Advances in Computational Mathematics

Article	Citations
Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation	74
An all-frequency stable integral system for Maxwell’s equations in 3-D penetrable media: continuous and discrete model analysis	43
On the balanced truncation error bound and sign parameters from arrowhead realizations	25
An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane	23
Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling	22
The Kolmogorov N-width for linear transport: exact representation and the influence of the data	20
An alternative approach for order conditions of Runge-Kutta-Nyström methods	16
Matching pursuit with unbounded parameter domains	15
Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs	14
Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation	13
$$\mathcal {H}_2$$ optimal rational approximation on general domains	12
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems	12
Dictionary-based model reduction for state estimation	11
Reconstruction of low-rank aggregation kernels in univariate population balance equations	11
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem	11
Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets	11
Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber	10
Complex-scaled infinite elements for resonance problems in heterogeneous open systems	10
On basis constructions in finite element exterior calculus	10
Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes	10
A hybrid collocation-perturbation approach for PDEs with random domains	9
Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides	9
Tensor rank bounds for point singularities in ℝ3	9
Multivariate quadrature of a singular integrand	9
Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems	9

Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains	9
Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow	9
Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation	9
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions	8
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction	8
Ellipsoidal conformal and area-/volume-preserving parameterizations and associated optimal mass transportations	8
Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces	8
Fast and accurate solvers for simulating Janus particle suspensions in Stokes flow	8
Exponential tractability of L2-approximation with function values	8
Improved a posteriori error bounds for reduced port-Hamiltonian systems	8
A posteriori virtual element method for the acoustic vibration problem	7
A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model	7
High-order conservative energy quadratization schemes for the Klein-Gordon-Schrödinger equation	7
Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow	7
Nonlocal optimized schwarz methods for time-harmonic electromagnetics	7
A generalisation of de la Vallée-Poussin procedure to multivariate approximations	7
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields	7
Topological phase estimation method for reparameterized periodic functions	6
Rapid evaluation of the spectral signal detection threshold and Stieltjes transform	6
Numerical methods for forward fractional Feynman–Kac equation	6
Variational methods for solving numerically magnetostatic systems	6
Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian	6
Retraction-based first-order feasible methods for difference-of-convex programs with smooth inequality and simple geometric constraints	6
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution I: fundamentals	6
A structure-preserving algorithm for surface water flows with transport processes	6
Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies	6
Numerical analysis of nonlinear degenerate parabolic problems with application to eddy current models	6
Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms	6
Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms	5
An unconditionally stable and $$L^2$$ optimal quadratic finite volume scheme over triangular meshes for anisotropic elliptic equations	5
Data-driven uncertainty quantification in macroscopic traffic flow models	5
Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system	5
Approximation of functions from Korobov spaces by deep convolutional neural networks	5
A new framework for polynomial approximation to differential equations	5
Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media	5
Generalised Wendland functions for the sphere	5
Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus	5
Wavelet adaptive proper orthogonal decomposition for large-scale flow data	5
Multilevel Monte Carlo simulation for the Heston stochastic volatility model	5
$$\mathcal {H}$$-inverses for RBF interpolation	5
An hp-version Legendre spectral collocation method for multi-order fractional differential equations	5
Convergence analysis of the Dirichlet-Neumann Waveform Relaxation algorithm for time fractional sub-diffusion and diffusion-wave equations in heterogeneous media	5
On the recovery of initial status for linearized shallow-water wave equation by data assimilation with error analysis	5
Convergence of projected subgradient method with sparse or low-rank constraints	5
Persistence Curves: A canonical framework for summarizing persistence diagrams	5
Limited memory restarted ℓp-ℓq minimization methods using generalized Krylov subspaces	5
Directional wavelet packets originating from polynomial splines	5
One-step optimization method for equilibrium problems	4
Control strategies for transport networks under demand uncertainty	4
Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation	4

A probabilistic reduced basis method for parameter-dependent problems	4
Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds	4
A new linearized fourth-order conservative compact difference scheme for the SRLW equations	4
