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Special Section: 2022 Copper Mountain Conference on Iterative Methods SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-19 Andreas Stathopoulos
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page Si-Si, April 2024.
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Rounding-Error Analysis of Multigrid [math]-Cycles SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-19 Stephen F. McCormick, Rasmus Tamstorf
SIAM Journal on Scientific Computing, Ahead of Print. Abstract. Earlier work on rounding-error analysis of multigrid was restricted to cycles that used one relaxation step before coarsening and none afterwards. The present paper extends this analysis to two-grid methods that use one relaxation step both before and after coarsening. The analysis is based on floating point arithmetic and focuses on a
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A Reduced Conjugate Gradient Basis Method for Fractional Diffusion SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-18 Yuwen Li, Ludmil Zikatanov, Cheng Zuo
SIAM Journal on Scientific Computing, Ahead of Print. Abstract. This work is on a fast and accurate reduced basis method for solving discretized fractional elliptic partial differential equations (PDEs) of the form [math] by rational approximation. A direct computation of the action of such an approximation would require solving multiple (20[math]30) large-scale sparse linear systems. Our method constructs
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Energy Stable and Conservative Dynamical Low-Rank Approximation for the Su–Olson Problem SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-18 Lena Baumann, Lukas Einkemmer, Christian Klingenberg, Jonas Kusch
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page B137-B158, April 2024. Abstract. Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finely resolved. A strategy to reduce such computational costs is dynamical low-rank approximation (DLRA), which represents and evolves
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Local Characteristic Decomposition–Free High-Order Finite Difference WENO Schemes for Hyperbolic Systems Endowed with a Coordinate System of Riemann Invariants SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-15 Ziyao Xu, Chi-Wang Shu
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1352-A1372, April 2024. Abstract. The weighted essentially nonoscillatory (WENO) schemes are popular high-order numerical methods for hyperbolic conservation laws. When dealing with hyperbolic systems, WENO schemes are usually used in cooperation with the local characteristic decomposition, as the componentwise WENO reconstruction/interpolation
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The Runge–Kutta Discontinuous Galerkin Method with Compact Stencils for Hyperbolic Conservation Laws SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-12 Qifan Chen, Zheng Sun, Yulong Xing
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1327-A1351, April 2024. Abstract. In this paper, we develop a new type of Runge–Kutta (RK) discontinuous Galerkin (DG) method for solving hyperbolic conservation laws. Compared with the original RKDG method, the new method features improved compactness and allows simple boundary treatment. The key idea is to hybridize two different spatial
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Enhancing Training of Physics-Informed Neural Networks Using Domain Decomposition–Based Preconditioning Strategies SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-11 Alena Kopaničáková, Hardik Kothari, George E. Karniadakis, Rolf Krause
SIAM Journal on Scientific Computing, Ahead of Print. Abstract. We propose to enhance the training of physics-informed neural networks. To this aim, we introduce nonlinear additive and multiplicative preconditioning strategies for the widely used L-BFGS optimizer. The nonlinear preconditioners are constructed by utilizing the Schwarz domain decomposition framework, where the parameters of the network
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Direct/Iterative Hybrid Solver for Scattering by Inhomogeneous Media SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-11 Oscar P. Bruno, Ambuj Pandey
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1298-A1326, April 2024. Abstract. This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities. The method relies on a hybrid direct/iterative combination of
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Multivariate Hermite Interpolation on Riemannian Manifolds SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-11 Ralf Zimmermann, Ronny Bergmann
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1276-A1297, April 2024. Abstract. In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for Hermite interpolation, the sampled derivative information is converted
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Approximating the Shape Operator with the Surface Hellan–Herrmann–Johnson Element SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-08 Shawn W. Walker
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1252-A1275, April 2024. Abstract. We present a finite element technique for approximating the surface Hessian of a discrete scalar function on triangulated surfaces embedded in [math], with or without boundary. We then extend the method to compute approximations of the full shape operator of the underlying surface using only the known
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A Direct Probing Method of an Inverse Problem for the Eikonal Equation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-05 Kazufumi Ito, Ying Liang
