Related papers: Optimal convergence for adaptive IGA boundary elem…
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 analyzes the approximation properties of spaces of piece-wise tensor product polynomials over box meshes with a focus on application to IsoGeometric Analysis (IGA). The errors are measured in Lebesgue norms. Estimates of…
This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…
As an important metric for mesh quality evaluation, the isotropy property holds significant value for applications such as texture UV-mapping, physical simulation, and discrete geometric analysis. Classical isotropy remeshing methods adjust…
For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method. This adaptive method can control the error in the natural mixed variational norm when the space of harmonic…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The…
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…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…
We investigate the calibration of estimations to increase performance with an optimal monotone transform on the estimator outputs. We start by studying the traditional square error setting with its weighted variant and show that the optimal…
This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. Boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional…