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An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-15 Marco Bernreuther, Stefan Volkwein
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator is adopted to the presence of the discrete empirical interpolation method (DEIM) as approximation technique for the nonsmoothness. The separability of the estimated
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Book Reviews SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Anita T. Layton
SIAM Review, Volume 66, Issue 2, Page 391-399, May 2024. As I sat down to write this introduction, I became curious how the books chosen for review have changed over the past decades. So I scanned through a few SIREV Book Review section introductions written 10, 20 or more years ago by former section editors. That act of procrastination allows me to put the current collection of reviews in “historical
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Dynamics of Signaling Games SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Hannelore De Silva, Karl Sigmund
SIAM Review, Volume 66, Issue 2, Page 368-387, May 2024. This tutorial describes several basic and much-studied types of interactions with incomplete information, analyzing them by means of evolutionary game dynamics. The games include sender-receiver games, owner-challenger contests, costly advertising, and calls for help. We model the evolution of populations of players reacting to each other and
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The Poincaré Metric and the Bergman Theory SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Steven G. Krantz
SIAM Review, Volume 66, Issue 2, Page 355-367, May 2024. We treat the Poincaré metric on the disc. In particular we emphasize the fact that it is the canonical holomorphically invariant metric on the unit disc. Then we generalize these ideas to the Bergman metric on a domain in complex space. Along the way we treat the Bergman kernel and study its invariance and uniqueness properties.
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Education SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Hélène Frankowska
SIAM Review, Volume 66, Issue 2, Page 353-353, May 2024. In this issue the Education section presents two contributions. The first paper, “The Poincaré Metric and the Bergman Theory,” by Steven G. Krantz, discusses the Poincaré metric on the unit disc in the complex space and the Bergman metric on an arbitrary domain in any dimensional complex space. To define the Bergman metric the notion of Bergman
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Nonsmooth Optimization over the Stiefel Manifold and Beyond: Proximal Gradient Method and Recent Variants SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, Tong Zhang
SIAM Review, Volume 66, Issue 2, Page 319-352, May 2024. We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this class of problems converge slowly in practice, involve subproblems that can be as difficult as the original problem, or lack rigorous convergence guarantees. In
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SIGEST SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 The Editors
SIAM Review, Volume 66, Issue 2, Page 317-317, May 2024. The SIGEST article in this issue is “Nonsmooth Optimization over the Stiefel Manifold and Beyond: Proximal Gradient Method and Recent Variants,” by Shixiang Chen, Shiqian Ma, Anthony Man-Cho So, and Tong Zhang. This work considers nonsmooth optimization on the Stiefel manifold, the manifold of orthonormal $k$-frames in $\mathbb{R}^n$. The authors
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A New Version of the Adaptive Fast Gauss Transform for Discrete and Continuous Sources SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Leslie F. Greengard, Shidong Jiang, Manas Rachh, Jun Wang
SIAM Review, Volume 66, Issue 2, Page 287-315, May 2024. We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a new hierarchical merging scheme. For continuous source distributions sampled on adaptive tensor product grids, we exploit
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Research Spotlights SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Stefan M. Wild
SIAM Review, Volume 66, Issue 2, Page 285-285, May 2024. The Gauss transform---convolution with a Gaussian in the continuous case and the sum of $N$ Gaussians at $M$ points in the discrete case---is ubiquitous in applied mathematics, from solving ordinary and partial differential equations to probability density estimation to science applications in astrophysics, image processing, quantum mechanics
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Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection Methods SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Julianne Chung, Silvia Gazzola
SIAM Review, Volume 66, Issue 2, Page 205-284, May 2024. This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the numerical linear algebra community and have proved important in solving inverse problems due to their inherent
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Survey and Review SIAM Rev. (IF 10.2) Pub Date : 2024-05-09 Marlis Hochbruck
SIAM Review, Volume 66, Issue 2, Page 203-203, May 2024. Inverse problems arise in various applications---for instance, in geoscience, biomedical science, or mining engineering, to mention just a few. The purpose is to recover an object or phenomenon from measured data which is typically subject to noise. The article “Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection
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A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-08 Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado
The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-mechanical model suitable for simulating electrically assisted forming processes
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Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-08 Xinyue Gao, Yi Qin, Jian Li
In this paper, a new time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise is developed and studied. This model considers heat transfer between the free flow in the pipe region and the porous media flow in the porous media region. Darcy’s law and stochastic Navier-Stokes equations are used to control the flows in the pipe and porous media regions, respectively. The
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Local behaviors of Fourier expansions for functions of limited regularities Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-09 Shunfeng Yang, Shuhuang Xiang
Based on the explicit formula of the pointwise error of Fourier projection approximation and by applying van der Corput-type Lemma, optimal convergence rates for periodic functions with different degrees of smoothness are established. It shows that the convergence rate enjoys a decay rate one order higher in the smooth parts than that at the singularities. In addition, it also depends on the distance
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On the maximum principle and high-order, delay-free integrators for the viscous Cahn–Hilliard equation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-03 Hong Zhang, Gengen Zhang, Ziyuan Liu, Xu Qian, Songhe Song