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1235-A1251, April 2024. Abstract. In this paper, we propose a direct probing method to solve the inverse problem of the Eikonal equation. This problem involves the determination of the inhomogeneous wave-speed distribution from first-arrival time data at measurement surfaces corresponding to distributed point sources. The viscosity solution
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Overcoming the Numerical Sign Problem in the Wigner Dynamics via Adaptive Particle Annihilation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-03 Yunfeng Xiong, Sihong Shao
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page B107-B136, April 2024. Abstract. The infamous numerical sign problem poses a fundamental obstacle to particle-based stochastic Wigner simulations in high-dimensional phase space. Although the existing particle annihilation (PA) via uniform mesh significantly alleviates the sign problem when dimensionality D [math] 4, the mesh size grows
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Computation of Two-Dimensional Stokes Flows via Lightning and AAA Rational Approximation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-03 Yidan Xue, Sarah L. Waters, Lloyd N. Trefethen
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1214-A1234, April 2024. Abstract. Low Reynolds number fluid flows are governed by the Stokes equations. In two dimensions, Stokes flows can be described by two analytic functions, known as Goursat functions. Brubeck and Trefethen [SIAM J. Sci. Comput., 44 (2022), pp. A1205–A1226] recently introduced a lightning Stokes solver that uses
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Parallel Randomized Tucker Decomposition Algorithms SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-02 Rachel Minster, Zitong Li, Grey Ballard
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1186-A1213, April 2024. Abstract. The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly
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Efficient Solution of Parameter Identification Problems with [math] Regularization SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-02 Jan Blechta, Oliver G. Ernst
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1160-A1185, April 2024. Abstract. We consider the identification of spatially distributed parameters under [math] regularization. Solving the associated minimization problem by Gauss–Newton iteration results in linearized problems to be solved in each step that can be cast as boundary value problems involving a low-rank modification of
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An Entropy Stable Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Conservation Laws SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-01 Yong Liu, Jianfang Lu, Chi-Wang Shu
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1132-A1159, April 2024. Abstract. Entropy inequalities are crucial to the well-posedness of hyperbolic conservation laws, which help to select the physically meaningful one from among the infinite many weak solutions. Recently, several high order discontinuous Galerkin (DG) methods satisfying entropy inequalities were proposed; see [T
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Dimensions of Exactly Divergence-Free Finite Element Spaces in 3D SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-04-01 L. Ridgway Scott, Tabea Tscherpel
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1102-A1131, April 2024. Abstract. We examine the dimensions of various inf-sup stable mixed finite element spaces on tetrahedral meshes in three dimensions with exact divergence constraints. More precisely, we compare the standard Scott–Vogelius elements of higher polynomial degree and low-order methods on split meshes, the Alfeld and
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A Unified Framework of the SAV-ZEC Method for a Mass-Conserved Allen–Cahn Type Two-Phase Ferrofluid Flow Model SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-29 Guo-Dong Zhang, Xiaoming He, Xiaofeng Yang
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page B77-B106, April 2024. Abstract. This article presents a mass-conserved Allen–Cahn type two-phase ferrofluid flow model and establishes its corresponding energy law. The model is a highly coupled, nonlinear saddle point system consisting of the mass-conserved Allen–Cahn equation, the Navier–Stokes equation, the magnetostatic equation, and
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Making the Nyström Method Highly Accurate for Low-Rank Approximations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-29 Jianlin Xia
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1076-A1101, April 2024. Abstract. The Nyström method is a convenient strategy to obtain low-rank approximations to kernel matrices in nearly linear complexity. Existing studies typically use the method to approximate positive semidefinite matrices with low or modest accuracies. In this work, we propose a series of heuristic strategies
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Parallel Two-Stage Reduction to Hessenberg-Triangular Form SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-28 Thijs Steel, Raf Vandebril
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page B56-B76, April 2024. Abstract. We present a two-stage algorithm for the parallel reduction of a pencil to Hessenberg-triangular form. Traditionally, two-stage Hessenberg-triangular reduction algorithms achieve high performance in the first stage but struggle to achieve high performance in the second stage. Our algorithm extends techniques