The $$L_q$$-weighted dual programming of the linear Chebyshev approximation and an interior-point method	4
Ternary image decomposition with automatic parameter selection via auto- and cross-correlation	4
Live load matrix recovery from scattering data in linear elasticity	4
On convergence of the generalized Lanczos trust-region method for trust-region subproblems	4
Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations	4
Convergence analysis of oversampled collocation boundary element methods in 2D	4
Numerical investigation of agent-controlled pedestrian dynamics using a structure-preserving finite volume scheme	4
An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution II: computing moments and sparse grid acceleration	4
Implicit finite volume method with a posteriori limiting for transport networks	4
A high-order algorithm for time-domain scattering in three dimensions	4
Second-order accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials	4
Supercloseness analysis of a stabilizer-free weak Galerkin finite element method for viscoelastic wave equations with variable coefficients	4
A unified local projection-based stabilized virtual element method for the coupled Stokes-Darcy problem	4
Variational Bayesian inversion for the reaction coefficient in space-time nonlocal diffusion equations	4
Arbitrary high-order structure-preserving methods for the quantum Zakharov system	3
Dual frames compensating for erasures—a non-canonical case	3
Fast gradient methods for uniformly convex and weakly smooth problems	3
An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations	3
Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients	3
Numerical simulation of resistance furnaces by using distributed and lumped models	3
Linear multi-step methods and their numerical stability for solving gradient flow equations	3
Continuous window functions for NFFT	3
An optimal control framework for adaptive neural ODEs	3
Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators	3
A rotational pressure-correction discontinuous Galerkin scheme for the Cahn-Hilliard-Darcy-Stokes system	3
Correction: A Grassmann manifold handbook: basic geometry and computational aspects	3
Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations	3
Averaging property of wedge product and naturality in discrete exterior calculus	3
Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements	3
Estimating the error in matrix function approximations	3
State-dependent Riccati equation feedback stabilization for nonlinear PDEs	3
Numerical exponential decay of thermoelastic waves connected in parallel	3
Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation	3
Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems	3
Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems	3
A sparse approximation for fractional Fourier transform	3
Rectangular eigenvalue problems	3
A family of C1 quadrilateral finite elements	3
Two-scale finite element discretizations for nonlinear eigenvalue problems in quantum physics	3
A posteriori error estimates for wave maps into spheres	3
Uniqueness of phase retrieval from three measurements	3
A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law	3
Structure-preserving interpolation of bilinear control systems	3
Efficient computation of the sinc matrix function for the integration of second-order differential equations	3
A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation	2
Randomized GCUR decompositions	2
A rational RBF interpolation with conditionally positive definite kernels	2
Accurate singular values of a class of parameterized negative matrices	2
Geometric Hermite interpolation in $$\mathbb {R}^{n}$$ by refinements	2
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification	2
Essentially optimal finite elements for multiscale elliptic eigenvalue problems	2
Finding geodesics joining given points	2
Computing low-rank rightmost eigenpairs of a class of matrix-valued linear operators	2
On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems	2
A scaling fractional asymptotical regularization method for linear inverse problems	2
Multilevel correction adaptive finite element method for solving nonsymmetric eigenvalue problems	2
A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations	2
A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations	2
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?	2
An adaptive discontinuous finite volume element method for the Allen-Cahn equation	2
Nonsmooth data optimal error estimates by energy arguments for subdiffusion equations with memory	2
Correction: A posteriori virtual element method for the acoustic vibration problem	2
Space-time error estimates for deep neural network approximations for differential equations	2
Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization	2
An optimal ansatz space for moving least squares approximation on spheres	2
Frame-normalizable sequences	2
Robust preconditioning techniques for multiharmonic finite element method with application to time-periodic parabolic optimal control problems	2
Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation	2
Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problem	2
Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation	2
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems	2
Extrapolated regularization of nearly singular integrals on surfaces	2
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients	2
Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems	2
An efficient approximation to the stochastic Allen-Cahn equation with random diffusion coefficient field and multiplicative noise	2
Half-quadratic alternating direction method of multipliers for robust orthogonal tensor approximation	2
High-order corrected trapezoidal rules for a class of singular integrals	2

