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1525 papers in math.NA · page 12
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Nonconforming scheme converges for generalized Darcy-Forchheimer flows
A nonconforming method for a generalized Darcy-Forchheimer model
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Thin-sheet VIE solver includes normal fields for metasurface modeling
A Thin Sheet Volume Integral Equation Solver for Simulation of Bianisotropic Metasurfaces
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Restitution sets viscosity in granular continuum model
Continuum granular flow model with restitution-derived viscoelastic damping
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Spherical cap discrepancy complexity drops with dimension
Spherical Cap $L_2$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant
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Exact solution derived for sequential Caputo fractional equation
On a Boundary-Initial Value Problem for Fractional Differential Equation with Sequential Caputo derivatives
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Local weak solutions proven for thermally driven phase separation
A Temperature-Coupled Cahn-Hilliard-Stokes-Heat Model for Thermally Driven Phase Separation
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Hybrid integrator stabilizes chaotic forecasts with bounded gradients
A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting
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Stabilized scheme removes mesh-size limits from Schrödinger eigenvalue bounds
Old and new Schr\"odinger eigenvalue localisation
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Neural surrogate predicts nutrient flow 956x faster than FEM
Data-Driven Surrogate Models for Agromaritime Applications: Finite Element-Neural Network Integration
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Neural networks select stable frequency parameters for HP-splines
Accuracy and stability of Artificial Neural Networks for HP-Splines frequency parameter selection
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B-splines bound Hausdorff dimensions of continued-fraction fractals
Rigorous High-Order Hausdorff Dimension Estimation of Limit Sets of Continued Fraction Iterated Function Systems via B-Splines
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Integral reformulation proves unique solution for bulk-surface Laplace with open edge
Bulk-Surface Coupled PDE with an Open Boundary
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Stable scheme solves anisotropic diffusion on curvilinear meshes
A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields: Curvilinear coordinates and multi-block domains
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The paper develops an incremental SVD compression technique for the history term in mixed…
Incremental SVD Compression for Nonlinear Oldroyd Equations with General Memory Kernels
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Hybrid solver runs CO2 sequestration models over three times faster
CO$_2$ sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)
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Three-temperature model tracks injected fluid heating in geothermal reservoirs
Heat Transfer Modeling in Enhanced Geothermal Energy: A Three-Temperature Approach for Solid, Injected, and Residing Fluids
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Blended LWFR solves relativistic hydrodynamics on adaptive curved meshes
Admissible Lax-Wendroff Flux Reconstruction Method with Automatic Differentiation on Adaptive Curved Meshes for Relativistic Hydrodynamics
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Stable Laguerre differentiation matrices built without cancellation
Construction of Laguerre pseudospectral differentiation matrices
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Constrained polynomials cut error in noisy quantum linear solvers
Constrained Optimal Polynomials for Quantum Linear System Solvers
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Graph method decouples MNA with controlled sources to index-1
A topological decoupling of modified nodal analysis including controlled sources
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Weak sequential non-expansiveness implies weak convergence of fixed point iterations
Weakly convergent fixed point iterations for weakly sequentially non-expansive mappings
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Source model must match inverse solver assumptions in EEG imaging
Forward--Inverse Interplay in FEM-Based EEG Source Imaging: Distributional Signatures of Advanced Source Models and Inverse Solvers
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Denoiser-driven iteration proven convergent as regularization
On the convergence of an adaptive denoiser driven iterative regularization with early stopping
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Explicit quantum circuits simulate 3D elastic waves
Hamiltonian simulation for 3D elastic wave equations in homogeneous elastic media
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Cayley transform yields convergence bounds for Born series on any domain
Cayley-transform analysis and numerical validation of the convergent Born series for the Helmholtz equation
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Fixed-width network cuts error geometrically at each layer
Geometric Layer-wise Approximation Rates for Deep Networks
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Spacetime integrals enable direct acoustic source sampling
Quantitative Direct Sampling for Initial Acoustic Sources
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Learned moment closures for 2D radiative transfer stay hyperbolic by design
Machine learning moment closure models for the radiative transfer equation IV: enforcing symmetrizable hyperbolicity in two dimensions
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Ghost penalty inflates residual effectivity in unfitted reduced-order models
A posteriori error analysis, Pod-Deim reduced order geometrically parametrized models and unfitted FEMs
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Bubble patches keep error bounded as diffusion shrinks in channel flow
Error estimates for the patch bubble method for convection-dominated channel flow problem
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H(div)-conforming HDG methods for Stokes equations produce exactly divergence-free…
Pressure-Robust $H(\mathrm{div})$-Conforming HDG Methods for the Steady Stokes Equations with an Application to Tangential Boundary Control
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Proximal primal-dual computes explicit formulas for generalized JKO schemes
A Proximal Primal-Dual Approach to Generalized JKO Schemes for Doubly Nonlinear Parabolic Equations
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Space-time FR recovers DG and SD schemes with built-in entropy stability
A Space-time Approach to Entropy-Stable Discontinuous Galerkin and Flux Reconstruction
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RBF variational solvers reach high accuracy on elliptic problems at similar cost
Stable Mesh-Free Variational Radial Basis Function Approximation for Elliptic PDEs and Obstacle Problems
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Proximal HHO method attains higher-order convergence for obstacle problems
Proximal Discontinuous Galerkin Methods for Variational Inequalities
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Adaptive radius lifts accuracy for high-dimensional fractional PDEs
Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs
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Diophantine frequencies and source condition yield regular solutions
Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations
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Weakly admissible meshes give splines full local approximation power
Local power of approximation in hierarchical spline spaces on weakly admissible meshes
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Spectral method handles singularities in nonlocal phase separation
Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation
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Real shift on coarsest grid enables scalable Helmholtz multigrid
Scalable Multigrid Solver for the Helmholtz Equation: Real-Shifted Coarse Grid Correction
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Transition condition handles dynamics at mechanism topology switches
Forward Dynamics of Variable Topology Mechanisms - The Case of Constraint Activation
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MCP penalty on framelets improves blind image deblurring
Framelet-Based Blind Image Restoration with Minimax Concave Regularization
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Mapped PINNs solve infinite wave problems without boundary losses
Mapping-based Hard-constrained Physics-Informed Neural Networks for unbounded wave problems
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Finite iterations produce O(h^{M+1}) symplectic defects
Symplectic Error of Implicit Symplectic Integrators: A Qualitative Structural Analysis
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Reduced bases cut thermal topology optimization time by up to 16x
Comparison of model order reduction techniques with one-shot procedure for topology optimization for thermal applications
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This paper develops an augmented Lagrangian preconditioner for solving the…
Preconditioners for the Onsager-Stefan-Maxwell equations for multicomponent diffusion
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One global PCE yields closed-form conditional Sobol indices
Analytical Extraction of Conditional Sobol' Indices via Basis Decomposition of Polynomial Chaos Expansions
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High-order terms ensure convergence in multi-scale composite simulations
High-Order Multi-Scale Method and Its Convergence Analysis for Nonlinear Thermo-Electro-Mechanical Coupling Problems of Composite Structures
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Higher-degree Taylor tubes cut runtime in validated IVP solvers
Taylor Tube Method for Validated IVP
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Knit deformation splits into reorientation and bending
Geometric quantification for nonlinear deformation in knitted fabrics