219 papers
This paper extends diffraction tomography to accommodate focused beam scanning by modeling incident fields as Herglotz waves, deriving a new Fourier diffraction relation that enables quantitative reconstruction and reveals how different scan geometries impact the imaging results.
This paper establishes that in raster scan diffraction tomography using focused beams, the object's scattering potential is generically uniquely determined in dimensions higher than two, whereas in two dimensions, only a specific subset of Fourier coefficients can be uniquely recovered while others remain ambiguous.
This paper introduces two new families of multirate time step adaptivity controllers and a set of fifth-order embedded MERK methods, demonstrating their superior performance and flexibility in efficiently solving problems with multiple time scales through adaptive simulations.
This paper presents a fast direct boundary element solver for two-dimensional elastodynamic transmission problems that utilizes a mixed Burton-Miller and PMCHWT formulation with proxy-based low-rank approximation to achieve linear computational complexity and efficient handling of multiple right-hand sides, regardless of inclusion shape.
This paper presents and analyzes a complex scaling-based integral equation method that enables the efficient, high-order, and exponentially accurate numerical solution of wave scattering problems involving the junction of two semi-infinite periodic structures by analytically continuing the formulation into the complex plane to overcome slow kernel decay and prove its well-posedness.
This paper presents a residual-driven multiscale method within the GMsFEM framework that reformulates Darcy flow in perforated domains into a pressure-only system using velocity elimination and adaptive online enrichment to achieve high accuracy with significantly reduced computational costs.
This paper introduces a scalable and parameter-robust solver for a cell-by-cell poroelasticity model of brain tissue, utilizing a three-field formulation with norm-equivalent preconditioning and Algebraic Multigrid approximations to efficiently simulate complex physiological processes like cellular swelling in detailed biological geometries.
This paper bridges the gap between theory and practice for randomized iterative methods like Gauss-Seidel and Kaczmarz by deriving tighter asymptotic performance bounds through new spectral radius techniques and Perron-Frobenius theory, while simultaneously resolving a 2007 open problem by quantifying the performance benefits of relaxation.
This paper disproves the conjecture that a high-order explicit time-stepping scheme introduced by Buvoli remains stable as accuracy approaches infinity, while simultaneously establishing its superior stability over classical methods, deriving a criterion for maximum permissible accuracy, and providing a unified -stability analysis for extensional PDEs under the CFL condition.
This paper introduces a novel subgradient definition based on Busemann functions for convex optimization on Hadamard spaces, enabling the generalization of stochastic and incremental subgradient methods with guaranteed complexity bounds to nonpositively curved metric spaces such as BHV tree space.
This paper introduces a model-agnostic framework that improves function extrapolation by projecting baseline approximations onto feasible sets defined by anchor functions, thereby providing rigorous, proven bounds that guarantee error reduction in extrapolation regions.
This paper introduces a two-phase approximation method that resolves singularities in three-dimensional harmonic Dirichlet problems by decomposing the solution into a singular component handled via Green's formula with high-order quadrature and a regular component recovered through collocation with a harmonic basis.
This paper proposes an efficient offline-online subspace decomposition preconditioner that leverages localized defect structures to robustly solve elliptic diffusion problems with multiscale heterogeneous coefficients, significantly reducing the computational cost of uncertainty quantification in Monte-Carlo simulations.
This paper introduces a scalable s-step Preconditioned Conjugate Gradient method that leverages a Chebyshev-stabilized basis and Forward Gauss-Seidel iterations to solve reduced Gram systems, achieving classical convergence with significantly reduced synchronization overhead on modern GPU architectures.
This paper proposes and analyzes a two-grid penalty approximation scheme for decoupled Markovian doubly reflected BSDEs, which overcomes error amplification from obstacle evaluation by simulating the forward process on a finer grid, thereby establishing explicit error bounds and optimal tuning rules to achieve a target convergence rate of .
This paper establishes rigorous error estimates for the hyperbolic scaling limits of linear discrete kinetic models on networks by reformulating symmetric n-edge junctions into independent initial-boundary value problems and deriving asymptotic expansions via the energy method.
This paper introduces ALMTON, a globally convergent third-order Newton method for unconstrained nonconvex optimization that achieves an complexity by using adaptive quadratic regularization to maintain a tractable cubic model solvable via a single semidefinite program per iteration, thereby outperforming existing third-order and second-order baselines in convergence consistency and robustness.
This paper introduces LS-ReCoNN, a novel deep learning framework that solves parametric transmission problems by decomposing the solution into regular and singular components and employing a least-squares-based training strategy to accurately capture interface discontinuities and junction singularities across diverse parameter values.
This paper establishes conditional stability for the backward problem of degenerate viscous Hamilton-Jacobi equations with general non-quadratic Hamiltonians using Carleman estimates and linearization, and proposes numerical identification algorithms based on the adjoint state method and Van Cittert iteration, validated by numerical tests.
This paper investigates linear-quadratic Dirichlet control problems governed by non-coercive elliptic equations on non-convex polygonal domains using energy regularization, establishing solution regularity in weighted Sobolev spaces and deriving optimal error estimates for finite element discretizations that employ graded meshes and a specialized discrete projection.