Advances in Computational Mathematics

Article	Citations
Data-driven uncertainty quantification in macroscopic traffic flow models	101
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	51
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	28
Dictionary-based model reduction for state estimation	27
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	26
Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow	25
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	15
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution I: fundamentals	15
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	14
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	14
Variational methods for solving numerically magnetostatic systems	13
Tensor rank bounds for point singularities in ℝ3	13
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	13
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	12
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	12
Averaging property of wedge product and naturality in discrete exterior calculus	12
Uniqueness of phase retrieval from three measurements	11
Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements	11
Implicit finite volume method with a posteriori limiting for transport networks	11
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	10
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	10
Adaptive quarklet tree approximation	9
WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation	9
Toward a certified greedy Loewner framework with minimal sampling	9
Weak approximation of SDEs for tempered distributions and applications	9

Randomized GCUR decompositions	9
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains	8
Max filtering with reflection groups	8
Adaptive and local regularization for data fitting by tensor-product spline surfaces	8
Stray field computation by inverted finite elements: a new method in micromagnetic simulations	8
Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations	8
Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problem	8
SVD-based algorithms for tensor wheel decomposition	7
A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction	7
Non-symmetric isogeometric FEM-BEM couplings	7
An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms	7
A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations	7
Accurate computations with matrices related to bases {tieλt}	7
Approximation in the extended functional tensor train format	7
Randomized continuous frames in time-frequency analysis	7
Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization	7
Splitting scheme for backward doubly stochastic differential equations	7
Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations	7
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	7
Error estimates for mixed and hybrid FEM for elliptic optimal control problems with penalizations	6
An H1 convergence of the spectral method for the time-fractional non-linear diffusion equations	6
Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul’yev methods	6
Simultaneous identification of initial value and source strength in a transmission problem for a parabolic equation	6
The role of mesh quality and mesh quality indicators in the virtual element method	6
An efficient computation of the inverse of the single layer matrix for the resolution of the linear elasticity problem in BEM	6
An adaptive finite element DtN method for the acoustic-elastic interaction problem	6
A fast time domain solver for the equilibrium Dyson equation	6
A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem	6
A posteriori error analysis and adaptivity for a VEM discretization of the Navier–Stokes equations	6
On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems	6
A fast and oblivious matrix compression algorithm for Volterra integral operators	6
On a non-uniform $$\alpha $$-robust IMEX-L1 mixed FEM for time-fractional PIDEs	6
A hybrid boundary integral-PDE approach for the approximation of the demagnetization potential in micromagnetics	5
Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces	5
Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies	5
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	5
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	5
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems	5
Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus	5
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields	5
A posteriori virtual element method for the acoustic vibration problem	5
$$\mathcal {H}_2$$ optimal rational approximation on general domains	5
Generalised Wendland functions for the sphere	5
On convergence of the generalized Lanczos trust-region method for trust-region subproblems	4
High-order corrected trapezoidal rules for a class of singular integrals	4
Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations	4
Approximation of curve-based sleeve functions in high dimensions	4
Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes	4
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	4
Convergence analysis of the Dirichlet-Neumann Waveform Relaxation algorithm for time fractional sub-diffusion and diffusion-wave equations in heterogeneous media	4

A rational RBF interpolation with conditionally positive definite kernels	4
Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems	4
Correction: A posteriori virtual element method for the acoustic vibration problem	4
A block-randomized stochastic method with importance sampling for CP tensor decomposition	4
Numerical analysis of a chemotaxis model for tumor invasion	4
A second-order scheme based on blended BDF for the incompressible MHD system	4
One-step optimization method for equilibrium problems	4
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	4
Frame-normalizable sequences	4
Approximation of functions from Korobov spaces by deep convolutional neural networks	4
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology	4
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes	4
A scaling fractional asymptotical regularization method for linear inverse problems	4
Fast gradient methods for uniformly convex and weakly smooth problems	4
Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets	3
Optimal control for a coupled spin-polarized current and magnetization system	3
A new approach to proper orthogonal decomposition with difference quotients	3
Exponentially fitted methods with a local energy conservation law	3
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	3
Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations	3
Mixed precision path tracking for polynomial homotopy continuation	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	3
Comparison of integral equations for the Maxwell transmission problem with general permittivities	3
Development and analysis of two new finite element schemes for a time-domain carpet cloak model	3
Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	3
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	3
Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	3
A Grassmann manifold handbook: basic geometry and computational aspects	3
An alternative approach for order conditions of Runge-Kutta-Nyström methods	3
H2Opus: a distributed-memory multi-GPU software package for non-local operators	3
Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
Efficient algorithms for Tucker decomposition via approximate matrix multiplication	3
Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations	3
An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition	3
The hot spots conjecture can be false: some numerical examples	3
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	3
Error analysis of a hybrid numerical method for optimal control problem governed by parabolic PDEs in random cylindrical domains	3
Obstructions for Gabor frames of the second-order B-spline	3
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	3
Semi-active damping optimization of vibrational systems using the reduced basis method	3
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	3
Exponential mean-square stability properties of stochastic linear multistep methods	3
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry	3
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	3
Convergence rates for boundedly regular systems	3
Low-rank exponential integrators for stiff differential Riccati equations	3
A mixed virtual element method for nearly incompressible linear elasticity equations	3
A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes	3
A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform	3
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	3
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds	2
Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise	2
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	2
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	2
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	2
A sparse approximation for fractional Fourier transform	2
Explicit multivariate approximations from cell-average data	2
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	2
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	2
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	2
Balanced truncation for quadratic-bilinear control systems	2
New low-order mixed finite element methods for linear elasticity	2
A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation	2
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	2
Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	2
Computing low-rank rightmost eigenpairs of a class of matrix-valued linear operators	2
A family of C1 quadrilateral finite elements	2
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification	2
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	2
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	2
Solving elliptic optimal control problems via neural networks and optimality system	2
An optimal ansatz space for moving least squares approximation on spheres	2
Exponential tractability of L2-approximation with function values	2
Numerical methods for forward fractional Feynman–Kac equation	2
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	2
A stochastic perturbation analysis of the QR decomposition and its applications	2
Correction to: Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian	2

The essence of invertible frame multipliers in scalability	2
Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method	2
Space-time error estimates for deep neural network approximations for differential equations	2
Accurate singular values of a class of parameterized negative matrices	2
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	2
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	2
Stable approximate evaluation of unbounded matrix operator and its application to an inverse problem	2
Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber	2
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	2
Persistence Curves: A canonical framework for summarizing persistence diagrams	2
Decoupled weak Galerkin finite element method for Maxwell’s equations	2
A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions	2
On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation	2
Computing the action of the matrix generating function of Bernoulli polynomials on a vector with an application to non-local boundary value problems	2
Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem	2
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	2
Complex-scaled infinite elements for resonance problems in heterogeneous open systems	1
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes	1
One-bit Sigma-Delta modulation on the circle	1
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	1
Linear approximation method for solving split inverse problems and its applications	1
Matching pursuit with unbounded parameter domains	1
Two-scale finite element discretizations for nonlinear eigenvalue problems in quantum physics	1
Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation	1
On the stability of the representation of finite rank operators	1
A high-order algorithm for time-domain scattering in three dimensions	1
Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction	1
A fast solver for elastic scattering from axisymmetric objects by boundary integral equations	1
Half-quadratic alternating direction method of multipliers for robust orthogonal tensor approximation	1
An electrical engineering perspective on naturality in computational physics	1
Inexact GMRES iterations and relaxation strategies with fast-multipole boundary element method	1
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation	1
When is there a representer theorem?	1
Efficient computation of the sinc matrix function for the integration of second-order differential equations	1
Exact posterior distribution for nonconjugate Pareto models	1
Correction: A Grassmann manifold handbook: basic geometry and computational aspects	1
A theoretical study of a bilateral term with a tensor-based fourth-order PDE for image super-resolution	1
High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation	1
An efficient rotational pressure-correction schemes for 2D/3D closed-loop geothermal system	1
Extrapolated regularization of nearly singular integrals on surfaces	1
The Kolmogorov N-width for linear transport: exact representation and the influence of the data	1
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	1
A discontinuous plane wave neural network method for Helmholtz equation and time-harmonic Maxwell’s equations	1
An inertial extragradient algorithm for equilibrium and generalized split null point problems	1
Fast numerical integration of highly oscillatory Bessel transforms with a Cauchy type singular point and exotic oscillators	1
Numerical analysis of a stabilized scheme applied to incompressible elasticity problems with Dirichlet and with mixed boundary conditions	1
Small errors imply large evaluation instabilities	1
The $$L_q$$-weighted dual programming of the linear Chebyshev approximation and an interior-point method	1
A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model	1
Convergence analysis of oversampled collocation boundary element methods in 2D	1
Convergence of projected subgradient method with sparse or low-rank constraints	1
Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data	1
A posteriori error estimates for wave maps into spheres	1
On an accurate numerical integration for the triangular and tetrahedral spectral finite elements	1
Piecewise orthogonal collocation for computing periodic solutions of renewal equations	1
An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities	1
Correction: Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	1
Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects	1
Analysis of a $$\varvec{P}_1\oplus \varvec{RT}_0$$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions	1
High-resolution signal recovery via generalized sampling and functional principal component analysis	1
Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery	1
Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise	1
Limitations of neural network training due to numerical instability of backpropagation	1
Randomized greedy magic point selection schemes for nonlinear model reduction	1
Robust low tubal rank tensor recovery using discrete empirical interpolation method with optimized slice/feature selection	1
Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian	1
Sobolev regularity of bivariate isogeometric finite element spaces in case of a geometry map with degenerate corner	1
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations	1
Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling	1
Error bounds for a least squares meshless finite difference method on closed manifolds	1
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition	1
Local behaviors of Fourier expansions for functions of limited regularities	1
Noniterative localized exponential time differencing methods for hyperbolic conservation laws	1
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	1
An optimal control framework for adaptive neural ODEs	1
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	1
New degrees of freedom for differential forms on cubical meshes	1
Ternary image decomposition with automatic parameter selection via auto- and cross-correlation	1
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem	1
Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials	1
A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations	1
Online identification and control of PDEs via reinforcement learning methods	1
Analysis of a time filtered finite element method for the unsteady inductionless MHD equations	1
Finding roots of complex analytic functions via generalized colleague matrices	1
Interpolating refinable functions and $$n_s$$-step interpolatory subdivision schemes	1
Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems	1
Linear/Ridge expansions: enhancing linear approximations by ridge functions	1
Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data	1
On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes	1
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	1
A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation	1
The adjoint double layer potential on smooth surfaces in $$\mathbb {R}^3$$ and the Neumann problem	1
An unconditionally stable and $$L^2$$ optimal quadratic finite volume scheme over triangular meshes for anisotropic elliptic equations	1
A quasi-boundary-value method for solving a nonlinear space-fractional backward diffusion problem	1
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems	1