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Multilinear Hyperquiver Representations Found. Comput. Math. (IF 2.5) Pub Date : 2025-02-14 Tommi Muller, Vidit Nanda, Anna Seigal
We count singular vector tuples of a system of tensors assigned to the edges of a directed hypergraph. To do so, we study the generalisation of quivers to directed hypergraphs. Assigning vector spaces to the nodes of a hypergraph and multilinear maps to its hyperedges gives a hyperquiver representation. Hyperquiver representations generalise quiver representations (where all hyperedges are edges) and
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On the recovery of two function-valued coefficients in the Helmholtz equation for inverse scattering problems via neural networks Adv. Comput. Math. (IF 1.7) Pub Date : 2025-02-11 Zehui Zhou
Recently, deep neural networks (DNNs) have become powerful tools for solving inverse scattering problems. However, the approximation and generalization rates of DNNs for solving these problems remain largely under-explored. In this work, we introduce two types of combined DNNs (uncompressed and compressed) to reconstruct two function-valued coefficients in the Helmholtz equation for inverse scattering
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Representations of the Symmetric Group are Decomposable in Polynomial Time Found. Comput. Math. (IF 2.5) Pub Date : 2025-02-10 Sheehan Olver
We introduce an algorithm to decompose matrix representations of the symmetric group over the reals into irreducible representations, which as a by-product also computes the multiplicities of the irreducible representations. The algorithm applied to a d-dimensional representation of \(S_n\) is shown to have a complexity of \({\mathcal {O}}(n^2 d^3)\) operations for determining which irreducible representations
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On a non-uniform $$\alpha $$ -robust IMEX-L1 mixed FEM for time-fractional PIDEs Adv. Comput. Math. (IF 1.7) Pub Date : 2025-02-10 Lok Pati Tripathi, Aditi Tomar, Amiya K. Pani
A non-uniform implicit-explicit L1 mixed finite element method (IMEX-L1-MFEM) is investigated for a class of time-fractional partial integro-differential equations (PIDEs) with space-time-dependent coefficients and non-self-adjoint elliptic part. The proposed fully discrete method combines an IMEX-L1 method on a graded mesh in the temporal variable with a mixed finite element method in spatial variables
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Book Review:; Mathematical Pictures at a Data Science Exhibition SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Bamdad Hosseini
SIAM Review, Volume 67, Issue 1, Page 208-209, March 2025. The book Mathematical Pictures at a Data Science Exhibition aims to introduce the reader to the many mathematical ideas that congregate under the ever-expanding umbrella of data science. Given the meteoric rise of this field and the immense speed at which it often moves, this book acts as a welcome road map for graduate students and researchers
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Book Review:; Elegant Simulations. From Simple Oscillators to Many-Body Systems SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Omar Morandi
SIAM Review, Volume 67, Issue 1, Page 207-208, March 2025. Elegant Simulations covers various aspects of modeling and simulating mechanical systems described at the elementary level by many-interacting particles. The book presents the topics from an original and fresh point of view. The complex many-body dynamics is reproduced at the elementary level in terms of simple models that are easy to understand
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Book Review:; Essential Statistics for Data Science: A Concise Crash Course SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 David Banks
SIAM Review, Volume 67, Issue 1, Page 206-207, March 2025. This is a bold book! Professor Zhu wants to provide the basic statistical knowledge needed by data scientists in a super-short volume. It reminds me a bit of Larry Wasserman’s All of Statistics (Springer, 2014), but is aimed at Masters students (often from fields other than statistics) or advanced undergraduates (also often from other fields)
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Book Review:; Probability Adventures SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Nevena Marić
SIAM Review, Volume 67, Issue 1, Page 205-206, March 2025. The first look at Probability Adventures brought back memories of a conference in Ubatuba, Brazil, in 2001, where as a young Master’s student I worried that true science had to be deadly serious. Fortunately, several inspiring teachers came to the rescue. Andrei Toom’s words resonated deeply with me when he began his lecture by saying, “Every
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Book Review:; Numerical Methods in Physics with Python. Second Edition SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Gabriele Ciaramella
SIAM Review, Volume 67, Issue 1, Page 204-205, March 2025. Numerical Methods in Physics with Python by Alex Gezerlis is an excellent example of a textbook built on long and established teaching experience. The goals are clearly defined in the preface: Gezerlis aims to gently introduce undergraduate physics students to the branch of numerical methods and their concrete implementation in Python. To this
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Featured Review:; Numerical Integration of Differential Equations SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 John C. Butcher, Robert M. Corless
SIAM Review, Volume 67, Issue 1, Page 197-204, March 2025. The book under review was originally published under the auspices of the National Research Council in 1933 (the year John was born), and it was republished as a Dover edition in 1956 (three years before Rob was born). At 108 pages—including title page, preface, table of contents, and index—it’s very short. Even so, it contains a significant
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Anita T. Layton
SIAM Review, Volume 67, Issue 1, Page 195-196, March 2025.
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Neighborhood Watch in Mechanics: Nonlocal Models and Convolution SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Thomas Nagel, Tymofiy Gerasimov, Jere Remes, Dominik Kern
SIAM Review, Volume 67, Issue 1, Page 176-193, March 2025. Abstract.This paper is intended to serve as a low-hurdle introduction to nonlocality for graduate students and researchers with an engineering mechanics or physics background who did not have a formal introduction to the underlying mathematical basis. We depart from simple examples motivated by structural mechanics to form a physical intuition
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Graph Neural Networks and Applied Linear Algebra SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Nicholas S. Moore, Eric C. Cyr, Peter Ohm, Christopher M. Siefert, Raymond S. Tuminaro
SIAM Review, Volume 67, Issue 1, Page 141-175, March 2025. Abstract.Sparse matrix computations are ubiquitous in scientific computing. Given the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NNs). Unfortunately, multilayer perceptron (MLP) NNs are typically not natural for either graph or sparse matrix computations
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Limits of Learning Dynamical Systems SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Tyrus Berry, Suddhasattwa Das
SIAM Review, Volume 67, Issue 1, Page 107-137, March 2025. Abstract.A dynamical system is a transformation of a phase space, and the transformation law is the primary means of defining as well as identifying the dynamical system and is the object of focus of many learning techniques. However, there are many secondary aspects of dynamical systems—invariant sets, the Koopman operator, and Markov approximations—that
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The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Nina M. Gottschling, Vegard Antun, Anders C. Hansen, Ben Adcock
SIAM Review, Volume 67, Issue 1, Page 73-104, March 2025. Abstract.Methods inspired by artificial intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performance on challenging problems. However, the reliability and trustworthiness of such techniques is a major concern. In inverse problems in imaging, the focus of this paper, there is increasing
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Stefan M. Wild
SIAM Review, Volume 67, Issue 1, Page 71-71, March 2025.
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Risk-Adaptive Approaches to Stochastic Optimization: A Survey SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Johannes O. Royset
SIAM Review, Volume 67, Issue 1, Page 3-70, March 2025. Abstract.Uncertainty is prevalent in engineering design and data-driven problems and, more broadly, in decision making. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2025-02-06 Marlis Hochbruck
SIAM Review, Volume 67, Issue 1, Page 1-1, March 2025.
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Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation Adv. Comput. Math. (IF 1.7) Pub Date : 2025-02-05 Tiangang Cui, Josef Dick, Friedrich Pillichshammer
We study numerical integration over bounded regions in \(\mathbb {R}^s\), \(s \ge 1\), with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic constructions which aim to fill the space more evenly than random points. Ordinarily, such quasi-Monte Carlo point sets are designed for the uniform measure
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Safely Learning Dynamical Systems Found. Comput. Math. (IF 2.5) Pub Date : 2025-02-04 Amir Ali Ahmadi, Abraar Chaudhry, Vikas Sindhwani, Stephen Tu
A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the system is required to stay within a safety region for
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Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method Adv. Comput. Math. (IF 1.7) Pub Date : 2025-02-03 Shubhaditya Burela, Philipp Krah, Julius Reiss
Parametric model order reduction techniques often struggle to accurately represent transport-dominated phenomena due to a slowly decaying Kolmogorov n-width. To address this challenge, we propose a non-intrusive, data-driven methodology that combines the shifted proper orthogonal decomposition (POD) with deep learning. Specifically, the shifted POD technique is utilized to derive a high-fidelity, low-dimensional
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A scaling fractional asymptotical regularization method for linear inverse problems Adv. Comput. Math. (IF 1.7) Pub Date : 2025-01-31 Lele Yuan, Ye Zhang
In this paper, we propose a Scaling Fractional Asymptotical Regularization (S-FAR) method for solving linear ill-posed operator equations in Hilbert spaces, inspired by the work of (2019 Fract. Calc. Appl. Anal. 22(3) 699-721). Our method is incorporated into the general framework of linear regularization and demonstrates that, under both Hölder and logarithmic source conditions, the S-FAR with fractional
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Stabilizing Decomposition of Multiparameter Persistence Modules Found. Comput. Math. (IF 2.5) Pub Date : 2025-01-27 Håvard Bakke Bjerkevik
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. Until now, it has not been clear that there is any way to get around this and build a meaningful stability theory for multiparameter module decomposition. We introduce new tools, in particular
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Optimal Regularization for a Data Source Found. Comput. Math. (IF 2.5) Pub Date : 2025-01-27 Oscar Leong, Eliza O’ Reilly, Yong Sheng Soh, Venkat Chandrasekaran
