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Artificial neural networks with uniform norm-based loss functions Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-23 Vinesha Peiris, Vera Roshchina, Nadezda Sukhorukova
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The improvement of the truncated Euler-Maruyama method for non-Lipschitz stochastic differential equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-22 Weijun Zhan, Yuyuan Li
This paper is concerned with the numerical approximations for stochastic differential equations with non-Lipschitz drift or diffusion coefficients. A modified truncated Euler-Maruyama discretization scheme is developed. Moreover, by establishing the criteria on stochastic C-stability and B-consistency of the truncated Euler-Maruyama method, we obtain the strong convergence and the convergence rate
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The adjoint double layer potential on smooth surfaces in $$\mathbb {R}^3$$ and the Neumann problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-19 J. Thomas Beale, Michael Storm, Svetlana Tlupova
We present a simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for Laplace’s equation in three dimensions. An expansion in curvilinear coordinates leads us to modify the expression for the adjoint double layer so that the singularity is reduced when evaluating the integral on the surface. Then, to regularize the integral
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Discrete Weber Inequalities and Related Maxwell Compactness for Hybrid Spaces over Polyhedral Partitions of Domains with General Topology Found. Comput. Math. (IF 3.0) Pub Date : 2024-04-16 Simon Lemaire, Silvano Pitassi
We prove discrete versions of the first and second Weber inequalities on \(\varvec{H}({{\,\mathrm{{\textbf {curl}}}\,}})\cap \varvec{H}({{\,\textrm{div}\,}}_{\eta })\)-like hybrid spaces spanned by polynomials attached to the faces and to the cells of a polyhedral mesh. The proven hybrid Weber inequalities are optimal in the sense that (i) they are formulated in terms of \(\varvec{H}({{\,\mathrm{{\textbf
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$$\mathcal {H}_2$$ optimal rational approximation on general domains Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-18 Alessandro Borghi, Tobias Breiten
Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence, the underlying rational transfer functions are allowed to have poles in general domains in the complex plane. In particular, this covers the case of specific conservative
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Computing equivariant matrices on homogeneous spaces for geometric deep learning and automorphic Lie algebras Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-11 Vincent Knibbeler
We develop an elementary method to compute spaces of equivariant maps from a homogeneous space G/H of a Lie group G to a module of this group. The Lie group is not required to be compact. More generally, we study spaces of invariant sections in homogeneous vector bundles, and take a special interest in the case where the fibres are algebras. These latter cases have a natural global algebra structure
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Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-11 Ion Victor Gosea, Serkan Gugercin, Steffen W. R. Werner
An essential tool in data-driven modeling of dynamical systems from frequency response measurements is the barycentric form of the underlying rational transfer function. In this work, we propose structured barycentric forms for modeling dynamical systems with second-order time derivatives using their frequency domain input-output data. By imposing a set of interpolation conditions, the systems’ transfer
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Numerical simulation of resistance furnaces by using distributed and lumped models Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-10 A. Bermúdez, D. Gómez, D. González
This work proposes a methodology that combines distributed and lumped models to simulate the current distribution within an indirect heat resistance furnace and, in particular, to calculate the current to be supplied for achieving a desired power output. The distributed model is a time-harmonic eddy current problem, which is solved numerically using the finite element method. The lumped model relies
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Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-10 Ulrich Langer, Olaf Steinbach, Huidong Yang
As in our previous work (SINUM 59(2):660–674, 2021) we consider space-time tracking optimal control problems for linear parabolic initial boundary value problems that are given in the space-time cylinder \(Q = \Omega \times (0,T)\), and that are controlled by the right-hand side \(z_\varrho \) from the Bochner space \(L^2(0,T;H^{-1}(\Omega ))\). So it is natural to replace the usual \(L^2(Q)\) norm
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Sum-of-Squares Relaxations for Information Theory and Variational Inference Found. Comput. Math. (IF 3.0) Pub Date : 2024-04-05
Abstract We consider extensions of the Shannon relative entropy, referred to as f-divergences. Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing integrals, and (c) variational inference in probabilistic models. These problems are related to one another through convex duality, and for all of them, there
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Robust low tubal rank tensor recovery using discrete empirical interpolation method with optimized slice/feature selection Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-06 Salman Ahmadi-Asl, Anh-Huy Phan, Cesar F. Caiafa, Andrzej Cichocki
In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is investigated both theoretically and numerically. In particular, the details of the error bounds of the proposed TDEIM method are derived. The experimental
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Sparse Spectral Methods for Solving High-Dimensional and Multiscale Elliptic PDEs Found. Comput. Math. (IF 3.0) Pub Date : 2024-04-02
Abstract In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, “[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless march to larger and larger [bandwidths] continues” [Boyd in Chebyshev and Fourier spectral methods, second rev ed. Dover Publications, Mineola, NY, 2001
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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