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1525 papers in math.NA · page 20
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X-FFT solver captures material interfaces accurately in 3D
A stable and accurate X-FFT solver for linear elastic homogenization problems in 3D
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X-FFT solver achieves interface-conforming accuracy in 3D
A stable and accurate X-FFT solver for linear elastic homogenization problems in 3D
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Long-time limits found for condition numbers of real linear ODEs
Asymptotic condition numbers for linear ordinary differential equations: the generic real case
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SP-ADMM learns energy-stable Maxwell stencils from noisy data
An Energy Stable Approach for Learning Derivative Operators from Noisy Data for Maxwells Equations
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Wachspress transfinite interpolants enforce exact Dirichlet boundaries in PINNs
A Wachspress-based transfinite formulation for exactly enforcing Dirichlet boundary conditions on convex polygonal domains in physics-informed neural networks
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Stochastic control reaches global minima for non-convex problems
Stochastic Control Methods for Optimization
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Gauss-Seidel iteration converges globally for sinc-collocation ODE equations
On solving nonlinear simultaneous equations arising from the double-exponential Sinc-collocation method for initial value problems
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Method bounds PDE stability constant within factor of two
Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality
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α=-1 uniquely optimizes energy stability in anisotropic flow discretizations
A structure-preserving parametric approximation for anisotropic geometric flows via an $\alpha$-surface energy matrix
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Tubal products identified that make SVD truncation optimal for tensors
Sufficient and Necessary Conditions for Eckart-Young like Result for Tubal Tensors
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High-order schemes keep black hole equilibria exact in Einstein-Euler runs
High order numerical discretizations of the Einstein-Euler equations in the Generalized Harmonic formulation
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Sphere functions decompose into low-dimensional terms with parity
Sensitivity Analysis on the Sphere and a Spherical ANOVA Decomposition
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Frenet mapping straightens interfaces for exact jumps in triangular IFE
Frenet Immersed Finite Element Spaces on Triangular Meshes
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Scattering data recovers perturbations in topological waveguides
Inverse scattering for waveguides in topological insulators
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Hermite functions stay stable for trap-free Schrödinger equations
Computing nonlinear Schr\"odinger equations with Hermite functions beyond harmonic traps
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L^∞ bounds derived for kEDMD on stochastic Koopman operators
Koopman for stochastic dynamics: error bounds for kernel extended dynamic mode decomposition
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Port-Hamiltonian structure preserved in Cosserat rod discretization
Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework
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Virtual dual cells enforce divergence-free velocities in meshfree flows
A pressure-projection formulation in a least-squares meshfree method for the incompressible Navier-Stokes equations using a staggered-variable arrangement
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MD stress tensor drives continuum model of ring-polymer segregation
Hybrid multiscale method for polymer melts: analysis and simulations
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P-refinement restores rates in SBM for trimmed IGA
Local h-, p-, and k-Refinement Strategies for the Isogeometric Shifted Boundary Method Using THB-Splines
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Projection-relaxation keeps mass
Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schr\"odinger equations
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Time-frequency units give shallow nets N^{-1/2} Sobolev rates
Time-Frequency Analysis for Neural Networks
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Vicsek model plus contact forces reproduces cell flocking and jamming
From flocking to jamming in collective cell dynamics: a Vicsek-like model including contact forces
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Yee FDTD turns sharp interfaces into one-cell layers
Accuracy of the Yee FDTD Scheme for Normal Incidence of Plane Waves on Dielectric and Magnetic Interfaces
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Finite element method converges optimally for non-divergence elliptic PDEs
Analysis of a finite element method for second order uniformly elliptic PDEs in non-divergence form
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Bayesian updates let digital twins learn transition dynamics online
Adaptive digital twins for predictive decision-making: Online Bayesian learning of transition dynamics
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Meshless MUSCL solves BGK equation to fourth order with moving boundaries
A meshless MUSCL method for the BGK-Boltzmann equation
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GD on nonlinear models equals perceptron updates
Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration
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Metric choice alone generates LOD multiscale spaces
Metric-driven numerical methods
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Convexified games forecast COVID sentiment from real posts
Toward Practical Forecasts of Public Sentiments via Convexification for Mean Field Games: Evidence from Real World COVID-19 Discussion Data
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Models emulate NVIDIA Tensor Core behavior in low precision
Accurate Models of NVIDIA Tensor Cores
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Matched 1D sections enforce curvature continuity in surface reconstruction
Thin Plate Spline Surface Reconstruction via the Method of Matched Sections
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DG discretization removes splitting error from Navier-Stokes solver
A Discontinuous Galerkin Consistent Splitting Method for the Incompressible Navier-Stokes Equations
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FHBVMs extended to multi-order fractional DEs
A Multi-Order Extension of Fractional HBVMs (FHBVMs)
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ROMs allow up to 40 times larger stable timesteps than FOMs
Stable self-adaptive timestepping for Reduced Order Models for incompressible flows
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Agent framework evolves numerical solvers to 10^{-14} errors
ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
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Implicit two-stage scheme reaches fourth-order accuracy for stiff Lax-Wendroff problems
An L-Stable Implicit Two-Stage Fourth-Order Temporal Discretization Scheme for Lax-Wendroff-Type Solvers Applied to Stiff Problems
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Small steps make feedback integrators invariant near constraints
Feedback Integrators: Non-Asymptotic Invariance for One-Step Methods and Gain Selection under Euler Discretization
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Low-rank solvers make HBVMs practical for large Hamiltonian problems
Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods
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Matching-based AMG scales for large IgA elliptic systems
Parallel matching-based AMG preconditioners for elliptic equations discretized by IgA
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High-order transport conserves tracer variance in shallow water model
High order tracer variance stable transport with low order energy conserving dynamics for the thermal shallow water equations
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Adapted multiscale method stabilizes EM waves with sign-changing coeffs
Multiscale Methods for wave propagation in materials with sign-changing coefficients
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Funnel replaces filter in trust-region gray-box optimization
A trust-region funnel algorithm for gray-box optimization
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Local multilevel method solves eigenvalue problems in O(N) time
Local Multilevel Preconditioned Jacobi-Davidson Method for Elliptic Eigenvalue Problems on Adaptive Meshes
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New discretization keeps kernel compensation valid for anisotropic crystals
A Robust GPU-Accelerated Kernel Compensation Solver with Novel Discretization for Photonic Crystals in Anisotropic Media
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PAMPA scheme in DG form preserves bounds and removes oscillations
Robust PAMPA Scheme in the DG Formulation on Unstructured Triangular Meshes: bound preservation, oscillation elimination, and boundary conditions
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IPVEM achieves optimal uniform errors for fourth-order singular perturbations
Optimal error analysis of an interior penalty virtual element method for fourth-order singular perturbation problems
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Neural networks transfer functions between non-nested meshes
DataTransfer: Neural network based interpolation across non-nested meshes
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Quantum method solves non-periodic PDEs in polylog time
A Quantum Spectral Method for Non-Periodic Boundary Value Problems
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Transmission eigenvalues bifurcate under smooth refractive-index changes
Bifurcations in Interior Transmission Eigenvalues: Theory and Computation