1694 papers
The "Math — Na" category explores the fascinating world of numerical analysis, where mathematicians and computer scientists collaborate to solve complex equations that have no simple algebraic answers. Instead of seeking exact formulas, this field focuses on developing clever algorithms that approximate solutions with incredible precision, driving advancements in everything from weather forecasting to engineering simulations.
On Gist.Science, we process every new preprint in this category as it appears on arXiv, ensuring you stay ahead of the curve. We transform these dense, technical papers into accessible content by providing both plain-language overviews for general readers and detailed technical summaries for specialists.
Below are the latest numerical analysis papers we have recently curated, ready for you to explore.
This paper presents a parallelized, finite-volume micro-macro kinetic flux-vector splitting scheme for the multidimensional Boltzmann-ES-BGK equation that reduces computational cost by combining a fluid model with a projected kinetic correction, while correctly capturing transport coefficients and preserving compressible Navier-Stokes asymptotics across various Knudsen numbers.
This paper introduces a quantum-inspired tensor network framework that encodes discretized advection-diffusion-reaction fields as matrix product states and operators to enable stable, accurate, and compact time integration across one and two dimensions, demonstrating the potential of these methods as efficient structure-preserving tools for PDE simulation.
This paper presents the first convergence analysis and proof of acceleration for nonlinear GMRES (NGMRES) applied to both contractive and noncontractive fixed point iterations, demonstrating that the optimization problem's ratio gain drives acceleration while a newly identified quantity accurately predicts linear convergence rates and guides adaptive depth selection.
This paper demonstrates that neural networks with low regularity, including step-activated and quantized models suitable for efficient hardware implementation, can effectively solve elliptic partial differential equations using least-squares very weak formulations, thereby avoiding automatic differentiation while maintaining robust performance in singular and high-dimensional settings.
This paper establishes the first explicit strong convergence rates for a temporal approximation of the stochastic Korteweg-de Vries equation with small additive noise by decomposing the solution into deterministic and stochastic components, linearizing the latter, and utilizing Fourier analytic techniques to achieve convergence orders of under -regularity and under -regularity.
This paper establishes that adaptive finite element methods for symmetric second-order linear elliptic PDEs, utilizing non-residual error estimators and coupled with iterative algebraic solvers, achieve unconditional full R-linear convergence and optimal computational complexity under abstract assumptions, independent of user-chosen adaptivity parameters.
This paper proposes and analyzes an adaptive physics-preserving multiscale method that couples a P-IMPES scheme with a mixed constraint energy minimizing generalized multiscale finite element method to efficiently simulate two-phase flow in high-contrast porous media by dynamically updating multiscale spaces based on saturation-dependent mobility variations while guaranteeing local conservation and error bounds.
This paper develops a unified residual-based time discretization framework for evolution equations on nonlinear manifolds, establishing first- and second-order convergence rates for both discretization-first and variational approaches, and demonstrating its efficiency through explicit Gaussian approximations for time-dependent Schrödinger equations.
This paper establishes conditions for achieving optimal uniformity () in Quasi-Monte Carlo sequences by utilizing Artin-Schreier polynomials and a fast greedy procedure to construct high-dimensional, perfectly equidistributed sampling sequences.
This paper proposes an efficient higher-order local time integration scheme for Friedrichs' systems with mixed mesh sizes that utilizes a preconditioned Krylov subspace method to achieve iteration counts independent of small element diameters, thereby overcoming the limitations of previous leapfrog-Crank-Nicolson combinations.