Showing papers in "SIAM Journal on Scientific Computing in 2021"
TL;DR: The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge as discussed by the authors, and such constrai...
Abstract: The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constrai...
227 citations
TL;DR: Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics as discussed by the authors, and topology optimization is an important form of inv...
Abstract: Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is an important form of inv...
62 citations
TL;DR: A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented in this article.
Abstract: A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton--Jacobi--Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The...
50 citations
TL;DR: It is proved that for stochastic rounding the rounding errors are mean independent random variables with zero mean, implying that for a wide range of linear algebra computations the backward error for stoChastic rounding is unconditionally bounded by a multiple of $\sqrt{n}u$ to first order, with a certain probability.
Abstract: Stochastic rounding rounds a real number to the next larger or smaller floating-point number with probabilities 1 minus the relative distances to those numbers. It is gaining attention in deep lear...
41 citations
TL;DR: The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case as discussed by the authors.
Abstract: The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case...
40 citations
TL;DR: Numerical results show that the two-fidelity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.
Abstract: This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on a linear control variate framework. The approach allows for rigorous multifidelity extensions of the EnKF, ...
37 citations
TL;DR: In this paper, a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation was proposed, which is shown to be unconditionally stable in a variational setting.
Abstract: In this work, we propose a Crank--Nicolson-type scheme with variable steps for the time fractional Allen--Cahn equation. The proposed scheme is shown to be unconditionally stable (in a variational ...
36 citations
TL;DR: The maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appropriate initia...
Abstract: The maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appropriate initia...
36 citations
TL;DR: A key novel feature of the gradient reconstruction is to incorporate a jump term across the interface, thereby releasing the Nitsche penalty parameter from the constraint of being large enough.
Abstract: We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to approximate elliptic interface problems by means of a consistent penalty methoda la Nitsche. The curved interface can cut through the mesh cells in a rather general fashion. Robustness with respect to the cuts is achieved by using a cell-agglomeration technique, and robustness with respect to the contrast in the diffusion coefficients is achieved by using a different gradient reconstruction on each side of the interface. A key novel feature of the gradient reconstruction is to incorporate a jump term across the interface, thereby releasing the Nitsche penalty parameter from the constraint of being large enough. Error estimates with optimal convergence rates are established. A robust cell-agglomeration procedure limiting the agglomerations to the nearest neighbors is devised. Numerical simulations for various interface shapes corroborate the theoretical results.
35 citations
TL;DR: The binary fluid surfactant phase-field model, coupled with two Cahn--Hilliard equations and Navier--Stokes equations, is a very complex nonlinear system, which poses many challenges to the design of integrated circuits.
Abstract: The binary fluid surfactant phase-field model, coupled with two Cahn--Hilliard equations and Navier--Stokes equations, is a very complex nonlinear system, which poses many challenges to the design ...
34 citations
TL;DR: In this paper, optimal feedback control for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which is notoriously difficult when the state dimension is large.
Abstract: Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Ex...
TL;DR: In this paper, a space-time finite element method was proposed for the numerical solution of parabolic optimal control problems using Babuska's polynomial-time method on fully unstructured simplicial space time meshes.
Abstract: This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babuska'...
TL;DR: The random feature model is a parametric approximation to kernel interpolation or regression methods as discussed by the authors, and it is typically used to approximate functions map functions map, and it can be used to estimate functions map.
Abstract: Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions map...
TL;DR: In this article, a sparse approximate inverse inverse Cholesky factor of a dense covariance matrix is computed by minimizing the Kullback-Leibler divergence between the Gaussian distributions.
Abstract: We propose to compute a sparse approximate inverse Cholesky factor $L$ of a dense covariance matrix $\Theta$ by minimizing the Kullback--Leibler divergence between the Gaussian distributions $\math...
TL;DR: In this paper, a random batch Ewald (RBE) method was developed for molecular dynamics simulations of particle systems with long-range Coulomb interactions, which achieves an O(N)$ complexity in each step of simulat...
Abstract: We develop a random batch Ewald (RBE) method for molecular dynamics simulations of particle systems with long-range Coulomb interactions, which achieves an $O(N)$ complexity in each step of simulat...
TL;DR: An algorithm is developed that can be faster, given an arithmetic of precision lower than the working precision as well as (optionally) one of higher precision, and is extended to solve a linear least squares problem with a well conditioned coefficient matrix by forming and solving the normal equations.
Abstract: What is the fastest way to solve a linear system $Ax= b$ in arithmetic of a given precision when $A$ is symmetric positive definite and otherwise unstructured? The usual answer is by Cholesky facto...
TL;DR: A robust multilevel additive Schwarz preconditioner where at each level the condition number is bounded, ensuring a fast convergence for each nested solver.
Abstract: In this paper we present a multilevel preconditioner based on overlapping Schwarz methods for symmetric positive definite (SPD) matrices. Robust two-level Schwarz preconditioners exist in the literature to guarantee fast convergence of Krylov methods. As long as the dimension of the coarse space is reasonable, that is, exact solvers can be used efficiently, two-level methods scale well on parallel architectures. However, the factorization of the coarse space matrix may become costly at scale. An alternative is then to use an iterative method on the second level, combined with an algebraic preconditioner, such as a one-level additive Schwarz preconditioner. Nevertheless, the condition number of the resulting preconditioned coarse space matrix may still be large. One of the difficulties of using more advanced methods, like algebraic multigrid or even two-level overlapping Schwarz methods, to solve the coarse problem is that the matrix does not arise from a partial differential equation (PDE) anymore. We introduce in this paper a robust multilevel additive Schwarz preconditioner where at each level the condition number is bounded, ensuring a fast convergence for each nested solver. Furthermore, our construction does not require any additional information than for building a two-level method, and may thus be seen as an algebraic extension.
TL;DR: In this paper, the generalized multivariate transfer functions for polynomial systems are defined and a model-order reduction scheme is proposed for the generalized transfer functions. But this scheme is not suitable for general linear systems.
Abstract: In this work, we investigate a model-order reduction scheme for polynomial systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at c...
TL;DR: Two finite difference numerical schemes are proposed and analyzed for the droplet liquid film model with a singular Lennard--Jones energy potential involved and both first and second schemes show promising results.
Abstract: In this paper, two finite difference numerical schemes are proposed and analyzed for the droplet liquid film model with a singular Lennard--Jones energy potential involved Both first and second or
TL;DR: In this article, shape optimization problems are considered as optimal control problems via the method of mappings, instead of optimizing over a set of admissible shapes, a reference domain is introduced.
Abstract: In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes, a reference domain is introduc...
TL;DR: It is proved that convergence of Anderson acceleration for a class of nonsmooth fixed-point problems for which the nonlinearities can be split into a smooth contractive part and a nonsm smooth part which has a smoothcontractive part.
Abstract: We prove convergence of Anderson acceleration for a class of nonsmooth fixed-point problems for which the nonlinearities can be split into a smooth contractive part and a nonsmooth part which has a...
TL;DR: This work considers nonlinear convergence acceleration methods for fixed-point iteration of AA, nonlinear GMRES, and Nesterov-type acceleration, and determines coefficients that result in optimal asymptotic convergence factors, given knowledge of the spectrum of q'(x) at the fixed point.
Abstract: We consider nonlinear convergence acceleration methods for fixed-point iteration $x_{k+1}=q(x_k)$, including Anderson acceleration (AA), nonlinear GMRES (NGMRES), and Nesterov-type acceleration (co...
TL;DR: The discretisation in time of the Vlasov-Maxwell equations is extended to curvilinear coordinates and several (semi-)implicit methods either based on a Hamiltonian splitting or a discrete gradient method combined with an antisymmetric splitting of the Poisson matrix are discussed.
Abstract: Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vlasov--Maxwell equ...
TL;DR: In this article, a localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems, and the new method benefits from...
Abstract: In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The new method benefits from...
TL;DR: A novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference, union and intersection, which involves multiple independent, generally non-conforming and trimmed spline patches.
Abstract: We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union, and intersection. Particular...
TL;DR: In this article, numerical approximations of a phase field model for two-phase ferrofluids are presented, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic e...
Abstract: We consider in this paper numerical approximations of a phase field model for two-phase ferrofluids, which consists of the Navier--Stokes equations, the Cahn--Hilliard equation, the magnetostatic e...
TL;DR: In this article, a quality-Bayesian approach combining the direct sampling method and the Bayesian inversion is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial sampling.
Abstract: A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial ...
TL;DR: This paper presents an algorithm to perform a systematic exploratory search for the solutions of the optimization problem via second-order methods without a good initial guess, which combines the techniques of deflation, barrier methods and primal-dual active set solvers in a novel way.
Abstract: Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promot...
TL;DR: In this paper, a stabilizer-free and pressure-robust weak Galerkin finite element method for the Stokes equations with superconvergence on polytopal mesh in the primary velocity-preserving system was proposed.
Abstract: In this paper, we propose a new stabilizer-free and pressure-robust weak Galerkin finite element method for the Stokes equations with superconvergence on polytopal mesh in the primary velocity-pres...
TL;DR: This work applies a new scalar auxiliary variable approach to Keller--Segel and Poisson--Nernst--Planck equations and constructs efficient numerical schemes which, in addition to being positivity/bound preserving and energy dissipative, also conserve mass.
Abstract: We propose a new method to construct high-order, linear, positivity/bound preserving and unconditionally energy stable schemes for general dissipative systems whose solutions are positivity/bound p