In optimization-based approaches to inverse problems and to statistical estimation, it is common to augment criteria that enforce data fidelity with a regularizer that promotes desired structural properties in the solution. The choice of a suitable regularizer is typically driven by a combination of prior domain information and computational considerations. Convex regularizers are attractive computationally
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A difference finite element method based on nonconforming finite element methods for 3D elliptic problems Adv. Comput. Math. (IF 1.7) Pub Date : 2025-01-24 Jianjian Song, Dongwoo Sheen, Xinlong Feng, Yinnian He
In this paper, a class of 3D elliptic equations is solved by using the combination of the finite difference method in one direction and nonconforming finite element methods in the other two directions. A finite-difference (FD) discretization based on \(P_1\)-element in the z-direction and a finite-element (FE) discretization based on \(P_1^{NC}\)-nonconforming element in the (x, y)-plane are used to
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Sharp Bounds for Max-sliced Wasserstein Distances Found. Comput. Math. (IF 2.5) Pub Date : 2025-01-22 March T. Boedihardjo
We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from n samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability
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Optimal Convergence Rates for the Spectrum of the Graph Laplacian on Poisson Point Clouds Found. Comput. Math. (IF 2.5) Pub Date : 2025-01-22 Scott Armstrong, Raghavendra Venkatraman
We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold, yielding error estimates for relatively sparse graphs.
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Active Manifolds, Stratifications, and Convergence to Local Minima in Nonsmooth Optimization Found. Comput. Math. (IF 2.5) Pub Date : 2025-01-22 Damek Davis, Dmitriy Drusvyatskiy, Liwei Jiang
In this work, we develop new regularity conditions in nonsmooth analysis that parallel the stratification conditions of Whitney, Kuo, and Verdier. They quantify how subgradients interact with a certain “active manifold” that captures the nonsmooth activity of the function. Based on these new conditions, we show that several subgradient-based methods converge only to local minimizers when applied to
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Accuracy Controlled Schemes for the Eigenvalue Problem of the Radiative Transfer Equation Found. Comput. Math. (IF 2.5) Pub Date : 2025-01-21 Wolfgang Dahmen, Olga Mula
The criticality problem in nuclear engineering asks for the principal eigenpair of a Boltzmann operator describing neutron transport in a reactor core. Being able to reliably design, and control such reactors requires assessing these quantities within quantifiable accuracy tolerances. In this paper, we propose a paradigm that deviates from the common practice of approximately solving the corresponding
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An all-frequency stable integral system for Maxwell’s equations in 3-D penetrable media: continuous and discrete model analysis Adv. Comput. Math. (IF 1.7) Pub Date : 2025-01-16 Mahadevan Ganesh, Stuart C. Hawkins, Darko Volkov
We introduce a new system of surface integral equations for Maxwell’s transmission problem in three dimensions (3-D). This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the underlying linear operator has a uniformly bounded inverse as the frequency approaches zero, ensuring that there is no low-frequency breakdown. The system is derived
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On convergence of the generalized Lanczos trust-region method for trust-region subproblems Adv. Comput. Math. (IF 1.7) Pub Date : 2025-01-02 Bo Feng, Gang Wu
The generalized Lanczos trust-region (GLTR) method is one of the most popular approaches for solving large-scale trust-region subproblem (TRS). In Jia and Wang, SIAM J. Optim., 31, 887–914 2021. Z. Jia et al. considered the convergence of this method and established some a priori error bounds on the residual and the Lagrange multiplier. In this paper, we revisit the convergence of the GLTR method and
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A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform Adv. Comput. Math. (IF 1.7) Pub Date : 2025-01-03 Tobias Long, Robert Barnett, Richard Jefferson-Loveday, Giovanni Stabile, Matteo Icardi
Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even relatively small parameter variations, making the reduced models inefficient and inaccurate. This work proposes a model order reduction approach based on the Radon Cumulative
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Unfitted finite element method for the quad-curl interface problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-27 Hailong Guo, Mingyan Zhang, Qian Zhang, Zhimin Zhang
In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche’s method for \({\operatorname {curl}}{\operatorname {curl}}\)-conforming elements and double the degrees of freedom on interface elements. To ensure stability, we incorporate ghost penalty terms and a discrete divergence-free term. We establish the well-posedness of our method
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A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-18 Xiaojuan Liu, Maojun Li, Tao Yin, Shangyou Zhang
This paper studies the finite element method for solving the exterior Stokes problem in two dimensions. A nonlocal boundary condition is defined using a nonsingular-kernel Dirichlet-to-Dirichlet (DtD) mapping, which maps the Dirichlet data on an interior circle to the Dirichlet data on another circular artificial boundary based on the Poisson integral formula of the Stokes problem. The truncated problem
