Related papers: p-refined RBF-FD solution of a Poisson problem
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
\emph{Koopman Regularization} is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. \emph{Koopman Regularization} extracts a functionally independent set of…
We study the \emph{order-finding problem} for Read-once Oblivious Algebraic Branching Programs (ROABPs). Given a polynomial $f$ and a parameter $w$, the goal is to find an order $\sigma$ in which $f$ has an ROABP of \emph{width} $w$. We…
In this paper, we present a factor 16 approximation algorithm for the following NP-hard distance fitting problem: given a finite set X and a distance d on X, find a Robinsonian distance dR on X minimizing the l\infty-error ||d - dR||\infty…
In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable scales. Direct numerical resolution of such multiscale…
We study the problem of maximizing a monotone submodular function subject to a matroid independence constraint. For more than a decade, a rich body of work has studied this problem. Initially, a tight approximation of $ (1-\frac{1}{e})$ was…
It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the…
This paper proposes an original adaptive refinement framework using Radial Basis Functions-generated Finite Differences method. Node distributions are generated with a Poisson Disk Sampling-based algorithm from a given continuous density…
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
Radial Basis Function-generated Finite Differences (RBF-FD) is a popular variant of local strong-form meshless methods that do not require a predefined connection between the nodes, making it easier to adapt node-distribution to the problem…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
The feedback particle filter (FPF), a resampling-free algorithm proposed over a decade ago, modifies the particle filter (PF) by incorporating a feedback structure. Each particle in FPF is regulated via a feedback gain function (lacking a…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…
In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an…
In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman equation with coefficients…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…