220 papers
This paper derives explicit formulas for the dual Drazin inverse of dual complex anti-triangular block matrices and applies these results to solve open problems and extend existing group inverse findings for the adjacency matrices of DN-DS, DN-DLS, and DN-DW digraphs.
This paper presents a practical, step-by-step methodology for formulating finite elasto-plasticity in curvilinear coordinates using explicit basis changes rather than differential geometry, clarifying the treatment of deformation gradients, Jacobians, and shifters to enable robust finite element analysis of axisymmetric problems with large deformations.
This paper presents a general scheme for constructing optimal and numerically stable generalized Schultz iterative methods with variable coefficients to efficiently compute matrix inverses, supported by theoretical derivation and numerical testing.
This paper introduces and validates a novel semi-discrete optimal transport scheme for the compressible semi-geostrophic slice model that utilizes -exponential charts to efficiently construct -Laguerre tessellations, thereby enabling mass- and energy-conserving simulations of large-scale atmospheric dynamics while preserving key geometric structures.
This paper proposes a structure-preserving LOBPCG algorithm, enhanced with an improved Hetmaniuk-Lehoucq trick and an adaptive multi-level orthogonalization strategy, to efficiently and accurately solve the Bethe-Salpeter eigenvalue problem while naturally extending to symplectic eigensolvers.
LegONet introduces a compositional, plug-and-play framework for learning PDE solvers by utilizing structure-preserving operator blocks on shared spectral representations to separate boundary handling and mechanism learning, thereby enabling stable, reusable, and reconfigurable neural operators across diverse equations and conditions.
This paper demonstrates that partial differential equation propagation acts as a spectral preconditioner that improves Fourier ratio bounds, thereby enabling stable recovery of discretized fields from incomplete random spatial samples with sampling rates that are effectively independent of grid resolution.
This paper investigates the weak scalability of time parallel Schwarz methods for parabolic optimal control problems by developing novel theoretical tools to analyze convergence and spectral properties, thereby confirming the method's suitability for large-scale simulations on high-performance computing architectures.
This paper extends a low-dissipation central upwind scheme, originally developed for Euler equations, to the ideal magnetohydrodynamics (MHD) system by combining a cell-centered hydrodynamic solver with a face-based constrained transport method for magnetic fields, thereby achieving enhanced contact wave resolution, second-order accuracy, and machine-precision divergence-free magnetic fields in one and two dimensions.
This paper presents a data-driven numerical approach using Flow Map Learning to construct a deep neural network model of drag and lift forces, enabling real-time active flow control for over 20% drag reduction in cylinder flow without requiring online flow field simulations.
This paper establishes the unique determination of both linear and nonlinear coefficients in a semilinear Helmholtz equation from Neumann-to-Dirichlet boundary measurements using higher-order linearization and provides a Bayesian numerical reconstruction framework with uncertainty quantification.
This paper proposes a novel submesh-free, kernel-only stabilization for finite-strain virtual element methods in hyperelasticity that decouples deviatoric and volumetric channels to eliminate artificial stiffening in the nearly incompressible regime, thereby ensuring uniform stability and robustness across polygonal meshes.
This paper introduces a novel, simple, and compact control volume-based high-order limiter for the spectral volume method that effectively suppresses oscillations in discontinuous problems while preserving high-order accuracy and resolution through a nonlinear weighting reconstruction strategy.
This paper introduces a novel high-resolution ODE framework based on -resolution analysis to overcome the limitations of existing methods in studying first-order algorithms with momentum, providing deeper insights into their convergence properties and enabling provably optimal modifications for methods like PDHG and Heavy-Ball.
This paper presents a numerical technique for discretizing higher-order powers of the spectral fractional Laplacian with by utilizing the polyharmonic extension approach.
This paper establishes conditional stability estimates and derives a priori error estimates for a finite element-based least-squares reconstruction of parameter identification problems governed by elliptic equations with power-type nonlinearity, extending and sharpening previous linear results under weaker regularity assumptions.
This paper introduces a Gauss-Newton method for large-scale PDE-constrained inverse problems, such as Full-Waveform Inversion, that achieves fast convergence without requiring additional PDE solves beyond those needed for gradient evaluation.
This paper presents a unified framework that proves the equivalence of variational, Green's function, and characteristic-based methods for constructing reproducing kernels, enabling a data-driven, mesh-free approach to learning kernels that accurately approximate Koopman eigenfunctions and solve various linear transport equations.
This paper introduces a hybrid Monte Carlo algorithm for global time-dependent particle transport that utilizes automatic weight windows derived from a second-order accurate, noise-filtered hybrid MC/deterministic solution of low-order second-moment equations to achieve uniform particle distribution and enhanced computational efficiency.
This paper addresses the pressure-load inaccuracies in existing immersed interface methods for C0 triangulated surfaces by proposing a pressure-robust formulation that utilizes reconstructed continuous surface normal vectors—via L2 projection or inverse centroid-distance weighting—to significantly reduce numerical leakage.