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Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes

期刊: SIAM REVIEW, 2021; 63 (2)

The ubiquity of semilinear parabolic equations is clear from their numerous applications ranging from physics and biology to materials and social scie......

DeepXDE: A Deep Learning Library for Solving Differential Equations

期刊: SIAM REVIEW, 2021; 63 (1)

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged o......

Constructing Least-Squares Polynomial Approximations

期刊: SIAM REVIEW, 2020; 62 (2)

Polynomial approximations constructed using a least-squares approach form a ubiquitous technique in numerical computation. One of the simplest ways to......

A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods

期刊: SIAM REVIEW, 2019; 61 (1)

Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades an important research effort h......

JIF:7.22

Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study

期刊: SIAM REVIEW, 2019; 61 (4)

Whether the three-dimensional incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most chal......

JIF:7.22

Unifying Matrix Stability Concepts with a View to Applications

期刊: SIAM REVIEW, 2019; 61 (4)

Multiplicative and additive D-stability, diagonal stability, Schur D-stability, and H-stability are classical concepts which arise in studying linear ......

JIF:7.22

A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows

期刊: SIAM REVIEW, 2019; 61 (3)

We propose a new numerical technique to deal with nonlinear terms in gradient flows. By introducing a scalar auxiliary variable (SAV), we construct ef......

JIF:7.22

Second-Order Necessary Conditions for Stochastic Optimal Control Problems

期刊: SIAM REVIEW, 2018; 60 (1)

The main purpose of this paper is to present some of our recent results about the second-order necessary conditions for stochastic optimal controls wi......

JIF:7.22

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