Numerical Analysis (Mathematics) Papers of the Week

We develop and validate a physics-informed neural network (PINN) framework for computing the tidal Love numbers of black holes directly from their perturbation equations.

This results in excessive diffusion of vorticity and is one of the main reasons for the physical inaccuracy of the algorithm. We propose Kernelized Stable Fluids with Sparse Cholesky Preconditioning (KSF-Chol) in order to address this shortcoming and make the algorithm thereby suitable for engineering problems and scientific computing.

We present a preconditioning pipeline that accelerates Tensor Train (TT) linear solvers for symmetric positive-definite problems.

In this paper, we derive convergence bounds for the TriCG error norm and the TriMR residual norm.

However, existing learning architectures are not designed to simultaneously provide geometric equivariance and adaptability to layout windows with different physical extents, and thus their generalization capability is limited. To address this problem, we propose LithoSAGE, a spatially adaptive and geometrically equivariant neural operator method trained on lithography data.

We instead solve the backward pricing recursion, storing the continuation value as an $hp$ functional tensor train (hp-FTT) whose piecewise-polynomial cores are split at the barriers, so that worst-of barrier events act exactly, with rank one.

Spatially resolved modeling of optically pumped alkali-metal vapors requires the solution of a high-dimensional nonlinear diffusive quantum master equation (DQME) coupled to state-dependent light propagation. We develop a structure-preserving computational framework for this coupled three-dimensional system in the high-pressure limit.

We consider the optimal control problem of an elliptic PDE with random diffusion under pointwise box constraints on the control.

We present a geometric interface reconstruction method for Volume-of-Fluid (VOF) simulations that captures both curved interfaces and sharp features using only volume fraction data.

In this paper, we analyze the standard and the mass-lumped linear finite element methods for the Gross--Pitaevskii eigenvalue problem.

We construct and analyze a fully discrete finite volume scheme for the time-fractional Allen-Cahn equation with nondegenerate state-dependent mobility.

We establish Sobolev--Poincaré inequalities for piecewise $W^{2,p}$ functions in two and three dimensions over families of general polytopic (including shape-regular simplicial and Cartesian) meshes, allowing for degenerate facets.

We develop a one-level restricted additive Schwarz solver with perfectly matched layer transmission conditions (RAS--PML) for high-frequency Helmholtz systems.

For block LU, we present a fixed normwise strategy with essentially no selection cost, an LU-aware adaptive normwise strategy that can reduce the number of splits in subsequent trailing updates, and a componentwise strategy that uses information accumulated from preceding updates to guide the later selections.

We also characterize the regularizer's behavior as the auxiliary regularization scale tends to zero or infinity. We solve the reduced problem with a quasi-Newton method that evaluates the objective and its derivatives in the Fourier domain.

We propose energy-dissipative backward differentiation formula (BDF) methods for geometric flows in the Barrett--Garcke--Nürnberg (BGN) parametric finite element framework.

We study magnetic Bloch eigenvalue problems for two-dimensional magnetic Schrödinger operators with nonuniform periodic magnetic fields and periodic scalar potentials, and develop a hybrid Fourier-finite difference discretization.

By weighing each stage of the Radau IIA Runge--Kutta method differently we obtain preconditioners that are field-of-values equivalent, with constants independent of viscosity, timestep, and mesh size, to the system matrix.

We develop an adaptive Kalman filter for Generalized Shot Noise streamflow models, with recursive estimation of the measurement and process-noise covariances.

We present a theoretical and numerical analysis of novel IMEX Active Flux schemes for a hyperbolic approximation of the Korteweg-de Vries (KdV) equation.