Related papers: An adaptive Levin method for complicated domains
Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first…
The inverse Robin problem covers the determination of the Robin parameter in an elliptic partial differential equation posed on a domain $\Omega$. Given the solution of the Robin problem on a subdomain $\omega \subset \Omega$ together with…
In this paper we present a methodology that allows the efficient computation of the topological derivative for semilinear elliptic problems within the averaged adjoint Lagrangian framework. The generality of our approach should also allow…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
A new decomposition method for nonstationary signals, named Adaptive Local Iterative Filtering (ALIF), has been recently proposed in the literature. Given its similarity with the Empirical Mode Decomposition (EMD) and its more rigorous…
In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known…
Considering the space-time adaptive method for parabolic evolution equations introduced in [arXiv:2101.03956 [math.NA]], this work discusses an implementation of the method in which every step is of linear complexity. Exploiting the product…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging…
We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…