Related papers: Adaptive $\mathcal{H}$-Matrix Computations in Line…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $d\geq 1$ dimensions. Our main approach consists of…
This paper proposes a hierarchical adaptive sampling scheme for passivity characterization of large-scale linear lumped macromodels. Here, large-scale is intended both in terms of dynamic order and especially number of input/output ports.…
Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…
We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…
In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework…
Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
The main challenge for adaptive regulation of linear-quadratic systems is the trade-off between identification and control. An adaptive policy needs to address both the estimation of unknown dynamics parameters (exploration), as well as the…
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…
We prove lower bounds for the randomized approximation of the embedding $\ell_1^m \rightarrow \ell_\infty^m$ based on algorithms that use arbitrary linear (hence non-adaptive) information provided by a (randomized) measurement matrix $N \in…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…