SIAM Journal on Scientific Computing

The dimension and the smoothness of the integrands are the two key factors that affect the efficiency of the quasi--Monte Carlo (QMC) method. The first factor implies that the QMC method can have high performance on a problem with low effective dimension ...

We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the location of ...

We apply finite element methods to elliptic problems on closed Riemannian manifolds. The elliptic equations on manifolds are reduced to coupled equations on Euclidean spaces by using coordinate charts. The advantage of this strategy is to avoid global ...

We formulate the 2-Lagrange multiplier method for the Richards equation in heterogeneous soil. This allows a rigorous formulation of a discrete version of the Richards equation on subdomain decompositions involving cross points. Using Kirchhoff ...

We study the spatial semidiscretizations obtained by applying Runge--Kutta (RK) and partitioned Runge--Kutta (PRK) methods to multisymplectic Hamiltonian PDEs. These methods can be regarded as multisymplectic $hp$-finite element methods for wave equations. ...

When a sequence of numbers is slowly converging, it can be transformed into a new sequence which, under some assumptions, converges faster to the same limit. One of the best-known sequence transformations is the Shanks transformation, which can be ...

We propose algorithms for the solution of high-dimensional symmetrical positive definite (SPD) linear systems with the matrix and the right-hand side given and the solution sought in a low-rank format. Similarly to density matrix renormalization group (DMRG)...

This work is concerned with approximating multivariate functions in an unbounded domain by using a discrete least-squares projection with random point evaluations. Particular attention is given to functions with random Gaussian or gamma parameters. We first ...

We design and analyze up to third order accurate discontinuous Galerkin (DG) methods satisfying a strict maximum principle for Fokker--Planck equations. A procedure is established to identify an effective test set in each computational cell to ensure the ...

We introduce a new stabilization for the $S_N$DG (discrete ordinate discontinuous Galerkin) approximation of monochromatic radiation transport, and argue that solutions converge to solutions to the LDG method of Cockburn and Shu in the thick diffusion limit. ...

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue ...

We present an improved PAM (iPAM) method as the first fourth-order interface tracking method whose convergence rates are independent of $C^1$ (derivative) discontinuities of the interface. As an improved version of the polygonal area mapping (PAM) method [Q. ...

In this work, we discuss the problem of approximating a multivariate function by discrete least-squares projection onto a polynomial space using a specially designed deterministic point set. The independent variables of the function are assumed to be random ...

The purpose of this paper is twofold. First, we extend the applicability of Cattaneo's relaxation approach, one of the currently known relaxation approaches, to reformulate time-dependent advection-diffusion-reaction equations, which may include stiff ...

Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These extensions are ...

Many applications require efficient methods for solving continuous shortest path problems. Such paths can be viewed as characteristics of static Hamilton--Jacobi equations. Several fast numerical algorithms have been developed to solve such equations on the ...

We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel $U(\mathbf{x})$ and a density function $\rho(\...

A least squares mixed finite element method for deformations of hyperelastic materials using stress and displacement as process variables is presented and studied. The method is investigated in detail for the specific case of a neo-Hookean material law and ...

Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps, especially for American-style option contracts. We consider the pricing of options under such models, namely ...

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation element methods of arbitrary order for the compressible Navier--Stokes equations. The new methods are similar to strong ...

The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a noncharacteristic Cauchy problem for a parabolic partial ...

Sparse matrix-vector multiplication (spMVM) is the most time-consuming kernel in many numerical algorithms and has been studied extensively on all modern processor and accelerator architectures. However, the optimal sparse matrix data storage format is ...

Network data is ubiquitous and growing, yet we lack realistic generative network models that can be calibrated to match real-world data. The recently proposed block two-level Erdös--Rényi (BTER) model can be tuned to capture two fundamental properties: ...

Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we propose a blocked ...

Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm of Moler and Stewart is the most widely used algorithm for addressing such problems. Despite its ...

Fatode is a Fortran library for the integration of ordinary differential equations with direct and adjoint sensitivity analysis capabilities. The paper describes the capabilities, implementation, code organization, and usage of this package. Fatode implements ...

Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction ...

By combining the techniques of the two-grid method and the partition of unity, we derive two local and parallel finite element algorithms for the Stokes problem. The most interesting features of these algorithms are (1) the partition of unity technique ...

Recently exponential integrators have been receiving increased attention as a means of solving large stiff systems of ODEs. Preliminary performance analysis demonstrated that exponential integrators hold promise compared to state-of-the-art implicit ...

The 2013 SIAM Conference on Computational Science and Engineering (CS&E) was held February 25--March 1, 2013, in Boston, Massachusetts. The SIAM Journal on Scientific Computing (SISC) created this special section in association with the CSE13 conference. Of ...