arXiv subjects

Pieter Vanmechelen

Publications and source records attributed to Pieter Vanmechelen.

3 recordsLinked to original sources

arXiv2026

Comparison of random field discretizations for high-resolution Bayesian parameter identification in finite element elasticity

We compare three random field discretization strategies for probabilistic identification of spatially varying material parameters in high-resolution finite element models. These strategies are (i) the Karhunen-Loève expansion, (ii) a wavelet expansion, and (iii) local average subdivision. The methods are assessed in the context of multilevel Markov chain Monte Carlo applied to plane stress elasticity with high-resolution displacement observations. Emphasis is placed on numerical efficiency, initialization cost, Markov chain mixing, and cost-to-error behaviour as the discretization resolution increases. While all approaches yield comparable posterior estimates, significant differences are observed in multilevel variance reduction and sampling efficiency. In particular, local average subdivision exhibits improved mixing and lower cost-to-error ratios at fine resolutions, despite its higher nominal parameter dimension. The results provide practical guidance for selecting stochastic field representations in uncertainty quantification in finite element simulations of heterogeneous materials.

math.NA↗

arXiv2025

Multilevel Markov Chain Monte Carlo with likelihood scaling for Bayesian inversion with high-resolution observations

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent data resolution and introduce a suitable likelihood scaling to enable consistent cross-level comparisons. We theoretically show that this approach attains the same convergence rates as when using level-independent treatment of data, but at significantly reduced computational cost. The convergence analysis focuses on Lipschitz continuous transformations of Gaussian random fields with Matérn covariance structure. These results are illustrated using numerical experiments for a 2D plane stress problem, where the Young's modulus is estimated from discretisations of the displacement field.

math.NA↗

arXiv2022

Quasimodes in the cusp continuum in nonuniform magnetic flux tubes

The study of MHD waves is important both for understanding heating in the solar atmosphere and for solar atmospheric seismology. The analytical investigation of wave mode properties in a cylinder is of particular interest in this domain, as many atmospheric structures can be modeled as such in a first approximation. We use linearized ideal MHD to study quasimodes (global modes that are damped through resonant absorption) with a frequency in the cusp continuum, in a straight cylinder with a circular base and an inhomogeneous layer at its boundary which separates two homogeneous plasma regions inside and outside. We are in particular interested in the damping of these modes, and shall hence try to determine their frequency as a function of background parameters. After linearizing the ideal MHD equations, we find solutions to the second-order differential equation for the perturbed total pressure in the inhomogeneous layer in the form of Frobenius series around the regular singular points that are the Alfvén and cusp resonant positions, as well as power series around regular points. By connecting these solutions appropriately through the inhomogeneous layer and with the solutions of the homogeneous regions inside and outside the cylinder, we derive a dispersion relation for the frequency of the eigenmodes of the system. From the dispersion relation, it is also possible to find the frequency of quasimodes even though they are not eigenmodes. As an example, we find the frequency of the slow surface sausage quasimode as a function of the inhomogeneous layer's width, for values of the longitudinal wavenumber relevant for photospheric conditions. The results were found to match well the results found in another paper which studied the resistive slow surface sausage eigenmode. We also discuss the perturbation profiles of the quasimode and the eigenfunctions of continuum modes.

astro-ph.SR↗