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Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-17 Ben S. Ashby, Tristan Pryer
In this article, we present a numerical method for the Stokes flow of an Oldroyd-B fluid. The viscoelastic stress evolves according to a constitutive law formulated in terms of the upper convected time derivative. A finite difference method is used to discretise along fluid trajectories to approximate the advection and deformation terms of the upper convected derivative in a simple, cheap and cohesive
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A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-13 Jan Giesselmann, Kiwoong Kwon
We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional in the sense that an a posteriori computable quantity needs to be small enough—which can be ensured by mesh refinement—and optimal in the sense that the error estimator decays with the same order as the error under mesh
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Conley Index for Multivalued Maps on Finite Topological Spaces Found. Comput. Math. (IF 2.5) Pub Date : 2024-12-09 Jonathan Barmak, Marian Mrozek, Thomas Wanner
We develop Conley’s theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we establish the notions of isolated invariant sets and index pairs, and use them to introduce a well-defined Conley index. In addition, we verify some of its fundamental properties
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Generalized Pseudospectral Shattering and Inverse-Free Matrix Pencil Diagonalization Found. Comput. Math. (IF 2.5) Pub Date : 2024-12-09 James Demmel, Ioana Dumitriu, Ryan Schneider
We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any \(n \times n\) matrix pencil (A, B). The bulk of the algorithm rests on a randomized divide-and-conquer eigensolver for the generalized eigenvalue problem originally proposed by Ballard, Demmel and Dumitriu (Technical Report 2010). We demonstrate that this divide-and-conquer approach can be formulated
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Analysis of a time filtered finite element method for the unsteady inductionless MHD equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-09 Xiaodi Zhang, Jialin Xie, Xianzhu Li
This paper studies a time filtered finite element method for the unsteady inductionless magnetohydrodynamic (MHD) equations. The method uses the semi-implicit backward Euler scheme with a time filter in time and adopts the standard inf-sup stable fluid pairs to discretize the velocity and pressure, and the inf-sup stable face-volume elements for solving the current density and electric potential in
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Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-09 Khalil A. Hall-Hooper, Arvind K. Saibaba, Julianne Chung, Scot M. Miller
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for small problems but are not computationally feasible for problems with a very large number of unknown inverse parameters. In this work, we describe an empirical Bayes
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On the recovery of initial status for linearized shallow-water wave equation by data assimilation with error analysis Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-05 Jun-Liang Fu, Jijun Liu
We recover the initial status of an evolution system governed by linearized shallow-water wave equations in a 2-dimensional bounded domain by data assimilation technique, with the aim of determining the initial wave height from the measurement of wave distribution in an interior domain. Since we specify only one component of the solution to the governed system and the observation is only measured in
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Locally-Verifiable Sufficient Conditions for Exactness of the Hierarchical B-spline Discrete de Rham Complex in $$\mathbb {R}^n$$ Found. Comput. Math. (IF 2.5) Pub Date : 2024-12-04 Kendrick Shepherd, Deepesh Toshniwal
Given a domain \(\Omega \subset \mathbb {R}^n\), the de Rham complex of differential forms arises naturally in the study of problems in electromagnetism and fluid mechanics defined on \(\Omega \), and its discretization helps build stable numerical methods for such problems. For constructing such stable methods, one critical requirement is ensuring that the discrete subcomplex is cohomologically equivalent
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Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-04 Maya Briani, Emiliano Cristiani, Elia Onofri
In this paper, we develop new methods to join machine learning techniques and macroscopic differential models, aimed at estimate and forecast vehicular traffic. This is done to complement respective advantages of data-driven and model-driven approaches. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class
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Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling Adv. Comput. Math. (IF 1.7) Pub Date : 2024-12-03 Hongjia Chen, Teng Wang, Chun-Hua Zhang, Xiang Wang
In this paper, we consider the quadratic eigenvalue problem (QEP) expressed in various commonly used bases, including Taylor, Newton, and Lagrange bases. We propose to investigate the backward errors of the computed eigenpairs and condition numbers of eigenvalues for QEP solved by a class of block Kronecker linearizations. To improve the backward error and condition number of the QEP expressed in a
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Constrained and Unconstrained Stable Discrete Minimizations for p-Robust Local Reconstructions in Vertex Patches in the de Rham Complex Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-25 Théophile Chaumont-Frelet, Martin Vohralík
