数值分析

Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust. A finite EDMD matrix always has eigenvalues; the problem is that many of them may have nothing to do with…

We propose a semi-Lagrangian adaptive-rank (SLAR) method that combines the large time-step capability of semi-Lagrangian schemes with the efficiency of adaptive-rank tensor representations while simultaneously enforcing local conservation…

The Bethe-Salpeter equation, which has many applications in both theoretical and applied physics, is generally solved via a matrix eigenvalue problem with a rich algebraic structure. The numerical solution of such structured eigenproblem…

Numerical simulation of quantum computing hardware and open quantum systems governed by the Lindblad equation is challenging due to the high dimensionality of the density matrix and the need to preserve fundamental physical properties. In…

We propose and analyze a space-time discontinuous Galerkin method for the incompressible Stokes equations on moving domains within the arbitrary Lagrangian-Eulerian setting. We use a contravariant Piola map in the definition of the discrete…

The paper considers the Cauchy problem for a first-order integro-differential equation with memory in a finite-dimensional Hilbert space. The main computational difficulty of such problems is the need to store and process the solution at…

We present a fast and accurate potential theory-based method for the two-dimensional modified Helmholtz equation, treating the involved singular and nearly singular layer evaluations together with volume potentials within a single…

This paper investigates the role of viscosity in the error upper bounds of a consistent splitting scheme for the Navier-Stokes equations proposed by Huang and Shen [5]. In their original analysis the viscosity is fixed to unity. By…

We develop a quantum algorithm for the regularized Wasserstein proximal operator, which is a fundamental tool in optimal transport and mean-field games. The regularization introduces a small diffusive term into the continuity equation of…

We develop a reduced interface formulation for elliptic interface problems with highly conducting interfaces. The interface condition consists of continuity of the primal variable together with a jump in the normal flux proportional to the…

Electroelastic shells are widely used in soft actuators, sensors, and energy harvesters owing to their large electrically induced deformations. However, the accurate simulation of their complex nonlinear multiphysics coupling, including…

We present a fast algorithm for evaluating conditionally convergent Coulomb lattice sums, governed by the Laplace equation with periodic boundary conditions on arbitrary unit cells (oblique in 2D, triclinic in 3D) and arbitrary particle…

The main theme of approximation theory is to understand how well a general function $f$ can be approximated by a simpler function $g$ such as a polynomial or spline. In many applications, one wants $g$ to retain known properties of $f$ such…

This paper treats variable-order time-fractional subdiffusion with discontinuous coefficients across a curved interface using $L2\!-\!1_\sigma$ time stepping on graded meshes and a symmetric interior penalty FEM on body-fitted meshes.…

This paper introduces a new application of the perfectly matched layer (PML) for mitigating model top wave reflections in geophysical fluid models. Typically, a strong Laplacian or Rayleigh damping sponge layer is used near the upper…

We present a fast, high-order algorithm for the free-space fractional Fokker-Planck equation (FFPE) in arbitrary spatial dimension. Its fundamental solution, corresponding to a Dirac-delta initial condition, is obtained from the explicit…

The Gauss-Seidel projection method (GSPM) constitutes an efficient and numerically stable numerical framework for micromagnetic simulations of ferromagnetic media. This scheme attains first-order temporal accuracy and second-order spatial…

Mixed-precision variants of the Jacobi algorithm for symmetric positive definite eigenproblems and the one-sided Jacobi algorithm for singular value decompositions have recently been shown to compute eigenvalues and singular values to high…

This work introduces a novel high-order numerical framework for solving kinetic equations, designed to remain uniformly valid across all regimes of the mean free path, spanning from the rarefied kinetic scale to the incompressible…

Third medium contact provides a smooth continuum alternative to classical contact algorithms by replacing explicit contact constraints with a highly compliant fictitious medium. In this work, an auxiliary-field stabilization is introduced…