ordinary Differential Equations Using Perturbation Methods,” SIAM Rev., 64 (2022), pp. 485--499] described a method for finding exact solutions to resonantly forced linear ordinary differential equations, and for finding the general
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Education SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Helene Frankowska
SIAM Review, Volume 66, Issue 1, Page 147-147, February 2024. In this issue the Education section presents two contributions. The first paper, “Resonantly Forced ODEs and Repeated Roots,” is written by Allan R. Willms. The resonant forcing problem is as follows: find $y(\cdot)$ such that $L[y(x)]=u(x)$, where $L[u(x)]=0$ and $L=a_0(x) + \sum_{j=1}^n a_j(x) \frac{d^j}{dx^j}$. The repeated roots problem
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A Simple Formula for the Generalized Spectrum of Second Order Self-Adjoint Differential Operators SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Bjørn Fredrik Nielsen, Zdeněk Strakoš
SIAM Review, Volume 66, Issue 1, Page 125-146, February 2024. We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$ subject to homogeneous Dirichlet or Neumann boundary conditions, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral decomposition $K=Q \Lambda Q^T$, where $Q=Q(x
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SIGEST SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 The Editors
SIAM Review, Volume 66, Issue 1, Page 123-123, February 2024. The SIGEST article in this issue is “A Simple Formula for the Generalized Spectrum of Second Order Self-Adjoint Differential Operators,” by Bjørn Fredrik Nielsen and Zdeněk Strakoš. This paper studies the eigenvalues of second-order self-adjoint differential operators in the continuum and discrete settings. In particular, they investigate
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Easy Uncertainty Quantification (EasyUQ): Generating Predictive Distributions from Single-Valued Model Output SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Eva-Maria Walz, Alexander Henzi, Johanna Ziegel, Tilmann Gneiting
SIAM Review, Volume 66, Issue 1, Page 91-122, February 2024. How can we quantify uncertainty if our favorite computational tool---be it a numerical, statistical, or machine learning approach, or just any computer model---provides single-valued output only? In this article, we introduce the Easy Uncertainty Quantification (EasyUQ) technique, which transforms real-valued model output into calibrated
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Research Spotlights SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Stefan M. Wild
SIAM Review, Volume 66, Issue 1, Page 89-89, February 2024. As modeling, simulation, and data-driven capabilities continue to advance and be adopted for an ever expanding set of applications and downstream tasks, there has been an increased need for quantifying the uncertainty in the resulting predictions. In “Easy Uncertainty Quantification (EasyUQ): Generating Predictive Distributions from Single-Valued
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Finite Element Methods Respecting the Discrete Maximum Principle for Convection-Diffusion Equations SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Gabriel R. Barrenechea, Volker John, Petr Knobloch
SIAM Review, Volume 66, Issue 1, Page 3-88, February 2024. Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solutions of these equations satisfy, under certain conditions, maximum principles, which represent physical bounds of the solution. That the same bounds are respected by numerical approximations of the solution is often of
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Survey and Review SIAM Rev. (IF 10.2) Pub Date : 2024-02-08 Marlis Hochbruck
SIAM Review, Volume 66, Issue 1, Page 1-1, February 2024. Numerical methods for partial differential equations can only be successful if their numerical solutions reflect fundamental properties of the physical solution of the respective PDE. For convection-diffusion equations, the conservation of some specific scalar quantities is crucial. When physical solutions satisfy maximum principles representing
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Analysis of a $$\varvec{P}_1\oplus \varvec{RT}_0$$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions Adv. Comput. Math. (IF 1.7) Pub Date : 2024-02-05 Hongpeng Li, Xu Li, Hongxing Rui
In this paper, we investigate a low-order robust numerical method for the linear elasticity problem. The method is based on a Bernardi–Raugel-like \(\varvec{H}(\textrm{div})\)-conforming method proposed first for the Stokes flows in [Li and Rui, IMA J. Numer. Anal. 42 (2022) 3711–3734]. Therein, the lowest-order \(\varvec{H}(\textrm{div})\)-conforming Raviart–Thomas space (\(\varvec{RT}_0\)) was added
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Semi-Lagrangian finite element exterior calculus for incompressible flows Adv. Comput. Math. (IF 1.7) Pub Date : 2024-02-05 Wouter Tonnon, Ralf Hiptmair
We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions on arbitrary simplicial meshes. We recast the equations as a nonlinear transport problem for a momentum 1-form and discretize in space using methods from finite element exterior calculus. Numerical experiments show that the linearly implicit fully discrete version of
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Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-02-05 Robin Herkert, Patrick Buchfink, Bernard Haasdonk
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally, Hamiltonian structure of dynamical systems may be available and should be preserved during the reduction. In the current presentation, we address these two aspects by
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On the balanced truncation error bound and sign parameters from arrowhead realizations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-01-31 Sean Reiter, Tobias Damm, Mark Embree, Serkan Gugercin
Balanced truncation and singular perturbation approximation for linear dynamical systems yield reduced order models that satisfy a well-known error bound involving the Hankel singular values. We show that this bound holds with equality for single-input, single-output systems, if the sign parameters corresponding to the truncated Hankel singular values are all equal. These signs are determined by a
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Dual frames compensating for erasures—a non-canonical case Adv. Comput. Math. (IF 1.7) Pub Date : 2024-01-25 Ljiljana Arambašić, Diana Stoeva
In this paper, we study the problem of recovering a signal from frame coefficients with erasures. Suppose that erased coefficients are indexed by a finite set E. Starting from a frame \((x_n)_{n=1}^\infty \) and its arbitrary dual frame, we give sufficient conditions for constructing a dual frame of \((x_n)_{n\in E^c}\) so that the perfect reconstruction can be obtained from the preserved frame coefficients
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Exotic B-Series and S-Series: Algebraic Structures and Order Conditions for Invariant Measure Sampling Found. Comput. Math. (IF 3.0) Pub Date : 2024-01-19 Eugen Bronasco
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An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities Adv. Comput. Math. (IF 1.7) Pub Date : 2024-01-17 Shixi Wang, Hai Bi, Yidu Yang
The elastic transmission eigenvalue problem, arising from the inverse scattering theory, plays a critical role in the qualitative reconstruction methods for elastic media. This paper proposes and analyzes an a posteriori error estimator of the finite element method for solving the elastic transmission eigenvalue problem with different elastic tensors and different mass densities in \(\mathbb {R}^{d}~(d=2
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Variational methods for solving numerically magnetostatic systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-01-04 Patrick Ciarlet Jr., Erell Jamelot
In this paper, we study some techniques for solving numerically magnetostatic systems. We consider fairly general assumptions on the magnetic permeability tensor. It is elliptic, but can be nonhermitian. In particular, we revisit existing classical variational methods and propose new numerical methods. The numerical approximation is either based on the classical edge finite elements or on continuous
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A Grassmann manifold handbook: basic geometry and computational aspects Adv. Comput. Math. (IF 1.7) Pub Date : 2024-01-05 Thomas Bendokat, Ralf Zimmermann, P.-A. Absil
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A fractional osmosis model for image fusion Adv. Comput. Math. (IF 1.7) Pub Date : 2024-01-08 Mohammed Hachama, Fatiha Boutaous
This paper introduces a novel model for image fusion that is based on a fractional-order osmosis approach. The model incorporates a definition of osmosis energy that takes into account nonlocal pixel relationships using fractional derivatives and contrast change. The proposed model was subjected to theoretical and experimental investigation. The semigroup theory was used to demonstrate the existence
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Numerical investigation of agent-controlled pedestrian dynamics using a structure-preserving finite volume scheme Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-28 Jan-Frederik Pietschmann, Ailyn Stötzner, Max Winkler