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A Semi-Lagrangian Discontinuous Galerkin Method for Drift-Kinetic Simulations on GPUs SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-28 Lukas Einkemmer, Alexander Moriggl
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page B33-B55, April 2024. Abstract. In this paper, we demonstrate the efficiency of using semi-Lagrangian discontinuous Galerkin methods to solve the drift-kinetic equation using graphic processing units (GPUs). In this setting we propose a second order splitting scheme and a two-dimensional semi-Lagrangian scheme in the poloidal plane. The
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An Incremental Tensor Train Decomposition Algorithm SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-26 Doruk Aksoy, David J. Gorsich, Shravan Veerapaneni, Alex A. Gorodetsky
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1047-A1075, April 2024. Abstract. We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the tensor train incremental core expansion (TT-ICE), improves upon the current state-of-the-art algorithms for compressing in tensor train format by developing a
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Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-15 Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page C216-C248, April 2024. Abstract. Hamilton–Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multitime case. In this paper
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On the Convergence of Monolithic Multigrid for Implicit Runge–Kutta Time Stepping of Finite Element Problems SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-13 Robert C. Kirby
SIAM Journal on Scientific Computing, Ahead of Print. Abstract. Finite element discretizations of time-dependent problems also require effective time-stepping schemes. While implicit Runge–Kutta methods provide favorable accuracy and stability properties, they give rise to large and complicated systems of equations to solve for each time step. These algebraic systems couple all Runge–Kutta stages together
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High-Order Mass- and Energy-Conserving Methods for the Nonlinear Schrödinger Equation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-12 Genming Bai, Jiashun Hu, Buyang Li
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A1026-A1046, April 2024. Abstract. A class of high-order mass- and energy-conserving methods is proposed for the nonlinear Schrödinger equation based on Gauss collocation in time and finite element discretization in space, by introducing a mass- and energy-correction post-process at every time level. The existence, uniqueness, and high-order
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Sparse Recovery of Elliptic Solvers from Matrix-Vector Products SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-12 Florian Schäfer, Houman Owhadi
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A998-A1025, April 2024. Abstract. In this work, we show that solvers of elliptic boundary value problems in [math] dimensions can be approximated to accuracy [math] from only [math] matrix-vector products with carefully chosen vectors (right-hand sides). The solver is only accessed as a black box, and the underlying operator may be unknown
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Solving the Boltzmann Equation with a Neural Sparse Representation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-11 Zhengyi Li, Yanli Wang, Hongsheng Liu, Zidong Wang, Bin Dong
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page C186-C215, April 2024. Abstract. We consider the neural sparse representation to solve the Boltzmann equation with BGK and quadratic collision models, where a network-based ansatz that can approximate the distribution function with extremely high efficiency is proposed. Precisely, fully connected neural networks are employed in the time
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Analytical Galerkin Boundary Integrals of Laplace Kernel Layer Potentials in [math] SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-11 Nail A. Gumerov, Shoken Kaneko, Ramani Duraiswami
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A974-A997, April 2024. Abstract. A method for analytical computation of the double surface integrals for all layer potential kernels associated with the Laplace Green’s function in the Galerkin boundary element method in [math] using flat triangular elements with constant densities is presented. The method uses recursive dimensionality
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A Numerical Method for the Stability Analysis of Linear Age-Structured Models with Nonlocal Diffusion SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-11 Dimitri Breda, Simone De Reggi, Rossana Vermiglio
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A953-A973, April 2024. Abstract. We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal diffusion are more challenging since the associated semigroups have no
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AAA Rational Approximation on a Continuum SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-11 Tobin A. Driscoll, Yuji Nakatsukasa, Lloyd N. Trefethen
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A929-A952, April 2024. Abstract. AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as it goes. This enables fast computation of high-accuracy rational
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Accelerating Exponential Integrators to Efficiently Solve Semilinear Advection-Diffusion-Reaction Equations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-11 Marco Caliari, Fabio Cassini, Lukas Einkemmer, Alexander Ostermann
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A906-A928, April 2024. Abstract. In this paper, we consider an approach to improve the performance of exponential Runge–Kutta integrators and Lawson schemes in cases where the solution of a related, but usually much simpler, problem can be computed efficiently. While for implicit methods such an approach is common (e.g., by using preconditioners)
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A Posteriori Local Subcell Correction of High-Order Discontinuous Galerkin Scheme for Conservation Laws on Two-Dimensional Unstructured Grids SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-08 François Vilar, Rémi Abgrall
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A851-A883, April 2024. Abstract. In this paper, we present the two-dimensional unstructured grids extension of the a posteriori local subcell correction of discontinuous Galerkin (DG) schemes introduced in [F. Vilar, J. Comput. Phys., 387 (2018), pp. 245–279]. The technique is based on the reformulation of the DG scheme as a finite-volume
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A Block Lanczos Method for Large-Scale Quadratic Minimization Problems with Orthogonality Constraints SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-08 Bo Feng, Gang Wu
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A884-A905, April 2024. Abstract. Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale QMPO. Krylov subspace methods are popular for large-scale optimization
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Neural Control of Parametric Solutions for High-Dimensional Evolution PDEs SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 Nathan Gaby, Xiaojing Ye, Haomin Zhou
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page C155-C185, April 2024. Abstract. We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order model, such as a deep neural network, to approximate the solution of a given PDE, we realize that the evolution of the model parameters
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Learning the Dynamics for Unknown Hyperbolic Conservation Laws Using Deep Neural Networks SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 Zhen Chen, Anne Gelb, Yoonsang Lee
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A825-A850, April 2024. Abstract. We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form network (CFN) in which the network learns to approximate the numerical
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An Efficient Block Rational Krylov Solver for Sylvester Equations with Adaptive Pole Selection SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 A. Casulli, L. Robol
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A798-A824, April 2024. Abstract. We present an algorithm for the solution of Sylvester equations with right-hand side of low rank. The method is based on projection onto a block rational Krylov subspace, with two key contributions with respect to the state of the art. First, we show how to maintain the last pole equal to infinity throughout
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Using Witten Laplacians to Locate Index-1 Saddle Points SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 Tony Lelièvre, Panos Parpas
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A770-A797, April 2024. Abstract. We introduce a new stochastic algorithm to locate the index-1 saddle points of a function [math], with [math] possibly large. This algorithm can be seen as an equivalent of the stochastic gradient descent which is a natural stochastic process to locate local minima. It relies on two ingredients: (i) the
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A Grid-Overlay Finite Difference Method for the Fractional Laplacian on Arbitrary Bounded Domains SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 Weizhang Huang, Jinye Shen
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A744-A769, April 2024. Abstract. A grid-overlay finite difference method is proposed for the numerical approximation of the fractional Laplacian on arbitrary bounded domains. The method uses an unstructured simplicial mesh and an overlay uniform grid for the underlying domain and constructs the approximation based on a uniform-grid finite
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A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 Danimir T. Doncevic, Alexander Mitsos, Yue Guo, Qianxiao Li, Felix Dietrich, Manuel Dahmen, Ioannis G. Kevrekidis
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A719-A743, April 2024. Abstract. Metalearning of numerical algorithms for a given task consists of the data-driven identification and adaptation of an algorithmic structure and the associated hyperparameters. To limit the complexity of the metalearning problem, neural architectures with a certain inductive bias towards favorable algorithmic
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A New ParaDiag Time-Parallel Time Integration Method SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 Martin J. Gander, Davide Palitta
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A697-A718, April 2024. Abstract. Time-parallel time integration has received a lot of attention in the high performance computing community over the past two decades. Indeed, it has been shown that parallel-in-time techniques have the potential to remedy one of the main computational drawbacks of parallel-in-space solvers. In particular