The stabilization approach has been known to permit large time-step sizes while maintaining stability. However, it may “slow down the convergence rate” or cause “delayed convergence” if the time-step rescaling is not well resolved. By considering a fourth-order-in-space viscous Cahn–Hilliard (VCH) equation, we propose a class of up to the fourth-order single-step methods that are able to capture the
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Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-03 Pawan Goyal, Igor Pontes Duff, Peter Benner
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial functions, and the linear part corresponds to a linear structured model, such as second-order, time-delay, or fractional-order systems. Our approach relies on the Volterra
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Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-06 Huaijun Yang, Meng Li
In this paper, a linearized structure-preserving Galerkin finite element method is investigated for Poisson-Nernst-Planck (PNP) equations. By making full use of the high accuracy estimation of the bilinear element, the mean value technique and rigorously dealing with the coupled nonlinear term, not only the unconditionally optimal error estimate in \(L^2\)-norm but also the unconditionally superclose
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Stray field computation by inverted finite elements: a new method in micromagnetic simulations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-07 Tahar Z. Boulmezaoud, Keltoum Kaliche
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Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-02 Louis Lamérand, Didier Auroux, Philippe Ghendrih, Francesca Rapetti, Eric Serre
Two-dimensional transport codes for the simulation of tokamak plasma are reduced version of full 3D fluid models where plasma turbulence has been smoothed out by averaging. One of the main issues nowadays in such reduced models is the accurate modelling of transverse transport fluxes resulting from the averaging of stresses due to fluctuations. Transverse fluxes are assumed driven by local gradients
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Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-02 David Berghaus, Robert Stephen Jones, Hartmut Monien, Danylo Radchenko
We numerically compute the lowest Laplacian eigenvalues of several two-dimensional shapes with dihedral symmetry at arbitrary precision arithmetic. Our approach is based on the method of particular solutions with domain decomposition. We are particularly interested in asymptotic expansions of the eigenvalues \(\lambda (n)\) of shapes with n edges that are of the form \(\lambda (n) \sim x\sum _{k=0}^{\infty
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Fast numerical integration of highly oscillatory Bessel transforms with a Cauchy type singular point and exotic oscillators Adv. Comput. Math. (IF 1.7) Pub Date : 2024-05-02 Hongchao Kang, Qi Xu, Guidong Liu
In this article, we propose an efficient hybrid method to calculate the highly oscillatory Bessel integral \(\int _{0}^{1} \frac{f(x)}{x-\tau } J_{m} (\omega x^{\gamma } )\textrm{d}x\) with the Cauchy type singular point, where \( 0< \tau < 1, m \ge 0, 2\gamma \in N^{+}. \) The hybrid method is established by combining the complex integration method with the Clenshaw– Curtis– Filon– type method. Based
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Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-30 Julio Enrique Castrillón-Candás
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Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-29 Tobias Ehring, Bernard Haasdonk
Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value function of optimal control problems, which partially mitigates the dimensionality problem. The method is based on a greedy Hermite kernel interpolation scheme and
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Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-29 Leszek Demkowicz, Jens M. Melenk, Jacob Badger, Stefan Henneking
This paper is a continuation of Melenk et al., “Stability analysis for electromagnetic waveguides. Part 1: acoustic and homogeneous electromagnetic waveguides” (2023) [5], extending the stability results for homogeneous electromagnetic (EM) waveguides to the non-homogeneous case. The analysis is done using perturbation techniques for self-adjoint operators eigenproblems. We show that the non-homogeneous
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Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul’yev methods Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-29 Xuelong Gu, Yushun Wang, Wenjun Cai
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart of these properties, the linear part of the target system is usually discretized implicitly, resulting in a large linear or nonlinear system of equations. The fast Fourier transform is commonly used to solve the resulting linear or nonlinear systems with
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Dictionary-based model reduction for state estimation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-24 Anthony Nouy, Alexandre Pasco
We consider the problem of state estimation from a few linear measurements, where the state to recover is an element of the manifold \(\mathcal {M}\) of solutions of a parameter-dependent equation. The state is estimated using prior knowledge on \(\mathcal {M}\) coming from model order reduction. Variational approaches based on linear approximation of \(\mathcal {M}\), such as PBDW, yield a recovery
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Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition Adv. Comput. Math. (IF 1.7) Pub Date : 2024-04-24 Simone Brivio, Stefania Fresca, Nicola Rares Franco, Andrea Manzoni
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality reduction obtained through proper orthogonal decomposition (POD) for the sake of efficiency, (ii) an autoencoder architecture that further reduces the dimensionality
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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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$$\mathcal {H}_2$$ 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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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
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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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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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Sum-of-Squares Relaxations for Information Theory and Variational Inference Found. Comput. Math. (IF 3.0) Pub Date : 2024-04-05 Francis Bach
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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 Craig Gross, Mark Iwen
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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 Philipp Bringmann, Jonas W. Ketteler, Mira Schedensack
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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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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