Advances in Computational Mathematics

Article	Citations
Data-driven uncertainty quantification in macroscopic traffic flow models	94
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	47
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	27
Dictionary-based model reduction for state estimation	26
Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow	24
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	24
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	15
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	14
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution I: fundamentals	14
Variational methods for solving numerically magnetostatic systems	13
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	13
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	12
Tensor rank bounds for point singularities in ℝ3	12
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	11
Averaging property of wedge product and naturality in discrete exterior calculus	11
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	11
WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation	10
Implicit finite volume method with a posteriori limiting for transport networks	10
Uniqueness of phase retrieval from three measurements	10
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	10
Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements	10
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	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

Adaptive quarklet tree approximation	9
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
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains	8
Max filtering with reflection groups	8
Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization	7
Approximation in the extended functional tensor train format	7
Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations	7
Splitting scheme for backward doubly stochastic differential equations	7
Adaptive and local regularization for data fitting by tensor-product spline surfaces	7
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
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
An a posteriori error estimate for a dual mixed method applied to Stokes system with non-null source terms	7
Randomized continuous frames in time-frequency analysis	7
A fast time domain solver for the equilibrium Dyson equation	6
A posteriori error analysis and adaptivity for a VEM discretization of the Navier–Stokes equations	6
An efficient computation of the inverse of the single layer matrix for the resolution of the linear elasticity problem in BEM	6
A fast and oblivious matrix compression algorithm for Volterra integral operators	6
An extrapolated Crank-Nicolson virtual element scheme for the nematic liquid crystal flows	6
On a non-uniform $$\alpha $$-robust IMEX-L1 mixed FEM for time-fractional PIDEs	6
Error estimates for mixed and hybrid FEM for elliptic optimal control problems with penalizations	6
On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems	6
A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem	6
The role of mesh quality and mesh quality indicators in the virtual element method	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
A hybrid boundary integral-PDE approach for the approximation of the demagnetization potential in micromagnetics	6
Simultaneous identification of initial value and source strength in a transmission problem for a parabolic equation	6
An adaptive finite element DtN method for the acoustic-elastic interaction problem	5
Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces	5
$$\mathcal {H}_2$$ optimal rational approximation on general domains	5
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems	5
Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels	5
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	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
Convergence analysis of the Dirichlet-Neumann Waveform Relaxation algorithm for time fractional sub-diffusion and diffusion-wave equations in heterogeneous media	5
Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies	5
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	4
Generalised Wendland functions for the sphere	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
Continuous window functions for NFFT	4
Approximation of curve-based sleeve functions in high dimensions	4
Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes	4
Fast gradient methods for uniformly convex and weakly smooth problems	4

On convergence of the generalized Lanczos trust-region method for trust-region subproblems	4
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	4
Approximation of functions from Korobov spaces by deep convolutional neural networks	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
Frame-normalizable sequences	4
Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus	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
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
One-step optimization method for equilibrium problems	4
Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations	3
Translation partitions of unity, symmetry properties, and Gabor frames	3
Comparison of integral equations for the Maxwell transmission problem with general permittivities	3
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	3
Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem	3
A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems	3
A new approach to proper orthogonal decomposition with difference quotients	3
Exponentially fitted methods with a local energy conservation law	3
Semi-active damping optimization of vibrational systems using the reduced basis method	3
Efficient algorithms for Tucker decomposition via approximate matrix multiplication	3
Exponential mean-square stability properties of stochastic linear multistep methods	3
Inverse problem for determining free parameters of a reduced turbulent transport model for tokamak plasma	3
Uniform error bound of a conservative fourth-order compact finite difference scheme for the Zakharov system in the subsonic regime	3
The hot spots conjecture can be false: some numerical examples	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
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry	3
An alternative approach for order conditions of Runge-Kutta-Nyström methods	3
Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $$L^p(\mathbb R^n)$$	3
H2Opus: a distributed-memory multi-GPU software package for non-local operators	3
Weighted positive nonlinear finite volume method for dominated anisotropic diffusive equations	3
Mixed precision path tracking for polynomial homotopy continuation	3
Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery	3
Low-rank exponential integrators for stiff differential Riccati equations	3
Convergence rates for boundedly regular systems	3
An adaptive finite volume method for the diffraction grating problem with the truncated DtN boundary condition	3
Development and analysis of two new finite element schemes for a time-domain carpet cloak model	3
A mixed virtual element method for nearly incompressible linear elasticity equations	3
Error analysis of a hybrid numerical method for optimal control problem governed by parabolic PDEs in random cylindrical domains	3
Optimal control for a coupled spin-polarized current and magnetization system	3
Full recovery from point values: an optimal algorithm for Chebyshev approximability prior	3
A Grassmann manifold handbook: basic geometry and computational aspects	3
Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes	3
Asymptotic convergence analysis and influence of initial guesses on composite Anderson acceleration	3
Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations	3
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	2
An optimal ansatz space for moving least squares approximation on spheres	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
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	2
Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem	2
Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals	2
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	2
New low-order mixed finite element methods for linear elasticity	2
Space-time error estimates for deep neural network approximations for differential equations	2
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	2
Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise	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
Exponential tractability of L2-approximation with function values	2
On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation	2
Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber	2
Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	2
A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions	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
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
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	2
Balanced truncation for quadratic-bilinear control systems	2
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	2
Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method	2
A family of C1 quadrilateral finite elements	2
Computing low-rank rightmost eigenpairs of a class of matrix-valued linear operators	2
Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets	2
Persistence Curves: A canonical framework for summarizing persistence diagrams	2

Numerical methods for forward fractional Feynman–Kac equation	2
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification	2
Explicit multivariate approximations from cell-average data	2
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions	2
Error bounds for a least squares meshless finite difference method on closed manifolds	2
The essence of invertible frame multipliers in scalability	2
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	2
Stable approximate evaluation of unbounded matrix operator and its application to an inverse problem	2
Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	2
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	2
Accurate singular values of a class of parameterized negative matrices	2
Numerical investigation into the dependence of the Allen–Cahn equation on the free energy	2
Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds	2
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	2
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	2
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	2
On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes	1
Limitations of neural network training due to numerical instability of backpropagation	1
A discontinuous plane wave neural network method for Helmholtz equation and time-harmonic Maxwell’s equations	1
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems	1
High-resolution signal recovery via generalized sampling and functional principal component analysis	1
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes	1
An efficient rotational pressure-correction schemes for 2D/3D closed-loop geothermal system	1
Analysis of a time filtered finite element method for the unsteady inductionless MHD equations	1
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	1
Robust low tubal rank tensor recovery using discrete empirical interpolation method with optimized slice/feature selection	1
Online identification and control of PDEs via reinforcement learning methods	1
An electrical engineering perspective on naturality in computational physics	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
Ternary image decomposition with automatic parameter selection via auto- and cross-correlation	1
A new local projection stabilization virtual element method for the Oseen problem on polygonal meshes	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
On an accurate numerical integration for the triangular and tetrahedral spectral finite elements	1
An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities	1
Noniterative localized exponential time differencing methods for hyperbolic conservation laws	1
Learning via variably scaled kernels	1
Correction: Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	1
When is there a representer theorem?	1
A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations	1
Randomized greedy magic point selection schemes for nonlinear model reduction	1
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	1
A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation	1
Interpolatory model reduction of quadratic-bilinear dynamical systems with quadratic-bilinear outputs	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
An inertial extragradient algorithm for equilibrium and generalized split null point problems	1
Sobolev regularity of bivariate isogeometric finite element spaces in case of a geometry map with degenerate corner	1
Inexact GMRES iterations and relaxation strategies with fast-multipole boundary element method	1
Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction	1
Matching pursuit with unbounded parameter domains	1
Linear approximation method for solving split inverse problems and its applications	1
The adjoint double layer potential on smooth surfaces in $$\mathbb {R}^3$$ and the Neumann problem	1
Convergence analysis of oversampled collocation boundary element methods in 2D	1
Convergence of projected subgradient method with sparse or low-rank constraints	1
Piecewise orthogonal collocation for computing periodic solutions of renewal equations	1
A high-order algorithm for time-domain scattering in three dimensions	1
Extrapolated regularization of nearly singular integrals on surfaces	1
Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials	1
Half-quadratic alternating direction method of multipliers for robust orthogonal tensor approximation	1
Clothoid fitting and geometric Hermite subdivision	1
Finding roots of complex analytic functions via generalized colleague matrices	1
A theoretical study of a bilateral term with a tensor-based fourth-order PDE for image super-resolution	1
Efficient computation of the sinc matrix function for the integration of second-order differential equations	1
Interpolating refinable functions and $$n_s$$-step interpolatory subdivision schemes	1
Exact posterior distribution for nonconjugate Pareto models	1
Correction: A Grassmann manifold handbook: basic geometry and computational aspects	1
One-bit Sigma-Delta modulation on the circle	1
Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems	1
Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation	1
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations	1
Linear/Ridge expansions: enhancing linear approximations by ridge functions	1
Local behaviors of Fourier expansions for functions of limited regularities	1
Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects	1
Numerical analysis of a stabilized scheme applied to incompressible elasticity problems with Dirichlet and with mixed boundary conditions	1
Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise	1
A posteriori error estimates for wave maps into spheres	1
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	1
New degrees of freedom for differential forms on cubical meshes	1
An optimal control framework for adaptive neural ODEs	1
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem	1
Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data	1
Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation	1
A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model	1
A fast solver for elastic scattering from axisymmetric objects by boundary integral equations	1
Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data	1
Fast numerical integration of highly oscillatory Bessel transforms with a Cauchy type singular point and exotic oscillators	1
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation	1
Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery	1
Analysis of a $$\varvec{P}_1\oplus \varvec{RT}_0$$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions	1
A quasi-boundary-value method for solving a nonlinear space-fractional backward diffusion problem	1