SIAM Journal on Scientific Computing

Energy-corrected finite element methods provide an attractive technique for dealing with elliptic problems in domains with re-entrant corners. Optimal convergence rates in weighted $L^2$-norms can be fully recovered by a local modification of the stiffness ...

In this paper we propose several techniques for tangential redistribution of points on evolving surfaces. This is an important issue in numerical approximation of any Lagrangian evolution model, since the quality of the mesh has a significant impact on the ...

The hierarchical tensor format allows for the low-parametric representation of tensors even in high dimensions $d$. The efficiency of this representation strongly relies on an appropriate hierarchical splitting of the different directions $1,\ldots,d$ such ...

We develop a multilevel approach to solving a blind deconvolution problem, with the ultimate intent of recovering signals which are known to have edges. First, we discuss how to generate a hierarchy of blind deconvolution problems by means of the Haar ...

We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special ...

Adaptive mesh refinement and the Börgers algorithm are combined to generate a body-fitted mesh which can resolve the interface with fine geometric details. Standard linear finite element method based on such body-fitted meshes is applied to the elliptic ...

Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential ...

We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In Part I of this paper [T. Bui-Thanh, O. Ghattas, J. Martin, and G. Stadler, SIAM J. Sci. Comput., 35 (2013), pp. A2494--A2523] we considered ...

We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy of the ...

In lattice quantum chromodynamics (QCD) computations a substantial amount of work is spent in solving discretized versions of the Dirac equation. Conventional Krylov solvers show critical slowing down for large system sizes and physically interesting ...

In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For this purpose, we present new boundary correctors which preserve the common ...

Motivated by a geometric problem, we introduce a new nonconvex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified and a novel ...

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise. We first analyze ...

We investigate the use of algebraic multigrid (AMG) methods for the solution of large sparse linear systems arising from the discretization of scalar elliptic partial differential equations with Lagrangian finite elements of order at most 4. The resulting ...

Many methods in computer graphics require the integration of functions on low-to-middle--dimensional spaces. However, no available method can handle all the possible integrands accurately and rapidly. This paper presents a robust numerical integration ...

In this work, we are concerned with the high-order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the backward SDE, ...

Motivated by uncertainty quantification and compressed sensing, we build up in this paper the framework for sparse interpolation. The main contribution of this work is twofold: (i) we investigate the theoretical limit of the number of unisolvent points for ...

We introduce a class of numerical methods for highly oscillatory systems of stochastic differential equations with general noncommutative noise. We prove global weak error bounds of order two uniformly with respect to the stiffness of the oscillations, which ...

The tempered fractional diffusion equation is a generalization of the standard fractional diffusion equation that includes the truncation effects inherent to finite-size physical domains. As such, that equation better describes anomalous transport processes ...

In this paper we discuss discrete conservation laws for diffusion equations over triangular surface meshes from the viewpoint of duality. Conservation laws are very important for us to model physical phenomenon on curved spaces. The key idea of our method is ...

A regularization technique based on a class of high-order, compactly supported piecewise polynomials is developed that regularizes the time-dependent, singular Dirac-delta sources in spectral approximations of hyperbolic conservation laws. The ...

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable distance to the ...

We introduce the feature rejection algorithm for meshing (FRAM) to generate a high quality conforming Delaunay triangulation of a three-dimensional discrete fracture network (DFN). The geometric features (fractures, fracture intersections, spaces between ...

High-dimensional inverse problems present a challenge for Markov chain Monte Carlo (MCMC)-type sampling schemes. Typically, they rely on finding an efficient proposal distribution, which can be difficult for large-scale problems, even with adaptive ...

In this paper we consider stabilized finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three different stabilized ...

In this paper we discuss numerical methods for solving time-harmonic Maxwell equations in three-dimensional absorbing media. We propose a new variational problem on the space spanned by the plane-wave basis functions for the discretization of these types of ...

This article considers the iterative solution of a finite element discretization of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyze, and numerically ...

Consider a symmetric matrix $A(v)\in\mathbb{R}^{n\times n}$ depending on a vector $v\in\mathbb{R}^n$ and satisfying the property $A(\alpha v)=A(v)$ for any $\alpha\in\mathbb{R}\backslash\{0\}$. We will here study the problem of finding $(\lambda,v)\in\mathbb{...

New preconditioning strategies for solving $m \times n$ overdetermined large and sparse linear least squares problems using the conjugate gradient for least squares (CGLS) method are described. First, direct preconditioning of the normal equations by the ...

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The resulting system of ...