Morley type virtual element method for von Kármán equations	2
Computing eigenvalues of quasi-rational Said–Ball–Vandermonde matrices	2
Riemannian optimization for phase retrieval from masked Fourier measurements	2
Maximal volume matrix cross approximation for image compression and least squares solution	2
Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation	2
A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation	2
A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform	2
On pointwise error estimates for Voronoï-based finite volume methods for the Poisson equation on the sphere	2
Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery	2
Numerical algorithms for water waves with background flow over obstacles and topography	2
Approximation of curve-based sleeve functions in high dimensions	2
A second-order scheme based on blended BDF for the incompressible MHD system	2
Interpolation of 3D data streams with C2 PH quintic splines	2
A block-randomized stochastic method with importance sampling for CP tensor decomposition	1
Unfitted finite element method for the quad-curl interface problem	1
Convex combination of alternating projection and Douglas–Rachford operators for phase retrieval	1
An adaptive time-stepping Fourier pseudo-spectral method for the Zakharov-Rubenchik equation	1
On the maximum principle and high-order, delay-free integrators for the viscous Cahn–Hilliard equation	1
Numerical analysis of a chemotaxis model for tumor invasion	1
Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise	1
Toward a certified greedy Loewner framework with minimal sampling	1
Explicit multivariate approximations from cell-average data	1
Neural and spectral operator surrogates: unified construction and expression rate bounds	1
Max filtering with reflection groups	1
Stabilization of spline bases by extension	1
Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations	1
Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise	1
An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities	1
A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels	1
Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system	1
Adaptive quarklet tree approximation	1
A space-time certified reduced basis method for quasilinear parabolic partial differential equations	1
Solving the backward problem for time-fractional wave equations by the quasi-reversibility regularization method	1
A continuation method for fitting a bandlimited curve to points in the plane	1
Finding roots of complex analytic functions via generalized colleague matrices	1
A deterministic algorithm for constructing multiple rank-1 lattices of near-optimal size	1
Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method	1
Learning via variably scaled kernels	1
An unfitted finite element method with direct extension stabilization for time-harmonic Maxwell problems on smooth domains	1
Numerical computation of a preimage domain for an infinite strip with rectilinear slits	1
A DCA-Newton method for quartic minimization over the sphere	1
The Butzer-Kozakiewicz article on Riemann derivatives of 1954 and its influence	1
Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems	1
Design and analysis of the Extended Hybrid High-Order method for the Poisson problem	1
A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations	1
Semi-Lagrangian finite element exterior calculus for incompressible flows	1
Mass- and energy-conserving Gauss collocation methods for the nonlinear Schrödinger equation with a wave operator	1
A space–time DG method for the Schrödinger equation with variable potential	1
Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction	1
Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data	1
Cs-smooth isogeometric spline spaces over planar bilinear multi-patch parameterizations	1
On an accurate numerical integration for the triangular and tetrahedral spectral finite elements	1
Optimized Ventcel-Schwarz methods for the Cahn-Hilliard equation discretized by the stabilized linear Crank-Nicolson scheme	1
Stray field computation by inverted finite elements: a new method in micromagnetic simulations	1
A multilevel Newton’s method for the Steklov eigenvalue problem	1
Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations	1
Convergence rates for boundedly regular systems	1
A difference finite element method based on nonconforming finite element methods for 3D elliptic problems	1
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes	1
Artificial neural networks with uniform norm-based loss functions	1
A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions	1
A novel robust fractional-time anisotropic diffusion for multi-frame image super-resolution	1
The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation	1
New degrees of freedom for differential forms on cubical meshes	1
Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes	1
Weights for moments’ geometrical localization: a canonical isomorphism	1
Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations	1
Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data	1
Linear approximation method for solving split inverse problems and its applications	1
Analysis of a $$\varvec{P}_1\oplus \varvec{RT}_0$$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions	1
Piecewise orthogonal collocation for computing periodic solutions of renewal equations	1
A quadratic finite volume method for nonlinear elliptic problems	1
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology	1
Convergence analysis of the scaled boundary finite element method for the Laplace equation	1
Weak approximation of SDEs for tempered distributions and applications	1
Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials	1
Balanced truncation for quadratic-bilinear control systems	1