219 papers
This paper introduces the Pretrained Finite Element Method (PFEM), a framework that combines a physics-informed neural operator pretraining stage with a conventional FEM warm-start stage to achieve highly efficient and accurate solutions for partial differential equations across complex geometries and material properties.
This paper presents a comprehensive taxonomy and practical guide for selecting numerical differentiation methods suited to various scientific applications, accompanied by the open-source Python package PyNumDiff for differentiating noisy data.
This paper introduces FEALPy, a modular, cross-platform numerical simulation engine built on a unified tensor abstraction that seamlessly integrates diverse numerical methods with deep learning workflows across multiple computational backends and hardware systems.
This paper introduces efficient splitting methods, specifically Douglas-Rachford and Davis-Yin, to implement optimization-based limiters that enforce invariant-domain preservation in high-order numerical schemes for gas dynamics, demonstrating their robustness and performance through applications to discontinuous Galerkin methods on compressible flow benchmarks.
This paper introduces a mass-lumped Virtual Element Method combined with explicit Strong Stability-Preserving Runge-Kutta time stepping for two-dimensional parabolic problems on general polygonal meshes, establishing theoretical stability under a classical CFL condition and demonstrating optimal convergence rates and robustness against mesh distortion through numerical experiments.
This paper presents a novel entropy-stable nodal discontinuous Galerkin scheme for the Euler equations with gravity that achieves well-balancing for general hydrostatic and moving equilibrium states through a linear entropy correction to the source term, while maintaining compatibility with positivity-preserving limiters and demonstrating robustness in numerical experiments.
This paper proposes a multiphase cubic MARS method that achieves high-order accuracy in both time and space for tracking interfaces of multiple materials with arbitrary topology and geometry by utilizing graph-based representations, adaptive marker distribution, and robust junction handling.
This paper introduces a "solver-in-the-loop" framework for 3D Electrical Impedance Tomography that combines a pre-trained 3D generative prior with a rigorous boundary integral equation solver to enforce physical constraints as hard conditions, thereby achieving superior geometric accuracy and data efficiency in reconstructing complex interfaces compared to traditional optimization and deep learning methods.
This paper introduces WG-IDENT, a robust framework that combines weak formulations, B-spline representations with spectrally optimized knots, and a novel group feature trimming technique to accurately identify Partial Differential Equations with spatially varying coefficients from heavily noisy spatiotemporal data.
This paper introduces a novel transformation-based, doubly-adaptive quasi-Milstein scheme for jump-diffusion SDEs with discontinuous drift and degenerate diffusion, achieving a strong convergence rate of order 1 in under assumptions weaker than those in existing literature.
This paper proposes and analyzes a stochastic algorithm that provably converges almost surely to the operator norm of the difference between two linear maps—one accessible only via forward evaluation and the other only via adjoint evaluation—by performing a random search on a generalized Rayleigh quotient with optimal step sizes.
This paper analyzes the theoretical foundations, error bounds, and numerical approximations of the State-Dependent Riccati Equation (SDRE) approach for nonlinear optimal control, introducing a residual-minimizing decomposition strategy and demonstrating through numerical experiments that the Newton-Kleinman iterative method offers superior stability and cost-effectiveness compared to the offline-online approach.
This paper introduces a noise-aware system identification framework that jointly recovers deterministic drifts and full noise structures from trajectory data without prior assumptions, enabling efficient and accurate modeling of complex, high-dimensional stochastic dynamics with correlated or state-dependent noise.
This paper proposes and validates a robust nonlinear multilevel solution strategy for the Diffusive Wave equation on highly perforated urban domains by integrating a specialized multiscale coarse space with Schwarz-based nonlinear preconditioning methods to ensure scalability and efficiency.
This paper proposes a robust, contour integral-based algorithm tailored for the Jordan-Wielandt matrix pencil to efficiently compute a few generalized singular values with rapid convergence and high accuracy, overcoming the limitations of directly applying the standard FEAST algorithm.
This paper proposes a non-intrusive, structure-preserving model order reduction method based on generalized manifold Galerkin reduction that generates reduced-order port-Hamiltonian models for both linear and nonlinear systems while maintaining stability and passivity, demonstrating superior accuracy compared to existing techniques.
This paper establishes the existence, uniqueness, and stability of solutions to the stochastic Benjamin-Bona-Mahony equation with multiplicative noise and derives optimal strong error estimates for a fully discrete finite element approximation under bounded noise, as well as sub-optimal convergence rates in probability for general noise via a localization technique.
This paper establishes the convergence of Lie-Trotter and Strang splitting schemes for the Gross-Pitaevskii equation with time-dependent potentials and non-zero boundary conditions in Zhidkov spaces, while demonstrating the conservation of generalized mass, near-preservation of energy, and investigating quantum vortex nucleation in relevant experimental settings.
This paper presents a discontinuous Galerkin numerical analysis of a nonlinear multiphysics model coupling the Westervelt wave equation and a convection-diffusion equation to simulate ultrasound-enhanced drug delivery, establishing well-posedness and optimal convergence rates for the semi-discrete system under suitable assumptions.
This paper establishes that while measure-valued sources on lower-dimensional sets degrade global convergence rates for finite element methods due to solution singularities, optimal local and error estimates are still achievable in subdomains strictly separated from the source support.