We provide a numerical realization of an optimal control problem for pedestrian motion with agents that was analyzed in Herzog et al. (Appl. Math. Optim. 88(3):87, 2023). The model consists of a regularized variant of Hughes’ model for pedestrian dynamics coupled to ordinary differential equations that describe the motion of agents which are able to influence the crowd via attractive forces. We devise
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A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-27 Bo Zheng, Yueqiang Shang
Abstract Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible Navier-Stokes equations, where non-homogeneous Dirichlet boundary conditions are considered and high Reynolds numbers are allowed. In this developed algorithm, we first solve an artificial
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Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-22 Xiu Ye, Shangyou Zhang
A conforming discontinuous Galerkin (CDG) finite element method is designed for solving second order non-self adjoint and indefinite elliptic equations. Unlike other discontinuous Galerkin (DG) methods, the numerical trace on the edge/triangle between two elements is not the average of two discontinuous \(P_k\) functions, but a lifted \(P_{k+2}\) function from four (eight in 3D) nearby \(P_k\) functions
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Matching pursuit with unbounded parameter domains Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-20 Wei Qu, Yanbo Wang, Xiaoyun Sun
In various applications, the adoption of optimal energy matching pursuit with dictionary elements is common. When the dictionary elements are indexed by parameters within a bounded region, exhaustion-type algorithms can be employed. This article aims to investigate a process that converts the optimal parameter selection in unbounded regions to a bounded and closed (compact) sub-domain. Such a process
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Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-13 Kewang Chen, Cornelis Vuik
Although Anderson acceleration AA(m) has been widely used to speed up nonlinear solvers, most authors are simply using and studying the stationary version of Anderson acceleration. The behavior and full potential of the non-stationary version of Anderson acceleration methods remain an open question. Motivated by the hybrid linear solver GMRESR (GMRES Recursive), we recently proposed a set of non-stationary
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Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-14 Alejandro N. Diaz, Matthias Heinkenschloss, Ion Victor Gosea, Athanasios C. Antoulas
This paper extends interpolatory model reduction to systems with (up to) quadratic-bilinear dynamics and quadratic-bilinear outputs. These systems are referred to as QB-QB systems and arise in a number of applications, including fluid dynamics, optimal control, and uncertainty quantification. In the interpolatory approach, the reduced order models (ROMs) are based on a Petrov-Galerkin projection, and
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Extremal Points and Sparse Optimization for Generalized Kantorovich–Rubinstein Norms Found. Comput. Math. (IF 3.0) Pub Date : 2023-12-11 Marcello Carioni, José A. Iglesias, Daniel Walter
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Computational Complexity of Decomposing a Symmetric Matrix as a Sum of Positive Semidefinite and Diagonal Matrices Found. Comput. Math. (IF 3.0) Pub Date : 2023-12-08 Levent Tunçel, Stephen A. Vavasis, Jingye Xu
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Toward a certified greedy Loewner framework with minimal sampling Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-05 Davide Pradovera
We propose a strategy for greedy sampling in the context of non-intrusive interpolation-based surrogate modeling for frequency-domain problems. We rely on a non-intrusive and cheap error indicator to drive the adaptive selection of the high-fidelity samples on which the surrogate is based. We develop a theoretical framework to support our proposed indicator. We also present several practical approaches
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Piecewise orthogonal collocation for computing periodic solutions of renewal equations Adv. Comput. Math. (IF 1.7) Pub Date : 2023-12-07 Alessia Andò, Dimitri Breda
We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally, we show some numerical experiments confirming the theoretical results and a couple of applications in view of bifurcation analysis.
