数值分析

Discontinuous Galerkin (DG) methods are known to suffer from increasingly restrictive explicit time-step constraints as the polynomial order increases, limiting their efficiency at high orders for explicit time-stepping schemes. In this…

In this work we introduce the concept of admissible integral $k$-mesh for sampling differential forms with contiuous coefficients on a real body $E\subset \R^n$, and provide two techniques for the construction of admissible integral…

This work develops an efficient real-time inverse formulation for inferring the aerodynamic surface pressures on a hypersonic vehicle from sparse measurements of the structural strain. The approach aims to provide real-time estimates of the…

This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest…

Transmission lines, crucial to the power grid, are subjected to diverse environmental conditions such as wind, temperature, humidity, and pollution. While these conditions represent a consistent impact on the transmission lines, certain…

We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…

Coupled cluster methods are widely regarded as the gold standard of computational quantum chemistry as they are perceived to offer the best compromise between computational cost and a high-accuracy resolution of the ground state eigenvalue…

Although the MUltiple SIgnal Classification (MUSIC) algorithm has demonstrated suitability as a microwave imaging technique for detecting anomalies, there is a fundamental limit that it requires a switching device to be used which permits…

In this paper, we explore how different selections of basis functions impact the efficacy of frequency domain techniques in statistical independence tests, and study different algorithms for extracting low-dimensional algebraic relations…

In this work we address the problem of uniform approximation of differential forms starting from weak data defined by integration on rectifiable sets. We study approximation schemes defined by the projection operator L given by either…

A fluid-structure interaction (FSI) problem is solved via a monolithic coupling of the fluid, structure, and geometry subproblems. The iterative GMRES solver is accelerated with the FaCSI block preconditioner. In the FaCSI factorization,…

The Oseen eigenvalue problem plays a important role in the stability analysis of fluids. The problem is non-self-adjoint due to the presence of convection field. In this paper, we present a comprehensive investigation of the mixed…

Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…

We analyze a variable-step extension of a family of arbitrarily high-order exponential time differencing multistep (ETD-MS) schemes recently developed by the authors. We prove that the schemes are unconditionally stable in the sense that a…

In magnetostatics and eddy current problems, formulated in terms of the magnetic vector potential, the solution is not unique, because the addition of an irrotational function to the solution remains a valid solution. The tree-cotree…

This paper proposes a power method for computing the dominant eigenvalues of a non-Hermitian dual quaternion matrix (DQM). Although the algorithmic framework parallels the Hermitian case, the theoretical analysis is substantially more…

We present a high-order conservative, positivity-preserving, and non-oscillatory scheme for solving the Vlasov equation. The scheme attains formal fifth-order accuracy through a convex combination of positive and non-oscillatory polynomials…

We present Randomized-Accelerated FEAST (RA-FEAST), a hybrid algorithm that combines contour-integration-based eigensolvers with randomized numerical linear algebra techniques for efficiently computing partial eigendecompositions of…

We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…

We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…