We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree p. We show that the discrete minimizers in the spaces of piecewise polynomials of degree p conforming in the \(H^1\), \({\varvec{H}}(\textbf{curl})\), or \({\varvec{H}}({\text {div}})\) spaces are as good as the minimizers in these entire
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Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis Adv. Comput. Math. (IF 1.7) Pub Date : 2024-11-25 J.K. Djoko, T. Sayah
In two dimensions, we propose and analyse an iterative a posteriori error indicator for the discontinuous Galerkin finite element approximations of the Stokes equations under boundary conditions of friction type. Two sources of error are identified here, namely; the discretisation error and the linearization error. Under a smallness assumption on data, we prove that the devised error estimator is reliable
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Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-20 Brendan Keith, Thomas M. Surowiec
The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent
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Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies Adv. Comput. Math. (IF 1.7) Pub Date : 2024-11-18 M. Averseng, J. Galkowski, E. A. Spence
For h-FEM discretisations of the Helmholtz equation with wavenumber k, we obtain k-explicit analogues of the classic local FEM error bounds of Nitsche and Schatz (Math. Comput. 28(128), 937–958 1974), Wahlbin (1991, §9), Demlow et al.(Math. Comput. 80(273), 1–9 2011), showing that these bounds hold with constants independent of k, provided one works in Sobolev norms weighted with k in the natural way
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Higher-order iterative decoupling for poroelasticity Adv. Comput. Math. (IF 1.7) Pub Date : 2024-11-15 Robert Altmann, Abdullah Mujahid, Benjamin Unger
For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As the main result, we show that the convergence depends on the interplay between
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Classification of Finite Groups: Recent Developements and Open Problems Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-12 Bettina Eick
The theory of group classifications has undergone significant changes in the past 25 years. New methods have been introduced, some difficult problems have been solved and group classifications have become widely available through computer algebra systems. This survey describes the state of the art of the group classification problem, its history, its recent advances and some open problems.
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Computing the Noncommutative Inner Rank by Means of Operator-Valued Free Probability Theory Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-11 Johannes Hoffmann, Tobias Mai, Roland Speicher
We address the noncommutative version of the Edmonds’ problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algorithm for the calculation of this inner rank by relating the problem with the distribution of a basic object in free probability theory, namely operator-valued semicircular elements. We have to solve a matrix-valued quadratic equation, for which
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Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-11 Sadashige Ishida, Hugo Lavenant
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also
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Gabor Phase Retrieval via Semidefinite Programming Found. Comput. Math. (IF 2.5) Pub Date : 2024-11-07 Philippe Jaming, Martin Rathmair
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Anita T. Layton
SIAM Review, Volume 66, Issue 4, Page 795-805, November 2024. If you are teaching a course (or otherwise looking for a text) in the techniques and applications of mathematical modeling, or mathematical approaches that analyze or solve those equations, you may find one of the reviews in this issue's collection interesting. Our featured review was written by Shawn Ryan, on the book Mathematical Modeling
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Developing Workforce with Mathematical Modeling Skills SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Ariel Cintrón-Arias, Ryan Andrew Nivens, Anant Godbole, Calvin B. Purvis
SIAM Review, Volume 66, Issue 4, Page 778-792, November 2024. Mathematicians have traditionally been a select group of academics who produce high-impact ideas enabling substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics have represented a nearly constant proportion of approximately 1% of bachelor degrees awarded in the
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Sandpiles and Dunes: Mathematical Models for Granular Matter SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Piermarco Cannarsa, Stefano Finzi Vita
SIAM Review, Volume 66, Issue 4, Page 751-777, November 2024. Granular materials are everywhere, in the environment but also in our pantry. Their properties are different from those of any solid material, due to the possibility of sudden phenomena such as avalanches or landslides. Here we present a brief survey on their characteristics and on what can be found (from the past thirty years) in the recent
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Education SIAM Rev. (IF 10.8) Pub Date : 2024-11-07 Hélène Frankowska
SIAM Review, Volume 66, Issue 4, Page 749-749, November 2024. In this issue the Education section presents two contributions. The first paper, “Sandpiles and Dunes: Mathematical Models for Granular Matter,” by Piermarco Cannarsa and Stefano Finzi Vita, presents a review of mathematical models for formation of sand piles and dunes. In nature and everyday life various materials appear as conglomerates