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Efficient Random Walks on Riemannian Manifolds Found. Comput. Math. (IF 3.0) Pub Date : 2023-12-01 Simon Schwarz, Michael Herrmann, Anja Sturm, Max Wardetzky
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Approximation of curve-based sleeve functions in high dimensions Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-30 Robert Beinert
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A posteriori error analysis and adaptivity for a VEM discretization of the Navier–Stokes equations Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-30 Claudio Canuto, Davide Rosso
We consider the virtual element method (VEM) introduced by Beirão da Veiga et al. in 2016 for the numerical solution of the steady, incompressible Navier–Stokes equations; the method has arbitrary order \({k} \ge {2}\) and guarantees divergence-free velocities. For such discretization, we develop a residual-based a posteriori error estimator, which is a combination of standard terms in VEM analysis
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Continuous-stage adapted exponential methods for charged-particle dynamics with arbitrary magnetic fields Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-30 Ting Li, Bin Wang
This paper is devoted to the numerical symplectic approximation of the charged-particle dynamics (CPD) with a homogeneous magnetic field and its extension to a non-homogeneous magnetic field. By utilizing continuous-stage methods and exponential integrators, a general class of symplectic methods is formulated for CPD under a homogeneous magnetic field. Based on the derived symplectic conditions, two
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Fast Optimistic Gradient Descent Ascent (OGDA) Method in Continuous and Discrete Time Found. Comput. Math. (IF 3.0) Pub Date : 2023-11-29 Radu Ioan Boţ, Ernö Robert Csetnek, Dang-Khoa Nguyen
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Live load matrix recovery from scattering data in linear elasticity Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-28 Juan Antonio Barceló, Carlos Castro, Mari Cruz Vilela
We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown linear load given by a square matrix. For both backscattering data and fixed-angle scattering data, we show how to obtain numerical approximations of the so-called Born approximations and propose new iterative algorithms that provide sequences of approximations
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$$\mathcal {H}$$ -inverses for RBF interpolation Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-23 Niklas Angleitner, Markus Faustmann, Jens Markus Melenk
We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system matrix for this interpolation problem can be approximated at an exponential rate in the block rank in the \(\mathcal {H}\)-matrix format, if the block structure of the \(\mathcal {H}\)-matrix arises from a standard clustering
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Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-22 Jiajun Zhan, Liuqiang Zhong, Jie Peng
In this paper, we design and analyze the iterative two-grid methods for the discontinuous Galerkin (DG) discretization of semilinear elliptic partial differential equations (PDEs). We first present an iterative two-grid method that is just like the classical iterative two-grid methods for nonsymmetric or indefinite linear elliptic PDEs, namely, to solve a semilinear problem on the coarse space and
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An unconditionally stable and $$L^2$$ optimal quadratic finite volume scheme over triangular meshes for anisotropic elliptic equations Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-22 Xiaoxin Wu, Weifeng Qiu, Kejia Pan
In this paper, we propose an unconditionally stable and \(L^2\) optimal quadratic finite volume (FV) scheme for solving the two-dimensional anisotropic elliptic equation on triangular meshes. In quadratic FV schemes, the construction of the dual partition is closely related to the \(L^2\) error estimate. While many dual partitions over triangular meshes have been investigated in the literature, only
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Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-23 Chiara Sorgentone, Anna-Karin Tornberg
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The Butzer-Kozakiewicz article on Riemann derivatives of 1954 and its influence Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-23 P. L. Butzer, R. L. Stens
The article on Riemann derivatives by P. L. Butzer and W. Kozakiewicz of 1954 was the basis to generalizations of the classical scalar-valued derivatives to Taylor, Peano, and Riemann derivatives in the setting of semigroup theory. The present paper gives an overview of the 1954 article, describes its influence, and integrates it into the literature on related problems. It also describes the state
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Max filtering with reflection groups Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-21 Dustin G. Mixon, Daniel Packer
Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of minimum distortion in the setting where G is a reflection group. Our analysis involves an interplay between Coxeter’s classification and semidefinite programming.
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Multilevel Monte Carlo simulation for the Heston stochastic volatility model Adv. Comput. Math. (IF 1.7) Pub Date : 2023-11-20 Chao Zheng