Related papers: A fast direct solver for nonlocal operators in wav…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of Neville…
This paper proposes a direct-indirect mixed Burton-Miller boundary integral equation for solving Helmholtz scattering problems with transmissive scatterers. The proposed formulation has three unknowns, one more than the number of unknowns…
A brief summary of direct solution approaches for finite element methods (FEM) in computational electromagnetics (CEM) is given along with an alternative direct solution based on domain decomposition (DD). Unlike recent trends in…
The paper is concerned with the sparse approximation of functions having hybrid regularity borrowed from the theory of solutions to electronic Schr\"odinger equations due to Yserentant [43]. We use hyperbolic wavelets to introduce…
Operator splitting techniques have recently gained popularity in convex optimization problems arising in various control fields. Being fixed-point iterations of nonexpansive operators, such methods suffer many well known downsides, which…
In this work, we show that solvers of elliptic boundary value problems in $d$ dimensions can be approximated to accuracy $\epsilon$ from only $\mathcal{O}\left(\log(N)\log^{d}(N / \epsilon)\right)$ matrix-vector products with carefully…
In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…
In this paper, we propose a fast spectral-Galerkin method for solving PDEs involving integral fractional Laplacian in $\mathbb{R}^d$, which is built upon two essential components: (i) the Dunford-Taylor formulation of the fractional…
An algorithm for the direct inversion of the linear systems arising from Nystrom discretization of integral equations on one-dimensional domains is described. The method typically has O(N) complexity when applied to boundary integral…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…
A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented. The resultant matrix is symmetric positive definite, thus the preconditioning conjugate gradient or the…
In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…
Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…
Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed…
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets,…
In this paper, we develop a direct method of moving planes for the fractional Laplacian. Instead of conventional extension method introduced by Caffarelli and Silvestre, we work directly on the non-local operator. Using the integral…
We present an approach to handle Dirichlet type nonlocal boundary conditions for nonlocal diffusion models with a finite range of nonlocal interactions. Our approach utilizes a linear extrapolation of prescribed boundary data. A novelty is,…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…