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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
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Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-30 Jeffrey S. Ovall, Samuel E. Reynolds
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A338-A359, February 2024. Abstract. In recent years, there has been significant interest in the development of finite element methods defined on meshes that include rather general polytopes and curvilinear polygons. In the present work, we provide tools necessary to employ multiply connected mesh cells in planar domains, i.e., cells with
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New SISC Section on Scientific Machine Learning SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-24 Hans De Sterck
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page vii-viii, February 2024.
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Adaptive Precision Sparse Matrix–Vector Product and Its Application to Krylov Solvers SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-25 Stef Graillat, Fabienne Jézéquel, Theo Mary, Roméo Molina
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page C30-C56, February 2024. Abstract. We introduce a mixed precision algorithm for computing sparse matrix-vector products and use it to accelerate the solution of sparse linear systems by iterative methods. Our approach is based on the idea of adapting the precision of each matrix element to their magnitude: we split the elements into buckets
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Sketching with Spherical Designs for Noisy Data Fitting on Spheres SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-25 Shao-Bo Lin, Di Wang, Ding-Xuan Zhou
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A313-A337, February 2024. Abstract. This paper proposes a sketching strategy with spherical designs to equip the classical spherical basis function (SBF) approach for massive spherical data fitting. We conduct theoretical analysis and numerical verifications to demonstrate the feasibility of the proposed sketching strategy. From the theoretical
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A Fast Minimization Algorithm for the Euler Elastica Model Based on a Bilinear Decomposition SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-25 Zhifang Liu, Baochen Sun, Xue-Cheng Tai, Qi Wang, Huibin Chang
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A290-A312, February 2024. Abstract. The Euler elastica (EE) model with surface curvature can generate artifact-free results compared with the traditional total variation regularization model in image processing. However, strong nonlinearity and singularity due to the curvature term in the EE model pose a great challenge for one to design
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Deep Importance Sampling Using Tensor Trains with Application to a Priori and a Posteriori Rare Events SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-24 Tiangang Cui, Sergey Dolgov, Robert Scheichl
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page C1-C29, February 2024. Abstract. We propose a deep importance sampling method that is suitable for estimating rare event probabilities in high-dimensional problems. We approximate the optimal importance distribution in a general importance sampling problem as the pushforward of a reference distribution under a composition of order-preserving
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Learning Robust Marking Policies for Adaptive Mesh Refinement SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-24 Andrew Gillette, Brendan Keith, Socratis Petrides
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A264-A289, February 2024. Abstract. In this work, we revisit the marking decisions made in the standard adaptive finite element method (AFEM). Experience shows that a naïve marking policy leads to inefficient use of computational resources for adaptive mesh refinement (AMR). Consequently, using AMR in practice often involves ad-hoc or time-consuming
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A Conservative Low Rank Tensor Method for the Vlasov Dynamics SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-23 Wei Guo, Jing-Mei Qiu
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A232-A263, February 2024. Abstract. In this paper, we propose a conservative low rank tensor method to approximate nonlinear Vlasov solutions. The low rank approach is based on our earlier work [W. Guo and J.-M. Qiu, A Low Rank Tensor Representation of Linear Transport and Nonlinear Vlasov Solutions and Their Associated Flow Maps, preprint
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Riemannian Natural Gradient Methods SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-22 Jiang Hu, Ruicheng Ao, Anthony Man-Cho So, Minghan Yang, Zaiwen Wen
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A204-A231, February 2024. Abstract. This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By introducing the notion of Fisher information matrix in the manifold
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Weighted Trace-Penalty Minimization for Full Configuration Interaction SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-18 Weiguo Gao, Yingzhou Li, Hanxiang Shen
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A179-A203, February 2024. Abstract. A novel unconstrained optimization model named weighted trace-penalty minimization (WTPM) is proposed to address the extreme eigenvalue problem arising from the full configuration interaction (FCI) method. Theoretical analysis shows that the global minimizers of the WTPM objective function are the desired
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BDDC Preconditioners for Virtual Element Approximations of the Three-Dimensional Stokes Equations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-17 Tommaso Bevilacqua, Franco Dassi, Stefano Zampini, Simone Scacchi
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A156-A178, February 2024. Abstract. The virtual element method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a balancing domain decomposition by constraints (BDDC) preconditioner that allows using the conjugate
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A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-17 Ren-jun Qi, Xuan Zhao
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A130-A155, February 2024. Abstract. A unified discrete gradient structure of the second order nonuniform integral averaged approximations for the Caputo fractional derivative and the Riemann–Liouville fractional integral is established in this paper. The required constraint of the step-size ratio is weaker than that found in the literature
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pISTA: Preconditioned Iterative Soft Thresholding Algorithm for Graphical Lasso SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-16 Gal Shalom, Eran Treister, Irad Yavneh
SIAM Journal on Scientific Computing, Ahead of Print. Abstract. We propose a novel quasi-Newton method for solving the sparse inverse covariance estimation problem also known as the graphical least absolute shrinkage and selection operator (GLASSO). This problem is often solved using a second-order quadratic approximation. However, in such algorithms the Hessian term is complex and computationally
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A Multilevel Method for Many-Electron Schrödinger Equations Based on the Atomic Cluster Expansion SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-16 Dexuan Zhou, Huajie Chen, Cheuk Hin Ho, Christoph Ortner
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A105-A129, February 2024. Abstract. The atomic cluster expansion (ACE) [R. Drautz, Phys. Rev. B, 99 (2019), 014104] yields a highly efficient and interpretable parameterization of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we extend the practical applicability
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An Iterative Solver for the HPS Discretization Applied to Three Dimensional Helmholtz Problems SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-16 José Pablo Lucero Lorca, Natalie Beams, Damien Beecroft, Adrianna Gillman
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A80-A104, February 2024. Abstract. This manuscript presents an efficient solver for the linear system that arises from the hierarchical Poincaré–Steklov (HPS) discretization of three dimensional variable coefficient Helmholtz problems. Previous work on the HPS method has tied it with a direct solver. This work is the first efficient iterative
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A New Discretely Divergence-Free Positivity-Preserving High-Order Finite Volume Method for Ideal MHD Equations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-12 Shengrong Ding, Kailiang Wu
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A50-A79, February 2024. Abstract. This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously preserves two critical physical constraints: a discretely divergence-free (DDF) constraint on the magnetic field and the positivity-preserving
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Analysis of Schwarz Methods for Convected Helmholtz-Like Equations SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-10 M. J. Gander, A. Tonnoir
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A1-A22, February 2024. Abstract. We present and analyze Schwarz domain decomposition methods for a general diffusion problem with complex advection. The complex advection term changes completely the nature of the solution and makes it more Helmholtz like. In the case of constant parameters, we analyze in detail the influence of the outer
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On Optimal Zero-Padding of Kernel Truncation Method SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-10 Xin Liu, Qinglin Tang, Shaobo Zhang, Yong Zhang
SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A23-A49, February 2024. Abstract. The kernel truncation method (KTM) is a commonly used algorithm to compute the convolution-type nonlocal potential [math] where the convolution kernel [math] might be singular at the origin and/or far-field and the density [math] is smooth and fast decaying. In KTM, in order to capture the Fourier integrand’s
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Locally Conservative and Flux Consistent Iterative Methods SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2024-01-09 Viktor Linders, Philipp Birken
SIAM Journal on Scientific Computing, Ahead of Print. Abstract. Conservation and consistency are fundamental properties of discretizations of conservation laws, necessary to ensure physically meaningful solutions. In the context of systems of nonlinear hyperbolic conservation laws, conservation and consistency additionally play an important role in convergence theory via the Lax–Wendroff theorem. Here
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A Family of Immersed Finite Element Spaces and Applications to Three-Dimensional [math] Interface Problems SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2023-12-15 Long Chen, Ruchi Guo, Jun Zou
SIAM Journal on Scientific Computing, Volume 45, Issue 6, Page A3121-A3149, December 2023. Abstract. Efficient and accurate computation of [math] interface problems is of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in three-dimensional (3D) computation as they can circumvent generating complex 3D interface-fitted meshes. However, many unfitted
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Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2023-12-14 Mark Ainsworth, Charles Parker
SIAM Journal on Scientific Computing, Volume 45, Issue 6, Page A3095-A3120, December 2023. Abstract. We introduce and analyze a statically condensed iterated penalty (SCIP) method for solving incompressible flow problems discretized with [math]th order Scott–Vogelius elements. While the standard iterated penalty method is often the preferred algorithm for computing the discrete solution, it requires
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Dynamical Systems–Based Neural Networks SIAM J. Sci. Comput. (IF 3.1) Pub Date : 2023-12-12 Elena Celledoni, Davide Murari, Brynjulf Owren, Carola-Bibiane Schönlieb, Ferdia Sherry
SIAM Journal on Scientific Computing, Volume 45, Issue 6, Page A3071-A3094, December 2023. Abstract. Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is some underlying geometric structure inherent to the data or to the function to approximate, it is often desirable to take