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1525 papers in math.NA · page 13
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Reformulated integrator removes time-step limits for smectic simulations
Relaxed Generalized Scalar Auxiliary Variable Exponential Integrator for A Modified Landau-de Gennes Theory for Smectic Liquid Crystals
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Quantum solver keeps Hilbert space dimension logarithmic for nonlinear PDEs
Lindbladian Homotopy Analysis Method to Solve Nonlinear Partial Differential Equations
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Implicit compact-kernel MPM cuts contact gaps and cell-crossing noise
An Implicit Compact-Kernel Material Point Method for Computational Solid Mechanics
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Flux correction at T-junctions keeps multigrid consistent on octrees
Matrix-Free Multigrid with Algebraically Consistent Coarsening on Adaptive Octrees
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Iterative method recovers 3D nanostructures from one or two X-ray angles
Nonuniform Iterative Phasing Framework and Sampling Requirements for 3D Dynamical Inversion from Coherent Surface Scattering Imaging
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The paper tests diffusion synthetic acceleration (DSA) schemes for solving neutron…
Diffusion Synthetic Acceleration for polytopic discretisations of Boltzmann transport
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Fourier analysis yields inversion formulas for V-line tomography
THE ROLE OF FOURIER ANALYSIS IN TWO DIMENSIONAL TOMOGRAPHY
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Julia solver adds full differentiability to turbulent flow simulations
A differentiable software suite for accelerated simulation of turbulent flows
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Spectral method yields convergent 2D Boussinesq wave solutions
The numerical solution of 2D Boussinesq/Boussinesq models for internal waves with spectral methods
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Hand derivation supplies PINN gradient formulas for any depth
Physics-Informed Neural Networks: A Didactic Derivation of the Complete Training Cycle
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3D brain model matches Alzheimer's PET data better than network version
High-fidelity and Network-based Spatio-temporal Mathematical Models of Alzheimer's Disease Progression and their Validation Against PET-SUVR Imaging Data
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Balance ranking keeps small but key terms in discovered PDEs
Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms
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Virtual element methods solve quad-curl problems on polygons
Virtual element methods for a quad-curl problem on general planar domains
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μ below 1 guarantees convergence in stochastic reconfiguration
Momentum Stability and Adaptive Control in Stochastic Reconfiguration
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Dual multiplier turns curvature flows into energy-stable schemes
Dual formulations of geometric curvature flows and their discretizations
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Energy splitting trains neural operators to respect phase-field dissipation
DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splitting
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Evanescent waves cut instabilities in Trefftz Helmholtz solvers
Trefftz methods with evanescent plane waves
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Neural operators bound PDE errors uniformly across shape families
Neural Shape Operator Surrogates -- Expression Rate Bounds
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Adaptive mesh and GMRES control gives optimal complexity
Adaptive finite element methods with optimally preconditioned GMRES guarantee optimal complexity
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Lagrange multipliers enforce PDEs in Kriging predictions
Optimal Linear Interpolation under Differential Information: application to the prediction of perfect flows
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Coupled mixed-Lagrange elements keep optimal rates in elasticity with tiny mixed zones
A Coupling Method of Mixed and Lagrange Finite Elements for Linear Elasticity Problem
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This paper proposes a deep Ritz neural network method to compute steady-state solutions…
A Deep Ritz Method for High-Dimensional Steady States of the Cahn-Hilliard Equation
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Optimal decay rates found for Laguerre and Hermite coefficients of singular functions
Optimal asymptotic analyses on Laguerre and Hermite orthogonal approximation for functions of algebraic and logarithmic regularitiesYali
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Optimization follows natural laws from control transversality
On The Mathematics of the Natural Physics of Optimization
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Strang splitting solves KBF equation at second-order time accuracy
Fully discrete scheme for the fifth-order KdV-Burgers-Fisher equation using Strang splitting and Fourier collocation methods
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Weighted FOSLS keeps neural loss aligned with energy error at material jumps
Robust Deep FOSLS for Transmission Problems
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Ground state soliton marks sharp blow-up threshold in 3D ZK
Multi-domain spectral approach for Zakharov-Kuznetsov equations in 3D with cylindrical symmetry
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New bases evaluate Gauss-Legendre curves in O(n^{2} + dn) time
Evaluation of Gauss-Legendre curves
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Generalized relaxed projection algorithm converges for convex intersections
Generalized Composed Alternating Relaxed Projection Algorithm for Two-Set Feasibility Problem
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Linear Boţ-Nguyen acceleration equals weighted ergodic iteration
Bo\c{t}-Nguyen Acceleration, Weighted Mean Ergodic Iteration, and the Beta-Binomial Distribution
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Transformed Hermite approximations reduce to pullback Hermite expansions
Convergence theory for Hermite approximations under adaptive coordinate transformations
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3D-SVD matches Tucker quality for biological volumes at lower cost
Structured 3D-SVD: A Practical Framework for the Compression and Reconstruction of Biological Volumetric Images
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Modulation conditions prove blowup in 3D Keller-Segel equation
Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
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Reformulated integrator stabilizes smectic liquid crystal models
Generalized Scalar Auxiliary Variable Exponential Integrator for A Modified Landau-de Gennes Theory for Smectic Liquid Crystals
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Low-memory method certifies polynomial solutions
Low-Memory Numerical Certification
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Preconditioned iteration yields low-rank MPS eigenfunction approximations
Low-rank eigenvalue solvers for block-sparse matrix product states
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Finite volume scheme converges to dissipative weak solutions of NSK system
Convergence of a Finite Volume Scheme for the Navier-Stokes-Korteweg Model via Dissipative Solutions
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Richardson iteration bounds backward error by 1/k on PSD systems
Towards Universal Convergence of Backward Error in Linear System Solvers
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Sparse positive quadrature cuts points in viscoplastic cut-cell analysis
Efficient Thermo-Viscoplastic Analysis Using a Multi-Level hp-Finite Cell Method with Non-Negative Moment Fitting
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Inverse estimates stabilize DG for p-Laplacian on curved meshes
$hp$-Version robust interior penalty discontinuous Galerkin methods for the $p$-Laplacian on simplicial and on essentially arbitrarily-shaped element meshes
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Finite actuators stabilize 2D flows via receding horizon control
Finite-Dimensional MOR-Based RHC for Steering 2D Navier-Stokes Equations to Desired Trajectories
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Preconditioned Anderson acceleration speeds up Sylvester equation solvers
Efficient Solution of Generalized Sylvester Equations via Preconditioned Alternating Anderson Acceleration
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Neural flux operator keeps conservation laws intact in flow simulations
A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws
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Momentum extends natural gradients to nonlinear manifolds
Natural gradient descent with momentum
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DNS samples close 2D vorticity PDF equations
A data-driven approach for 2D vorticity PDF equations by a new conditional average estimation
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Compact stencils deliver stable high-order ghost-point boundary conditions
Efficient and well-conditioned ghost-point discretization of boundary operators on unfitted domains
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Correction functions turn interface jumps into solvable boundary integrals
A Correction Function-based KFBI Method for Brinkman Interface Problems
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HHO method attains O(τ² + h^{k+1}) accuracy for integro-differential equations
Energy norm error estimates of a hybrid high-order method for the linear parabolic integro-differential equations on general meshes
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Post-processed multiscale method attains higher-order convergence
A post-processed higher-order multiscale method for nondivergence-form elliptic equations
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Exact exponential rate resolved for contiguous Fourier submatrices
On the exponential rate of the condition number of Fourier submatrices and Vandermonde matrices