Related papers: An adaptive Levin method for complicated domains
Deep learning-based methods deliver state-of-the-art performance for solving inverse problems that arise in computational imaging. These methods can be broadly divided into two groups: (1) learn a network to map measurements to the signal…
The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical…
Here we consider the following fractional Hamiltonian system \begin{equation*} \begin{cases} \begin{aligned} (-\Delta)^{s} u&=H_v(u,v) \;\;&&\text{in}~\Omega,\\ (-\Delta)^{s} v&=H_u(u,v) &&\text{in}~\Omega,\\ u &= v = 0 &&\text{in} ~…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related…
In this work we present an adaptive boundary element method for computing the electromagnetic response of wave interactions in hyperbolic metamaterials. One unique feature of hyperbolic metamaterial is the strongly directional wave in its…
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
The acoustic wave equation is solved in time domain with a boundary element formulation. The time discretisation is performed with the generalised convolution quadrature method and for the spatial approximation standard lowest order…
We study the problem of learning multi-index models in high-dimensions using a two-layer neural network trained with the mean-field Langevin algorithm. Under mild distributional assumptions on the data, we characterize the effective…
In this paper we develop an $hp$-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton…
Recently, new adaptive techniques were developed that greatly improved the efficiency of solving PDEs using spectral methods. These adaptive spectral techniques are especially suited for accurately solving problems in unbounded domains and…
We consider h-adaptive algorithms in the context of the finite element method (FEM) and the boundary element method (BEM). Under quite general assumptions on the building blocks SOLVE, ESTIMATE, MARK, and REFINE of such algorithms, we prove…
In this paper we propose third-order methods for composite convex optimization problems in which the smooth part is a three-times continuously differentiable function with Lipschitz continuous third-order derivatives. The methods are…
An efficient method for finding all real roots of a univariate function in a given bounded domain is formulated. The proposed method uses adaptive mesh refinement to locate bracketing intervals based on bisection criterion for root finding.…
Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without…
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving…