Related papers: Stable Mesh-Free Variational Radial Basis Function…

We investigate error bounds for numerical solutions of divergence structure linear elliptic PDEs on compact manifolds without boundary. Our focus is on a class of monotone finite difference approximations, which provide a strong form of…

In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…

Truncated singular value decomposition is a reduced version of the singular value decomposition in which only a few largest singular values are retained. This paper presents a novel perturbation analysis for the truncated singular value…

This paper studies the problem of utilizing data-driven adaptive control techniques to guarantee stability and safety of uncertain nonlinear systems with high relative degree. We first introduce the notion of a High Order Robust Adaptive…

We propose and analyze a Stein variational reduced basis method (SVRB) to solve large-scale PDE-constrained Bayesian inverse problems. To address the computational challenge of drawing numerous samples requiring expensive PDE solves from…

For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…

We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…

A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid…

This paper proposes a Direct Rational Radial Basis Functions Partition of Unity (D-RRBF-PU) approach to compute derivatives of functions with steep gradients or discontinuities. The novelty of the method concerns how derivatives are…

A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…

We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture…

Quadrature formulas (QFs) based on radial basis functions (RBFs) have become an essential tool for multivariate numerical integration of scattered data. Although numerous works have been published on RBF-QFs, their stability theory can…

We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…

Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…

The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scattered nodes and that they allow a direct control over the…

We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…

In this paper, we propose a reduced order approach for 3D variational data assimilation governed by parametrized partial differential equations. In contrast to the classical 3D-VAR formulation that penalizes the measurement error directly,…

Accurate triangulation of the domain plays a pivotal role in computing the numerical approximation of the differential operators. A good triangulation is the one which aids in reducing discretization errors. In a standard collocation…

We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within Density Functional Theory (DFT), with particular emphasis on linear-scaling (LS)…

This paper proposes a novel structure-aware matrix completion framework assisted by radial basis function (RBF) interpolation for near-field radio map construction in extremely large multiple-input multiple-output (XL-MIMO) systems. Unlike…