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Asymptotic Dispersion Correction in General Finite Difference Schemes for Helmholtz Problems SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-06 Pierre-Henri Cocquet, Martin J. Gander
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A670-A696, April 2024. Abstract. Most numerical approximations of frequency-domain wave propagation problems suffer from the so-called dispersion error, which is the fact that plane waves at the discrete level oscillate at a frequency different from the continuous one. In this paper, we introduce a new technique to reduce the dispersion
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Numerical Surgery for Mean Curvature Flow of Surfaces SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-05 Balázs Kovács
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A645-A669, April 2024. Abstract. A numerical algorithm for mean curvature flow of closed mean convex surfaces with surgery is proposed. The method uses a finite element–based mean curvature flow algorithm based on a coupled partial differential equation system which directly provides an approximation for mean curvature and outward unit
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Two Conjectures on the Stokes Complex in Three Dimensions on Freudenthal Meshes SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-05 Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scott
SIAM Journal on Scientific Computing, Volume 46, Issue 2, Page A629-A644, April 2024. Abstract. In recent years, a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are pressure-robust; i.e., the error estimates for the velocity do not
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LFA-Tuned Matrix-Free Multigrid Method for the Elastic Helmholtz Equation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-03-05 Rachel Yovel, Eran Treister
SIAM Journal on Scientific Computing, Ahead of Print. Abstract. We present an efficient matrix-free geometric multigrid method for the elastic Helmholtz equation, and a suitable discretization. Many discretization methods had been considered in the literature for the Helmholtz equations, as well as many solvers and preconditioners, some of which are adapted for the elastic version of the equation.
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Space-Time Reduced Basis Methods for Parametrized Unsteady Stokes Equations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-29 Riccardo Tenderini, Nicholas Mueller, Simone Deparis
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page B1-B32, February 2024. Abstract. In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of hæmodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference schemes are employed for the time integration of the
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Rapid Evaluation of Newtonian Potentials on Planar Domains SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-20 Zewen Shen, Kirill Serkh
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A609-A628, February 2024. Abstract. The accurate and efficient evaluation of Newtonian potentials over general two-dimensional domains is important for the numerical solution of Poisson’s equation and volume integral equations. In this paper, we present a simple and efficient high-order algorithm for computing the Newtonian potential over
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New Artificial Tangential Motions for Parametric Finite Element Approximation of Surface Evolution SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-20 Beiping Duan, Buyang Li
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A587-A608, February 2024. Abstract. A new class of parametric finite element methods, with a new type of artificial tangential velocity constructed at the continuous level, is proposed for solving surface evolution under geometric flows. The method is constructed by coupling the normal velocity of the geometric flow with an artificial tangential
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AONN: An Adjoint-Oriented Neural Network Method for All-At-Once Solutions of Parametric Optimal Control Problems SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-15 Pengfei Yin, Guangqiang Xiao, Kejun Tang, Chao Yang
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page C127-C153, February 2024. Abstract. Parametric optimal control problems governed by partial differential equations (PDEs) are widely found in scientific and engineering applications. Traditional grid-based numerical methods for such problems generally require repeated solutions of PDEs with different parameter settings, which is computationally
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Nonlinearly Constrained Pressure Residual (NCPR) Algorithms for Fractured Reservoir Simulation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-12 Haijian Yang, Rui Li, Chao Yang
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A561-A586, February 2024. Abstract. The constrained pressure residual (CPR) algorithm is a family of well-known and industry-standard preconditioners for large-scale reservoir simulation. The CPR algorithm is a two-stage preconditioner to deal with different blocks stage-by-stage, and is often able to effectively improve the robustness
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Data-Driven and Low-Rank Implementations of Balanced Singular Perturbation Approximation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-07 Björn Liljegren-Sailer, Ion Victor Gosea
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A483-A507, February 2024. Abstract. Balanced singular perturbation approximation (SPA) is a model order reduction method for linear time-invariant systems that guarantees asymptotic stability and for which there exists an a priori error bound. In that respect, it is similar to balanced truncation (BT). However, the reduced models obtained
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Efficient Error and Variance Estimation for Randomized Matrix Computations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-08 Ethan N. Epperly, Joel A. Tropp
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A508-A528, February 2024. Abstract. Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out
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Stable Rank-Adaptive Dynamically Orthogonal Runge–Kutta Schemes SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-08 Aaron Charous, Pierre F. J. Lermusiaux
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A529-A560, February 2024. Abstract. We develop two new sets of stable, rank-adaptive dynamically orthogonal Runge–Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular value decomposition at a greatly reduced cost while preserving
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Behavior of the Discontinuous Galerkin Method for Compressible Flows at Low Mach Number on Triangles and Tetrahedrons SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-05 Jonathan Jung, Vincent Perrier
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A452-A482, February 2024. Abstract. In this article, we are interested in the behavior of discontinuous Galerkin schemes for compressible flows in the low Mach number limit. We prove that for any numerical flux conserving exactly contacts (e.g., exact Godunov, Roe, HLLC), the numerical scheme is accurate at low Mach number flows on simplicial
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A Second-Order, Linear, [math]-Convergent, and Energy Stable Scheme for the Phase Field Crystal Equation SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-05 Xiao Li, Zhonghua Qiao
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A429-A451, February 2024. Abstract. In this paper, we present a second-order accurate and linear numerical scheme for the phase field crystal equation and prove its convergence in the discrete [math] sense. The key ingredient of the error analysis is to justify the boundedness of the numerical solution, so that the nonlinear term, treated
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Data-Driven Kernel Designs for Optimized Greedy Schemes: A Machine Learning Perspective SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-01 Tizian Wenzel, Francesco Marchetti, Emma Perracchione
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page C101-C126, February 2024. Abstract. Thanks to their easy implementation via radial basis functions (RBFs), meshfree kernel methods have proved to be an effective tool for, e.g., scattered data interpolation, PDE collocation, and classification and regression tasks. Their accuracy might depend on a length scale hyperparameter, which is often
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Staggered Schemes for Compressible Flow: A General Construction SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-01 Remi Abgrall
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A399-A428, February 2024. Abstract. This paper is focused on the approximation of the Euler equations of compressible fluid dynamics on a staggered mesh. With this aim, the flow parameters are described by the velocity, the density, and the internal energy. The thermodynamic quantities are described on the elements of the mesh, and thus
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A Numerical Domain Decomposition Method for Solving Elliptic Equations on Manifolds SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-02-01 Shuhao Cao, Lizhen Qin
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A376-A398, February 2024. Abstract. A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulations or grids on manifolds. Our method is numerically tested on some four-dimensional manifolds such as the unit sphere [math]
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TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-30 Hai V. Nguyen, Tan Bui-Thanh
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page C77-C100, February 2024. Abstract. Deep learning (DL), in particular deep neural networks, by default is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering problems in which underlying physical properties—such as stability, conservation
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Bayesian Deep Learning Framework for Uncertainty Quantification in Stochastic Partial Differential Equations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-30 Jeahan Jung, Hyomin Shin, Minseok Choi
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page C57-C76, February 2024. Abstract. Bayesian physics-informed neural networks (B-PINNs) have emerged as an efficient tool for uncertainty quantification in partial differential equations (PDEs). However, their applicability has been limited to accounting for noisy data. They fail to effectively address the uncertainty arising from the randomness
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Computing Weak Distance between the 2-Sphere and Its Nonsmooth Approximations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-30 Kazuki Koga
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A360-A375, February 2024. Abstract. A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak distance between them using the Fourier transform on the ambient space